Yeah, yeah, I know. You read the title and immediately knew the number-one answer. It’s not exactly a surprise to anyone who has paid attention to the NBA this season, and I certainly made no attempt to hide it with my choice of thumbnail. Statistics don’t have to be surprising, though – let’s dive into the numbers anyway.

Background

Reddit is a popular social media network split into various communities based on different interests. Each community is known as a subreddit and they’re referred to with the prefix ‘r/’ before the community name. There’s a subreddit out there for anything you can think of. For example, you can browse r/sports for general sports discussion or r/soccer for general soccer discussion. Even more specifically, you can browse r/barca for news and discussion specifically pertaining to F.C. Barcelona.

In this article, we’ll focus on the NBA subreddit (r/nba), which is the most popular sport-specific community on the website.

At the time of this article being written, r/nba has over 4.6 million subscribers. r/soccer is the next closest sport-specific subreddit but still has more than one million fewer subscribers than r/nba. It is one of the most active communities on Reddit and is constantly buzzing with basketball discussion.

After every NBA game, any user can submit a post onto r/nba called a “Post Game Thread.” A typical post game thread (PGT) has a title including the two teams who played, the score of the game, and perhaps any other significant details (like a particularly outstanding individual performance). As an example, the title of the post game thread after today’s game between the Timberwolves and Grizzlies was titled “The Minnesota Timberwolves (1-0) pull out the Game 1 road win against the Memphis Grizzlies (0-1), 130-117, behind a 36 point playoff debut from Anthony Edwards.” The content of the post includes the box score for the game and it currently has 1531 comments as users discuss the game. Users can also upvote or downvote the post – a submission’s score is determined by subtracting the upvotes from the downvotes. The MIN-MEM post game thread has a score of 5781 with an upvote ratio of 97% (so 97% of the votes were upvotes, the other 3% were downvotes).

The goal of this article is to analyze post game threads from every game this season in order to determine which teams’ losses receive more positive attention that their wins. A year ago, I conducted the same analysis regarding the 2019-20 season. It was a rather simple project – for any given team, I obtained the median score of a post game thread in their wins and their losses and subtracted the two values. This year, I wanted to make the analysis more complex.

Methodology

I started by obtaining as many post game threads from the 2020-21 season as I could using the PushShift API on Python. If the original poster of a post game thread deleted the post after the fact (or their account was deleted), it was not included in this analysis. Thus, the data set is not fully complete. In the end, we obtained a post game thread for 73.2% of 2020-21 regular season games.

The next step was to collect relevant characteristics for these games that I thought may affect how high the score would be. This includes the difference in score, whether the game goes to overtime, the Vegas odds (so as to determine whether the game was an upset), whether the game went to overtime, etc. In addition, I included time variables like day of the week and hour of the day which may impact how many viewers a game had. Finally, a regression was ran using these independent variables to predict the dependent variable of a post game thread’s score.

Now we could turn to the 2022 regular season. I obtained 1117 post game threads (accounting for 90.8% of games played) along with the aforementioned relevant variables that may affect a post game thread’s final score. Then the previous regression was used to predict the score for each game and the actual score was subtracted from this value to represent the “score over expectation” (SOE).

The median SOE was calculated for each team in their wins and losses and these values were subtracted to determine their median SOE difference. A positive value suggests that their wins received more upvotes than their losses, while a negative value suggests that their losses were more well-received. Note: a logarithm was applied to the dependent variable to deal with heteroskedasticity.

Results

In the graph below I’ve plotted each team’s median SOE difference along with their win percentage.

In general, teams that win more receive more attention for their losses. That makes sense – the Suns were clearly the best team in the NBA in the regular season, so it’s bigger news when they lose games compared to their wins. The biggest tanking teams like the Rockets and Thunder receive more upvotes when they won, which also makes sense – a Houston win wasn’t exactly a common occurrence. The disparity isn’t as drastic as it is for winning teams like the Suns, though – teams don’t really care all that much about the worst teams in the league.

There are some winning teams that get more love for their wins than their losses. The Raptors and Cavaliers are the most obvious ones in this category, likely due to their great performance relative to preseason expectations. It was hard not to enjoy the Cavaliers’ success with a young core of Garland, Mobley, and Allen even with an incredibly injury-riddled season. It’s also not surprising to see the Warriors get more positive attention for wins than for losses. Despite being a recent dynasty, the Warriors somehow felt like a bit of comeback story due to their lack of success over the past two seasons. And of course, Steph Curry is one of the most beloved players in the NBA.

On the other side, the Nets lacked a spectacular record yet received far more attention for their losses than their wins. Why? Well, they entered the season with championship expectations and a big three of Kyrie Irving, James Harden, and Kevin Durant. Naturally, most fans are gonna be rooting against them.

There are also some variables that are unaccounted for. A big one is whether a comeback occurred. The Utah Jazz were extraordinarily adept at choking away large leads in the second half of games. If the Jazz lose a game in which they held a 25 point second half lead, obviously there will be more post game discussion than if they had lost in “normal” fashion.

Of course, the biggest thing that stands out is the Los Angeles Lakers – right there in the bottom center of the graph. A subpar team that everyone likes to see lose more than any other team.

The Los Angeles Lakers

The graph above clearly showed that the disparity in score for post game threads corresponding to Lakers wins and losses was greater than that for any other team despite their incredible mediocrity as a team. That’s not exactly a surprise, Let’s look into the numbers a bit more, though.

Shown below is a box plot of the score of post game threads after Lakers wins and after Lakers losses.

Only one Lakers win prompted a post game thread that had a higher score (4914) than the average post game thread for a Lakers loss. All it took was a 56 point performance from LeBron James against the Warriors in a tight win. And there were still 19 Lakers losses that led to post game threads with a higher score than that incredible game. An interesting parallel is a Bucks win on November 17th where Giannis dropped 47/9/3 against a LeBron-less Lakers team. This thread hit a score of 5635, 721 points higher than the LeBron 56 point performance over the Warriors. Why?

Some theorize that having a larger fanbase can drive positive narratives surrounding that team on the NBA subreddit. However, the Lakers have the largest fanbase in the league. Even though the Bucks are coming off of a championship, the size of their Internet following is meager relative to the Lakers’. However, the Lakers-Warriors post game thread had a 94% upvote ratio versus 96% for the Bucks-Lakers thread. One may point out that the Warriors also have an incredibly large fanbase that may have actually downvoted the post game thread for their team losing. By that logic, though, Lakers fans could do the same for the Bucks loss.

It seems that the factor that actually matters is what other fans think of a team. The Lakers aren’t a big enough fanbase to outweigh the hate that virtually every other fanbase has for their team.

We all know the Lakers aren’t exactly a team that’s widely adored among NBA fans. Most fans can be grouped into one of two categories: Lakers fans or Lakers haters. Our previous analysis from the 2020 season found that the Lakers were also the team that r/nba users enjoyed seeing lose the most. That was a bit different, though – the Lakers ended up winning the NBA Finals and were clearly a contender. The opposite was true this season – despite massive expectations, the Lakers fell short and ended up not only missing the playoffs, but even falling short of qualifying for the play-in tournament. Perhaps falling completely short of preseason expectations added to the enjoyment fans got out of seeing the Lakers lose.

Of course, there’s also the LeBron factor. Most fans know that LeBron James is one of the most polarizing figures in sports – he perhaps has more “haters” than any other athlete in the four major American pro sports leagues. It’s no surprise to see that hate translate to the team he plays for.

Last time I did a project aimed at answering this question, I wasn’t fully satisfied with the results due to the lack of variables accounted for. This time around, I’m more content with the depth of analysis done and I think the results speak for themselves.

The post Schadenfreude: Which NBA Teams’ Losses Drew the Most Attention? appeared first on The Spax.

Background

If you’ve been paying attention to social media at all recently, you’ve probably heard about Wordle. It’s a popular game where users are given six attempts at guessing that day’s mystery word. You guess a five-letter word and are given clues that help you reach the answer for that day. It has become a daily exercise for many users around the world and thanks to its creative design (you’ve probably seen those colorful diagrams consisting of green, yellow, and black squares), it has become a ubiquitous staple of life in many social circles.

Unsurprisingly, the success of Wordle has sparked the creation of variants. These parodies include copies of the game ported to different languages or more difficult versions of it, such as Quordle where users essentially have to solve four Wordles at the same time. There are also many variants of Wordle that are guessing games for a different topic, such as Worldle where users try to guess a country or Nerdle, a math spinoff.

As an avid NBA fan, one Wordle variant that caught my eye was Poeltl. Named after San Antonio Spurs center Jakob Poeltl, the game gives you eight attempts at guessing a mystery NBA player. In each guess, you input an active NBA player and you are then giving clues based on some characteristics.

For example, suppose my first guess for Poeltl #6 (03/02/2022) was CJ McCollum. Here’s the output:

McCollum’s team is not highlighted in green or yellow. If it was green, it would mean that the mystery player is currently on that team. If it was yellow, it would mean that the mystery player was previously on that team. As it is not highlighted at all, we know that the mystery player never played for the New Orleans Pelicans.

However, the conference is highlighted in green. As such, we know that the mystery player is currently on one of the other fourteen teams in the Western Conference.

We also know the player is not in the Southwest Division. That leaves the Pacific and Northwest divisions – only ten possible teams!

We are told that the player is a guard as well. If the color of the position was yellow, it would mean that the player could be a G-F or F-G (both a guard and forward). As that is not the case, we know that the mystery player is either solely a point guard or solely a shooting guard.

We also know that the player’s height is not 6’3. The arrow pointing up indicates that the true height is greater than 6’3, but the yellow color tells us that our guess was within two inches. Thus, the mystery player can only be 6’4 or 6’5.

The same mechanic can be reversed to help us with age. We know the mystery player is less than 30-years-old, and because McCollum’s age is not yellow, it means that our guess was not within two years of the mystery player’s true age. Thus, the player we’re looking for is at most 27-years-old.

Finally, jersey number. We got lucky! The mystery player shares the same number on their jersey as CJ McCollum. Otherwise, we would have used the same logic as we did with height and age to narrow our options down (use arrows & the presence or lack thereof of the yellow highlight).

That’s a lot of information to process. We got a lot of good information out of it, though – there can’t be that many 6’4 or 6’5 guards with the jersey number #3 on one of ten teams in the NBA who are also at most 27-years-old. In fact, only three players meet this criteria. The hard part, of course, is identifying who they are. In this case, the answer was Jordan Poole, 6’4 2–year-old shooting guard for the Golden State Warriors (Pacific Division).

Goal

After my first time playing this game, my first thought was that it was pretty fun and well-designed. My second thought was, “I wonder what the most optimal first guess is.” It was a popular question among fans of Wordle (and controversial). Some people liked to go with a word stacked with vowels like “adieu” while some analyses supported words like “salet” or “crate.”

In the case of Poeltl, I wondered what characteristics would make a good starting guess. Maybe you want a journeyman guy who has been on a lot of teams. Perhaps you’d like someone with average height and age so the arrows are more meaningful. How about a 6’6 journeyman 27-year-old with a jersey number in the 20s? That seems optimal. Does that exist? If they do, is that even an optimal guess? How much does it really matter?

I was bored and wanted to tackle these questions, so I decided to whip up Python and algorithmically determine the best starting guess in Poeltl.

Methodology

The first step was data collection – I needed all of the information that is a part of the game. That means obtaining the height, age, position, team, and former teams of every active NBA player. That could be complicated for something like position which isn’t really objective. Fortunately, experimentation made it obvious that the game got all of its data from nba.com/stats, so I did the same.

I put together a data frame of 496 players currently on an NBA roster. As far as I can tell, these players are the only ones you are allowed to guess in the game. Go ahead and try guessing Matt Ryan (no, not the quarterback) and their jersey number will come up as N/A. Why? They don’t have a jersey number listed on the Celtics’ team page. I was fairly confident that my data aligned perfectly with the data Poeltl uses.

I coded a function that takes two inputs: a guess and an answer. It outputs a dictionary representing the information that a user would hypothetically learn if they inputted that guess into Poeltl when the mystery player is that answer. Then once that dictionary is inputted into another function, the players that meet that criteria are outputted. Here’s an example using our previous CJ McCollum guess:

PossibleAnswers(GuessInformation('CJ McCollum','Jordan Poole')).player

['Jordan Poole', 'Terence Davis', 'Trent Forrest']

We already know the answer is Jordan Poole, so GuessInformation('CJ McCollum','Jordan Poole') will output a dictionary representing the information we learned from that first guess. If you wanted to use this to cheat prior to knowing the answer you could always input that manually, but that’s not the point here. Based on the information we received, PossibleAnswers reveals that there were only three possibile answers, one of which was obviously the true mystery player.

But suppose the mystery player was, I don’t know, Matt Ryan (again, not the quarterback). How many possibilities would there have been after our first guess?

len(PossibleAnswers(GuessInformation('CJ McCollum','Matt Ryan')).player)

126

Okay, wow. Not nearly as useful. The only information you really receive is that the mystery player is in the East, is not a guard, is taller than 6’5, and is younger than 28-years-old. That leaves a lot of possibilities.

As a matter of fact, based on possibilities leftover afterwards, Matt Ryan is the worst-case-scenario mystery player for a first guess of CJ McCollum.

For 50.4% of possible mystery players, a first guess of CJ McCollum would leave six or less possibilities based on the information given by the game. But there is that 13.9% of possible mystery players for which the McCollum guess would leave over 100 possibilities for. Overall, the mean number of possibilities left by a first guess of CJ McCollum is 22.3 and the average reduction in number of possibilities is 95.5%.

One issue – this assumes that all 496 active NBA players are possible answers to the game. Common sense tells us that a well-designed game would not allow this to be a possibility. Did you even know that a player named Matt Ryan was in the NBA? I sure didn’t until now.

According to an interview with the game’s creator Gabe Danon, there are “only 300 or so mystery players in Danon’s pool of candidates.” Hm. How do we tackle that?

I took a slightly unscientific approach and went through all 496 players and decided whether or not I thought they were relevant enough to be an answer. There were more objective methods I could’ve taken, but I’m confident enough in my NBA fandom to think that this process would be reasonable enough. I generally took out players I never heard of (while using games played and minutes per game as a reference to make sure I didn’t take out actual key players) or players who I knew of but didn’t think would be put into the game.

I think I was fairly generous. I ended up with 353 players. Maybe a little more than “only 300 or so” (Or would you use that wording to describe the number 353? Probably not, right?) but I think it’s preferrable to removing too many players. In any case, I do not think the results of this analysis would change dramatically.

I proceeded to track the mean number of possibilities left by a first guess of a player, the maximum number of possibilities left, and the average percent reduction in number of possibilities for all 496 possible guesses. I did this under the false assumption that any of the 496 players could be the answer, and then once more under the more reasonable assumption that the answer could only be in a self-filtered list of 353 players. Onto the results!

Results

The table below contains the results of our analysis for the scenario in which we assume that all 496 active NBA players could be the mystery player on a given day.

The first guess that provides information eliminating the most possibilities on average is Lindy Waters III, who is currently signed by the Oklahoma City Thunder on a two-way contract. The most options that you could be left with after guessing Waters first is just 15 out of 496.

LaMar Stevens is similar – 6’6, 24-years-old, and wears #8. Or Derrick Jones who is a 25-year-old 6’6 forward wearing #5 on their jersey.

What makes him such a great guess? Well, the median NBA jersey number is 13 and Waters rocks the number 12. The median age of active NBA players is 25, Waters is 24-years-old. Waters also happens to have the same height as the average NBA player at 6’6. By effectively splitting the playerbase in half with each of these three numeric characteristics, you’re bound to cut down on the possible answers with a first guess of Lindy Waters III.

How about the worst guesses? The worst guess by far is Boban Marjanovic, the 33-year-old 7’4 center for the Dallas Mavericks who wears a relatively high jersey number of 51. The percentage of players with a higher height, age, and jersey number than Boban are 5.4%, 0.0%, and 3.6% respectively. Yeah, you’re getting very little information there. In general, the worst guesses appear to be big men, specifically ones that are especially young or old.

Next, we apply our analysis to the filtered subset of players that were deemed to be realistic answers.

There is not much substantial change here – in fact, the correlation coefficient between the mean percent decrease for the two analyses is a whopping 0.997. The physical characteristics of the players removed from the data set are not significantly different from those that were not removed, so there is no reason to think that the results change all that much.

With that said, Lindy Waters III is no longer the most optimal guess. That title now belongs to Ish Wainright. Wainright is a 6’5 27-year-old forward who wears #12 for the Phoenix Suns. The average number of valid possibilities after a first guess of Ish Wainright is just three, while the maximum is 12. Wainright is three years older than Waters, which makes sense – the more ‘relevant’ players in the NBA (who are more likely to be a possible mystery player) are probably going to be older than the young guys who are relatively unknown. Thus, the most optimal guess on the filtered data set should be a bit older.

If you want an optimal guess that has the best shot at also being a potential answer, Wainright is probably not your best bet. Cody Martin might be a good shot, as he averages 26.8 minutes per game for the Charlotte Hornets and is essentially just as good of a first guess as Wainright. Other options include Taurean Prince, Jae’Sean Tate, and Derrick Jones Jr. Jaylen Brown and Zach LaVine are similarly fantastic picks if you want All-Star caliber guys.

Looking Past the First Guess

If you want to get the most theoretical information out of your first guess, Ish Wainright is your man. But what about the second guess? The third? Should we be considering how the game might play out after your first pick?

Recall that the function GuessInformation(guess,answer) outputs a dictionary representing the information learned from a guess. We can set guess="Ish Wainright" and iterate all 353 candidate mystery players as answer to get the 353 possible information dictionaries for Ish Wainright. For each one, we can then cut our data set down to the players that are still possible answers based on the information given, and we can then repeat the previous process to find the best second guess in each situation and track how many possible valid answers there still are after the second guess. If that number is equal to 1, it means our algorithm can get to the right answer within three guesses.

Using Ish Wainright as our first guess, the mean number of guesses needed to get to the mystery player is approximately 2.425 and the maximum is three. Using this strategy, it’ll never take more than three guesses to win Poeltl assuming that our list of 353 players includes all of the “300 or so” actual possible answers. Doing the same with Cody Martin results in a average of 2.419 guesses and a maximum of four. We could go through and do this for every player, but that would be computationally time-consuming so I’ll leave it at the top ten first guesses in the previous table:

There isn’t really much of a noticeable difference in any of these, similar to the best Wordle words. Given that its maximum attempts to guess the mystery player is just three while also eliminating the most possibilities on the first guess, I’d stick with Ish Wainright as the best first guess if you don’t care about the hole-in-one chance. Otherwise, Cody Martin might be the better choice.

Conclusion

I used Lindy Waters III as my first guess on the last two Poeltls (#5 and #6). Both times I was able to guess the mystery player on my second try because the information from the first guess actually left just one possibility (which is true about one-third of the time for the most optimal guesses).

However, I’m sure if I continued with this strategy I’d have some moments where I was unable to identify the right player even if I was given all of the information theoretically needed to do so. It’s worth mentioning that players like Wainright appear to be the strongest guesses for an entity that knows the jersey number, age, position, team, height, etc of every active NBA player. It’s likely (and true in my case) that a user won’t know every player’s jersey number, for example, in which case the value of a first guess like Ish Wainright would be diminished greatly.

When the discussion of optimizing Wordle occurs, it’s usually met with blowback by fans who think it ruins the fun of the game and that people shouldn’t be using the same first guess everyday. While I use my favorite starting word of “raise” everyday in Wordle, I do understand that perspective and in the case of Poeltl, I don’t think using Ish Wainright as a first guess is particularly enjoyable and I definitely won’t be doing that moving forward.

This exercise was simply an example of using simple coding and statistics to answer a random question that I had, and I now consider it as being successful.

As an aside, this research does makes me think that the game of Poeltl could maybe be updated to increase the difficulty of the game. Perhaps the introduction of a ‘hard mode’ would spice things up. The mechanic of telling you whether or not a player’s age or height is within two of your guess makes life far easier for the user and for avid fans, I don’t really see how you could miss the right answer in eight attempts unless it’s a lesser known player. I focused on guys like Lindy Waters III and Ish Wainright in this article, but essentially any first guess is going to severely limit the number of possibilities.

The average number of valid possibilities left after the first guess is just 10.39 – that’s a 97% drop. Then again, this is still under the assumption that you would be able to identify those possibilities based on information as mundane as jersey number. Take with that what you will! In any case, Poeltl is a fun game and I would definitely recommend it to any NBA fan.

The code used for this article can be found here.

The post Mathematically Optimizing an NBA Player Guessing Game appeared first on The Spax.

The history of the Portland Trail Blazers is not lacking in offensively skilled players at the guard position. From the sustained dominance of Clyde Drexler to the unrealized promise of Brandon Roy to the recent dynamic duo of Damian Lillard & CJ McCollum, the Blazers have been fortunate to consistently have guards that could be trusted to put up points reliably.

The Blazers picked up Anfernee Simons with the 24th overall pick of the 2018 NBA Draft, a reasonable position in the draft to take a gamble on a teenager with a ton of potential. Simons was drafted straight out of high school at just 18-years-old – naturally, he didn’t have expectations to be much of an instant contributor. Nonetheless, his talent was undeniable. While his slender frame and poor defense was criticized during draft season, these were traits that an 18-year-old could be excused for. Simons’ elite shooting along with his incredible speed, quickness and athleticism offered plenty reason for excitement.

As expected, Simons’ rookie season was not eventful. Up until the last game of the season, he had played in just 19 games for the Trail Blazers and averaged 2.0 points on 4.9 minutes per games. No one was expected a teenager to usurp a spot in the rotation from guards like Lillard, McCollum, Seth Curry, Nik Stauskas and Rodney Hood.

However, the Blazers gave us a tease of the future in their 2018-19 regular season finale.

Portland entered their final game of the regular season with a 52-29 record, slated to play the already eliminated Sacramento Kings. The Blazers had already clinched home-court advantage in the first round (the 3rd or 4th seed). Winning the game gave them a chance at the three seed, but when the team announced that Lillard and McCollum would sit due to “load management,” it appeared that they were content with entering the postseason with the four seed and a likely postseason matchup against the Utah Jazz. Or maybe they just wanted the rest for their stars and didn’t particularly care about the matchup. In any case, Anfernee Simons would start the first game of his career.

In a wild game in which they fielded just six players and trailed by as many as 28 points, the Blazers rallied back behind a stunning 37 points, 9 assists, and 6 rebounds from the 19-year-old Anfernee Simons. Simons played a full 48 minutes and shot 13-21 from the field and 7-11 from deep in his first career start to unexpectedly secure the three seed for the Blazers. In his breakout game, Simons was efficient from every spot on the floor and created shots for his teammates like a seasoned vet despite entering the draft with playmaking concerns. Oh, and the win ended up working out as far as seeding goes – the Blazers went as far as the Western Conference Finals.

Over the next two seasons, Simons played 134 games and maintained a consistent 8/1/2 average statline. He remained a distant guard in the rotation, but steadily showed progress – his 2020-21 season saw an uptick in efficiency as his 3P% jumped to 42.6%. The young guard was still just 21-years-old and continued to develop as a player. He also won the 2021 NBA Slam Dunk Contest – not particularly important but it’s a testament to his bonkers athletic capability.

The 2020-21 Trail Blazers entered the postseason with their main three stars healthy, Lillard, McCollum, and Nurkic. Also at their disposal were trade acquisitions Norman Powell and Robert Covington, both brought in to make an instant impact. Carmelo Anthony also came off of the bench as a key six man. Meanwhile, the Nuggets were missing both of their starting guards and thus entered the series with a backcourt of Facundo Campazzo and Austin Rivers. Nonetheless, the Nuggets won the series in six games despite a heroic effort from Lillard.

It was arguably the most embarrassing moment of the Lillard era in Portland, up there with the first-round sweep to the hands of the New Orleans Pelicans in 2018. The offseason was full of noise on Lillard potentially wanting out – if a fully healthy and tooled Portland squad lost to a hobbled Nuggets team despite Lillard averaging an efficient 34/10, clearly they weren’t even close to truly competing.

While Lillard has thus far stuck around, a lingering abdomen injury prevented him from maintaining his previous peak level of play and he has been sidelined indefinitely after receiving surgery. McCollum was traded to the New Orleans Pelicans in the middle of his eighth season with the Blazers. It was already clear at this point that the Blazers’ season was over, but the silver lining was that Anfernee Simons would finally have a chance to lead the team for longer than one meaningless game at the end of his rookie season.

Since Lillard’s last appearance on the court (December 31st), the 22-year-old Simons has played (and started) 24 games. He’s averaging 23.6 points and 6.0 assists per game while shooting 42.2% from three with a true shooting percentage of 61.4%. This stretch includes a blistering 43-point game in a close win over the Hawks, a clutch 29 in a nailbiter finish against LeBron’s Lakers, and a three game stretch of 30, 30, and 31 in wins over the Knicks, Bucks, and Grizzlies.

In this span, Simons also averaged more potential assists than playmakers like LaMelo Ball, LeBron James, Stephen Curry, and Josh Giddey. According to tracking data, Simons drove to the hoop 10.4 times per game in this stretch. Among other players with at least 10 drives per game, Simons’ had the seventh-best FG% behind DeMar DeRozan, Chris Paul, De’Aaron Fox, Jrue Holiday, Miles Bridges, and Dejounte Murray. Not bad company.

So, what’s so special about Simons? The numbers make it clear that his most impressive characteristic is his perimeter jump shooting. Over the past two seasons, Simons has quickly become one of the league’s premier spot-up shooters.

Among players with at least 50 catch-and-shoot 3PA, Simons’ boasts the third-highest C&S 3P% behind Joe Harris and Tony Snell. His efficiency on these shots is comparable to players like Zach LaVine and Seth Curry on similar volume. Oh, and he’s substantially older than anyone else labeled on the chart – LaVine is the second-youngest and is still four years older than Simons.

The impressive thing is that the bulk of Simons’ volume comes from games with Lillard and/or McCollum out and Simons expected to carry a heavy scoring load on a tanking roster as a 22-year-old. And he’s somehow pulling through!

We can also evaluate the change in Simons’ on-court impact with the use of an all-in-one lineup-based impact metric such as Estimated Plus-Minus, which is generally considered one of the better performing public metrics of its kind.

Since becoming a rotational player in his second season, Simons’ offensive EPM has steadily improved to +2.5 this season, which ranks in the 94th percentile of NBA players. His composite EPM has reached the positives for the first time in his career despite still being one of the worst defenders in the league statistically.

That’s obviously the elephant in the room – despite Simons becoming a truly elite offensive talent while being just 22-years-old, one can’t really ignore that he’s still a defensive liability. The bright side is that he doesn’t really lack the length to be a disruptive defender – he’s 6’4 with a solid 6’9 wingspan, he just has a slender frame at this point in time which isn’t surprising given his young age. If he can widen out and withstand more contact, there might be hope for Simons to reach average levels on defense – or even the level of a guy like Damian Lillard who’s below average but good enough offensively to make up for it (and then some). There isn’t really an excuse for him to continue being as bad defensively as he is now.

A big concern with Simons on the offensive end is his inability to get to the line. I also would hope that this improves as he bulks up – he isn’t able to seek out and absorb the contact around the rim necessary to consistently get to the line. NBA fans often forget that drawing fouls is a skill, one that some players are never able to master. Take CJ McCollum for example – he’s one of the more skilled one-on-one scorers in the league, but never being able to consistently get free throws at any point in his career severely limited his potential. One can only hope that Simons will be able to turn the tide on that aspect of his game.

In any case, his shooting ability genuinely seems generational and I could see him becoming a record-breaking shooter in his prime. The sky is the limit for his offensive game, and we can only hope that he’ll be able to patch up the holes in his game to unlock his potential as a player. While he clearly has some glaring weaknesses, he’s further along at 22-years-old than realistic projections expected. It’s hard not to be excited for his future.

The post The Next Great Portland Guard Has Arrived appeared first on The Spax.

Foul-baiting. It is a phenomenon utilized by many of the league’s stars. For good reason, a noticeable portion of them are polarizing to fans. Some professionals in this category include James Harden and Trae Young–both maestros in the technique of forcing the officials to call a foul on the victimized defender.

Fans of the sport have voiced their displeasure of these tacky calls, and the game with this absence has been magnified with the conclusion of the 2020 Olympics. With the event using the established FIBA ruleset, a multitude of NBA actions were not allowed in Tokyo. 

NBA Superstar Damian Lillard voiced his experience of the game overseas compared to the NBA, stating in an interview with Mikey Domagdala of the Inside Buzz, “Best scorers in the NBA score from three and get fouled in FIBA, not as many foul calls; more physical. Also, no defensive 3 seconds so the paint is more crowded and refs don’t blow the whistle. It’s hard. There’s so many things that allow scoring to be easier in the NBA”. 

It was only inevitable before the association took action. Preceding the 2021-22 NBA Season, the league determined that a multitude of typical actions taken by the players were “non-basketball moves.” Some of these include:

• veering off path https://streamable.com/3m6u2o 
• overt/leg extensions on jump shots https://streamable.com/oym12a 
• off-arm movement to initiate contact (hooking) https://streamable.com/krnqt5 
• abnormal launch angle https://streamable.com/9jgwlj 

With the first few weeks of the season proceeding smoothly, it seemed that free throw attempts were down across the board. 

With these changes altering the number of attempts, some notable offenders and coaching staff members outcry at the tally and the decision to not benefit the atypical movement.

“Sometimes, I feel like, coming into a game, it’s already predetermined. I already have that stigma of getting foul calls” said James Harden. In addition, his head Coach Steve Nash called him the “poster boy,” for the new rules, both seeming visibly upset in various games throughout the first month of play. Harden, through the first 20 games, had only averaged 6.8 FTA/game–down from his average of 10.4 throughout his stint in Houston.

Another star hit by the recent rule change, Trae Young, also had words about referees swallowing their whistle. Complementary to agreeing with Harden about the stigma players have noticed, he ends in an interview saying, “I just hope they call it within the rules because I know the rules, too. I’ve done my research and my book work, too.” Through the first 20 games, Young’s free throws attempted in each contest averaged at 5.5–down from 8.7 just a season ago.

Even with stars disagreeing with the rule modification, the players’ adaptation has caused a noticeable decrease in the number of shooting fouls called, but is this change here to stay? Or is it merely a temporary occurrence?

Looking at the remainder of games played for the two stars aforementioned, along with other players, their FTA has increased considerably compared to their first 20 games played.

*Jimmy Butler has played a much lower amount of games past the Heat’s 21st game; left early in multiple games through this span

Looking at the statistics, the players who take mostly jump shots (Young, Harden, Curry) have been most affected by the rule change in the first 20 games. All three of Embiid, Antetokounmpo, and Embiid take a large portion of their shots closer to the basket–an area that hasn’t been as targeted. 

Notably, every player’s free throw attempts after the first 20 games increased, excluding the injury-prone Jimmy Butler. The highest jumps (Young and Harden) have even upped their volume exceeding the amount totaled in their previous seasons.

Looking at the jumps between the two different points of the season, it is evident that officials have returned to benefitting foul maestros such as Harden and Young. But what exactly is the source for this resurgence?

A problem referees are facing is the health and safety protocol. According to Adrian Wojnarowski, more than ⅓ of NBA-level officials have been placed in the protocol, causing many games to undergo with either one fewer official or rookie referees taking the mantle. These prolonged absences can attribute to the resurgence of free throw attempts, with the understandable intimidation pushed upon inexperienced referees by the veteran NBA players.

With nearly half of the season remaining, the rule changes will be tested. Will the trend of free throw attempts stay as it has been? Or will the rule alteration prove successful with experienced referees returning to action? Regardless, with the sport rapidly changing, the association has to evolve.

The post How Have the NBA’s New Foul-Baiting Rules Affected League Gameplay? appeared first on The Spax.

Over the course of his ongoing NBA career, Danny Green has hit 1504 regular season three-pointers at an elite 40% clip. His combination of shooting and defensive ability have made him a valuable 3&D role player, leading to NBA titles for the San Antonio Spurs, Toronto Raptors, and Los Angeles Lakers. Needless to say, Green is one of the better catch-and-shoot perimeter players in recent memory.

However, Green is also known for the inconsistency of his shooting. While his career 40% three-point percentage casts no doubt on the general effectiveness of his jumper, it doesn’t tell us anything about his streakiness as a shooter. Green’s nickname “Icy-Hot” represents his reputation as a player who can be prone to extremely poor stretches of shooting or stretches where he seemingly can’t miss.

We know that we can measure a shooter’s efficiency by simply computing their made three-point field goals divided by their attempts. But how can we measure their consistency (or lack thereof)? How can we determine whether Green is actually a particularly inconsistent shooter or if his reputation just comes from the increased spotlight of a player almost always on a contending team?

We will represent a series of shot attempts as a binary sequence, or a series of ones and zeros. A one will represent a successful three-point shot while a zero will represent an unsuccessful three-point shot. We will only be considering three-point shots because while they do vary in terms of difficulty (shot distance, location, level of contest, catch-and-shoot vs. off the dribble, etc), their circumstances are generally more consistent than for other types of shots.

Consider the following sequence of ten successive shots.

We’ll quantify the streakiness of this binary sequence as where represents the length of the th gap between successes (ones) in and is equal to the total number of gaps. Thus, in this example we see that . Three consecutive successes at the start of the sequence correspond with three gaps of length zero, then we see a gap of length two followed by a gap of length one, and so on. Finally, we compute .

The number doesn’t tell us much on its own. The next step is to derive a p-value for this observed value by running a randomization test based on 10000 permutations of the binary sequence . In other words, we will randomize the order of the values in and repeat the process above to calculate . By doing this for 10000 iterations, we will be able to determine how extreme our observed value is compared to expectation.

Shown below is the histogram of the sum of squared gaps for all 10000 iterations of the randomization test.

Given the short length of in this example, there are only five possible values of . In total, for 7890 of the 10000 iterations, yielding a p-value of . A p-value of 1 represents perfect consistency while p-values closer to 0 are indicative of greater streakiness. There is no reason to think that the example binary sequence is inconsistent at all, but we’re interested in larger sample sizes. Let’s move on to the focus of this article.

I calculated the aforementioned p-value for the players in the top-100 for three-point attempts since the 2015-16 season. I also only analyzed the three-point attempts for each player from that 2015-16 season to today’s date. The choice of the 2015-16 season as a cutoff was somewhat arbitrary, but it felt appropriate as it was the first season after the Warriors proved that a jumpshooting team could win the Finals (or at least that was the mainstream narrative following the 2015 Finals).

Let’s go back to the example of Danny Green. The sum of squared gaps for the binary sequence representing his 2710 attempts in this dataset is equal to 7441. It’s not a particularly meaningful number on its own, but we can run our randomization test to determine just how abnormal this value is.

The p-value for this test is 0.0949, suggesting that Green’s shooting over the past seven seasons has been streakier than we’d expect on average assuming that he was a perfectly consistent shooter (i.e. all of the permutations of the binary sequence would be equally likely).

We can repeat the same process for each player and have the p-value represent their consistency (as a lower p-value suggests greater streakiness). A plot of the results is shown below (the full data is at the bottom of the article).

I plotted the p-value from the randomization test for each player on the x-axis and their three-point percentage on the y-axis. It should be noted that that three-point percentage isn’t a perfect measure of shooting ability because different players attempt shots of varying difficulty. For example, Joe Harris’ attempts are certainly easier to convert than Steph Curry’s. Still, 3PT% is a good estimate of shooting ability for this sample size.

The players on the left side of the plot tend to be streakier shooters, and a lot of those names aren’t super unexpected. Harden, Bertans, Thompson, Oubre, Smart, etc are all players who would generally be considered streaky by NBA fans and it seems that this reputation is justified. Of course, the shooting ability among these names varies a lot. Klay Thompson may be streaky, but he’s still one of the greatest shooters of all-time. When he’s hot, he’s hot.

On the other side, we see the shooters that have generally been more consistent. The top right includes some of the better shooters in recent memory, including the best shooter ever in Steph Curry. Curry’s combination of elite efficiency & consistency on his difficult shot selection is truly remarkable.

The bottom right has players who are poor shooters and, well, consistently poor. You don’t really hear about Aaron Gordon or Dennis Schroder’s reoccuring hot streaks from deep, so it makes sense to see them have high consistency.

This raises an interesting question regarding the value in consistency. I would think that a great shooter who is consistent would be preferable to a streakier elite shooter. You’re less likely to have to deal with poor shooting slumps and instead getting consistent production from the perimeter. What about inefficient shooters? Would you rather have a consistent poor shooter or an inconsistent poor shooter? Is it possible that inconsistency would be beneficial in this situation because a streaky player would have the potential to be a worthwhile shooter at times? Or is consistency always preferable?

Anyway, the full data for the 100 players with the most three-point attempts since 2016 is shown below.

The post Quantifying the Streakiness of NBA Shooters appeared first on The Spax.

In the 1500s, Nicolaus Copernicus first developed the heliocentric theory of astronomy. Copernicus proposed that the Earth revolved around the Sun as opposed to the previous widely held belief that the Earth was the center of the universe with all other objects orbiting it. The prefix “helio” refers to the Sun, while “centric” means “centered on.” Thus, the Sun is the center of our solar system.

At some point in time, the word heliocentric began to be used in the context of basketball team-building. In particular, a heliocentric offense refers to one centered around a single player, just as our solar system is centered around the Sun. For whatever reason, this phrase has stuck around in NBA conversation.

To be more specific, I’m choosing to think of a heliocentric star as a player who handles primary scoring and playmaking duties for a team. For example, I would not view the Brooklyn Nets as a heliocentric offense. Despite being led by arguably the league’s best player in Kevin Durant, James Harden clearly dominates the team’s playmaking role as the point guard. Some of the best examples of heliocentric players are guys like prime James Harden, LeBron James, Damian Lillard, Nikola Jokic, Oscar Robertson, and Luka Doncic. Everything on offense goes through them.

Let’s start by taking a look at the percentage of teams who had a single player led the squad in points and assists per game.

Since around 2010, the minimum percentage of heliocentric offenses (by an admittedly basic¹ definition) has had a relative floor of 30%. From 1980 to 2000, however, a rate above 25% was virtually unheard of.

Instead of just measuring how many teams appear to be heliocentric, we can dig deeper and measure the degree of one-dimensionality. For each player on a team, we can approximate the number of possessions² they were statistically involved in per 36 minutes. We can then determine the leader in offensive involvement for each team and then determine the average league-wide rate of offensive involvement for a team’s leader.

The trend over time here is even more obvious than before – the past six years have seen heights in league-wide offensive heliocentricity that we haven’t seen over the past 45 years since the merger. The 2000s saw an uptick with ball-dominant stars like Allen Iverson and Kobe Bryant, but it still didn’t reach the level we’re seeing today.

So, what’s the crux here? What exactly is the statistical driving force behind these trends? In fact, it appears that the correlation between player-level points and assists has increased linearly since the merger and is now an at all-time high.

What does this actually indicate? A positive correlation between points and assists means that there’s a relationship between how many points a player scores and how many assists they record. The absolute value of this number corresponds with the strength of the relationship. It makes sense that the correlation would always be positive, but the fact that it’s larger than ever suggests that scoring and playmaking is more linked than ever before – there are less players that specialize in one but not the other.

Consider the 1981-82 San Antonio Spurs. Shooting guard George Gervin led the team & league with 32.3 points per game. However, he averaged just 2.4 assists per game – point guard Johnny Moore controlled playmaking duties with 9.6 assists per game while averaging just 9.4 points. That’s a very stark contrast between scoring and playmaking on the same offense and it’s a dynamic that’s becoming increasingly unlikely.

Of course, this only begs the question: why are NBA teams trending in this direction? Is it better? Should George Gervin have been playmaking instead of Johnny Moore for the ’82 Spurs? Probably not – Gervin averaged more turnovers than Moore despite passing the ball far less. I’d guess that he didn’t fit the mold of guards like Oscar and Harden who could handle both offensively roles.

I’d theorize that a player like Gervin would become more adept at point guard duties if they developed in the basketball scene today. Similar to how prospects focus more on honing their perimeter shooting because of the increased value in the skill, I think that the league today places more importance in stars that can run a heliocentric offense.

Prior to being drafted by the Houston Rockets, Jalen Green was asked if there was any part of his game he’d like to show off to NBA scouts. His response reflects the effect of the evolving image of a prototypical perimeter star on the mindset of a draft prospect.

I wanna prove that I’m more than just a scorer. That I can pass and that I can sit down and play defense, win, and hit shots. I know a lot of people don’t think that I can pass, that I can only score, that I’m too small to play defense […] I just want to go out there and show my all-around game.

Jalen Green

Green looks like one of the best scoring prospects at the guard position in years. Fans certainly wouldn’t be disappointed if he was only one of the better scorers in the league. That’s not enough for him, though. He wants to be a guy like James Harden – a generational offensive talent who can simultaneously be one of the best scorers and playmakers in the game. And every team in the NBA would love a guy who can sustain that level of offensive impact on their own.

I should clarify that it’s not a necessity for a player to be able to handle both lead scoring and playmaking duties. There’s certainly a positional component to it – Jokic is quite unique as a heliocentric center. Just because he can succeed in doing so doesn’t mean you should expect Embiid to do the same. And while some players may be able to, it might not be in their team’s best interests. Once could argue that Giannis has led heliocentric offenses at times, but it’s clear that they operate best with a guard like Jrue Holiday who can ease those playmaking duties from him. And elite scorers like Kevin Durant or playmakers like Chris Paul (and Magic in the past) are still super valuable even if they’re not leading heliocentric offenses. It is definitely not a necessity.

One could argue that the value of heliocentric players comes in their ability to raise a team’s floor. If you have prime Harden or LeBron, you’re not gonna have a bad offense. By running the entire show on offense, more of the game is in their control. And when more of the game is in the control of an all-time great offensive player, they can make up for the deficiencies of other players in a way that Gervin may have struggled to do.

Of course, there’s something to be said about team balance. Heliocentric players carry a greater load and it can be difficult for them to carry that load throughout a postseason and into a championship series. Just look at Luka Doncic: the Mavericks offense has been entirely predicated around him handling the ball throughout the past three seasons. While he continues to perform in the postseason, it becomes clear in the later stages of games that he feels that effect on his body.

The best teams of all-time were led by great players, but they could not be reasonably characterized as heliocentric. Phil Jackson’s Bulls weren’t heliocentric with the triangle offense, and the Curry/Durant Warriors³ certainly didn’t feature an individual dominating every facet of the offense. The 1971 Bucks had Kareem Abdul-Jabbar dominate the scoring load while Oscar ran the traditional point position. The 2001 Lakers were the epitome of a superstar duo between Shaquille O’Neal and Kobe Bryant. Of course, obtaining a single James Harden or LeBron James is more realistic than building a team with a legendary duo like Kareem/Oscar, Shaq/Kobe, or Curry/Durant.

So yes, heliocentric offenses are becoming more and more commonplace in the NBA. Does a great offense have to be heliocentric? Of course not – but the individual offensive value of a heliocentric player has the potential to be massive.

The post The Rise of Heliocentrism In NBA Offenses appeared first on The Spax.

Background

I had a lot of fun writing my last two articles, which delved into the results of calculating RAPM on a 25 year (1997-2021) dataset and then for separate five year periods within that timeframe. I initially planned on following up with an article on postseason RAPM from 1997 to 2021, but I decided that it wasn’t worthwhile because of the small sample size of play-by-play data that the NBA playoffs have to offer. However, I did want to stick with the postseason theme, so here we are: using statistics that are available since the 1973 to break down individual playoff scoring.

The winner of a basketball game is the team that scores the most points. Thus, prolific scoring individuals have been a valuable asset for a basketball team since the creation of the sport. Every championship team has had a guy who could be trusted to step up on the scoring end in those clutch postseason scenarios. Keyword: postseason. The greatest scorers are those who can do it in the half court against great playoff defenses with everything on the line.

Evaluating scoring is simpler than other aspects of basketball. The best scorers can put up a lot of points efficiently. That means volume & efficiency. The problem arises when we make comparisons across eras, where both volume and efficiency varied greatly.

Different eras were faster paced than others, meaning a single game from the 1970s may have far more possessions than one from the aughts. In this article, we’ll measure volume with points scored per 100 team possessions (PP100). Unlike points per game (PPG), this metric accounts for pace.

What about efficiency? Well, we can’t just use true shooting percentage (TS%) to compare across eras for two main reasons. The primary reason is that like pace, leaguewide efficiency has varied greatly throughout the history of the NBA. League average TS% has risen from 51.6% in 2004 to 57.2% in 2021. Back in 1995 it was up to 54.3%, but 20 years prior it was at a mere 50.2%. Yeah, we can’t just compare true shooting percentage across eras without accounting for that. Also, different players face different teams, and some teams are more adept defensively than others. Thus, a solution to both of these problems is to calculate a player’s defense-adjusted true shooting percentage (rTS%). We’ll take a player’s TS% in a playoff series and subtract the average TS% allowed by their opponents in the regular season.

Example: Michael Jordan averaged 41.0 PPG on 55.8% TS% against the Phoenix Suns in the 1993 NBA Finals. In the 1993 regular season, the Phoenix Suns allowed a true shooting percentage of 53.2% to their opponents. Thus, we say that Jordan’s rTS% in the series was +2.6%. It’s not a perfect metric, of course. If the Suns’ best defender were injured for much of the regular season, their average TS% allowed might be higher than reality, underrating Jordan. Or the opposite effect if their best defender were injured in the Finals. In general, though, I think it’s a simple and effective solution.

We’ll be looking at data exclusively from 1973 to 2021. The reason for the 1973 cutoff is that per 100 possessions data is not available before then.

Results

I’ll begin with career playoff stats – that’s career PP100 and career rTS% in the playoffs. I won’t be able to get to all of the points on the plot, but you can use this interactive graph to check out any unlabeled dots. The graph is littered with all-time greats, so there’s many interesting tidbits hidden in there!

Note: Only players with at least 50 playoff games played are included in this analysis. The size of each point corresponds to games played during their post-1973 playoff career.

Quick rewind. In my last two articles on RAPM since 1997, there was one common theme: LeBron James was #1. There was no way around it – LeBron James was the most valuable player of the past 25 years. Well, the common theme throughout this article will be centered around the man LeBron is often compared to.

Jordan averaged 43.3 points per 100 possessions throughout his illustrious postseason career, by far the most in NBA history. Next up is Kevin Durant at 37.3. That’s a gap of six points per 100 possessions. It may not seem like a lot, but it is. That’s similar to the gap between Alex English’s scoring and Kevin Durant’s. Or Kobe Bryant and Blake Griffin. Prime Blake was a great player, but he wasn’t scoring like Kobe. That’s a substantial gap. And that’s the gap between Jordan and anyone else in league history when it comes to playoff scoring volume. What’s even more amazing is that Jordan scored those points with absolutely elite efficiency. A career rTS% of +4.4% might be behind modern greats like LeBron and Durant, but it’s most certainly more impressive considering the gargantuan gap in volume.

The tier behind Jordan is stacked with all-time great scorers like LeBron, Shaq, Durant, Curry, and Kobe. So basically all of the names you expected (remember, this is post-1973: no Jerry West or Wilt Chamberlain). The only clear guy missing is Karee , but that’s just due to his shorter scoring peak compared to other guys – he still stacks up nicely with a career 31.0 PP100 and +6.1 rTS%.

Some of the more efficient scorers on lower volume are Kevin McHale, Reggie Miller, and Kawhi Leonard. McHale was one of the greatest post scorers in league history at his peak while Miller was one of the greatest pure shooters of all-time, so neither one is surprising to see at the top of the graph. Kawhi Leonard also happens to be one of the all-time greats in terms of elevating his game in the playoffs – he was putting together another legendary postseason performance in 2021 before unfortunately tearing his ACL in the second round.

At the bottom of the graph, we see Russell Westbrook and Allen Iverson. Two legends of the game, but two players who were never able to be efficient scorers at high volume. Both guards have a career playoff rTS% of less than -2.0%. That’s pretty bad, but they were at least able to contribute over 33 points per 100 possessions for their teams.

While career playoff stats are certainly worth looking at, we can’t disregard peak performances. Retired players may have experienced late career drop-offs that drag down the rest of their stats compared to modern players who haven’t yet reached that stage in their career. Plus, some players just had short-lived peaks that are worth recognizing. Here are the top five year playoff scoring peaks since 1973. The size of each point corresponds to games played during the five year run.

The graph is already cluttered so I didn’t have space to throw in the seasons for which each player’s peak covered, but you can see that on the interactive graph here.

Once again, Jordan’s greatness is baffling. His efficiency actually decreased during the second threepeat as he lost athleticism and transitioned to more of a midrange oriented game. The version of Michael Jordan prior to his first retirement has a strong argument as being the greatest basketball player of all-time. From 1987 to 1992, Jordan played 82 playoff games and averaged 43.8 PP100 on +6.5% rTS%. He also casually won three MVPs and two Finals series during this span, of course.

We see an even more cluttered second tier with five year peaks from Durant, Shaq, LeBron, Kawhi, Dirk, and even Kobe, Harden, and Curry not too far off. LeBron’s peak was from 2015-2021, but his five postseasons before that also would’ve ranked quite highly. LeBron doesn’t really have a clear peak which just speaks to his ridiculous longevity. His efficiency in recent years has been higher than it was earlier in his career which made it my pick. Kawhi’s peak since 2015 has been similarly extraordinary, once you knock off the Spurs years where he was a low volume player.

Kareem’s efficiency in his peak from 1973 to 1980 (missed the playoffs once so it’s five postseason peak, not five calendar year peak) was staggering, although his volume was not quite as high as other players – perhaps because his first few seasons were cutoff by the 1973 year limit.

Terry Porter probably wasn’t a name you expected to see here, as he’s just a 2x All-Star surrounded by Hall of Famers, but he was a huge part of two Blazers Finals runs. +10.2% rTS% is no joke. Magic Johnson is also in both lists as a super efficient scorer albeit on quite low volume compared to other legends.

Another lesser known name is George Gervin, who’s right there alongside Steph Curry. Of course on far fewer games played, but it’s still pretty impressive. Gervin never won a title but he led the playoffs in PPG for five straight postseasons starting from 1978. He dropped 42 points in Game 7 of the 1979 Eastern Conference Finals, but his Spurs lost by two points and missed out on a Finals appearance.

You may have noticed that there’s two points that almost perfectly overlap at around 35 PP100 and +4.0% rTS% – that’s Hakeem Olajuwon and Karl Malone. Considering Hakeem’s greatest attribute was his defense while Karl Malone’s was his scoring, I think these numbers speak to the gap between the two players.

G.O.A.T. Scorer?

It’s a pretty common question in NBA circles, and I think these numbers help make the answer more clear. In my opinion, Michael Jordan is clearly the greatest scorer in NBA history and it’s not all that close. He led the league with 37.1 PPG in 1987 as a 23-year-old and proceeded to snag the regular season scoring title in every following full season he played until his retirement in 1998. That’s 10 scoring titles. Oh, and he was also clearly the greatest playoff scorer ever (see: this article). It’s a subjective topic, but there’s no discussion in my eyes as to who the G.O.A.T. scorer is. Obviously NBA history did not begin in 1973, but we do know that the pace of the game was super high in the 1960s so Wilt Chamberlain’s famous 50 PPG season wasn’t quite as impressive as it sounds. Both Wilt and West are all-time great scorers, but they’re not Jordan.

What about the rest of the rankings? It’s tough to say, largely because of how you balance different factors like volume, efficiency, peak, and longevity. Jordan’s an easy pick because he had the whole package, but how do you compare someone like Stephen Curry to LeBron James? Or James Harden to Kareem Abdul-Jabbar? Or Kobe Bryant to Shaquille O’Neal? If you asked me, I’d say it’s between Durant and LeBron for the #2 spot. I don’t think you can go wrong with either one and I think they’re a step ahead of the rest of the competition (although there’s certainly a strong argument for Kareem – it just depends how much you weigh different factors). I’d likely round out the top five with Shaquille O’Neal after Kareem at #4, but there’s just so many contenders. I’ve listed the usual names, but there’s other underrated candidates like Dirk and Wade. It’s certainly a tiresome (but fun) discussion. At the end of the day, I think the only thing that’s set in stone is Michael Jordan’s spot as the greatest scorer in league history.

The post The NBA’s Most Prolific Playoff Scorers Since 1973 appeared first on The Spax.

Background

In my most recent article, I described the process of calculating regularized adjusted plus-minus (RAPM) over a 25 year span, specifically from the 1996-97 season to the 2020-21 season.¹ You can check out a full interactive graph of the results here and a filterable table in the article. In summary, though, the results suggested that LeBron James led the league in on-court impact since 1997 with Kevin Garnett, Chris Paul, Stephen Curry, and Tim Duncan rounding out the top five among eligible² players.

While high-end sustained impact is certainly commendable, I wanted to use the same data to look into shorter stretches of time. Peak versus longevity is a common point of debate in historic basketball discussion. A guy like LeBron James has an all-time great peak along with incredible longevity, but what a player like Shaquille O’Neal? His longevity wasn’t bad by any means, but his peak was certainly even more impressive. A full analysis should look for the best peaks in our timeframe from 1997 to 2021.

Thus, I split the data into five year spans between the 1996-97 season and the 2020-21 season and I calculated the RAPM for each of these spans (21 in total) using the same methodology as the most recent article (that means playoff possessions are double weighted). On to the results!

Results

There’s a lot of data to look at here and it’s impossible to get to it all. If you’d like to dive into it yourself, you can check out a full interactive graph here. There will also be a searchable table at the bottom of the article.

I previously mentioned top five players in RAPM since 1997: LeBron, Garnett, Paul, Curry, and Duncan. Well, these five players are the only ones who make multiple appearances in the top 30 five year RAPM peaks since 1997. Here they are.

The top right is where you want to be – elite impact on high volume. As expected, that’s an area in which LeBron thrives.

It’s a bit hard to appreciate other players when these five guys are hogging all of the spotlight. Thus, let’s take a look at a graph of each player’s single highest peak (by highest RAPM). Obviously longevity matters so this isn’t a perfect measure, but I think it’ll allow us to check out some elite peaks from players that haven’t been mentioned.

From 2012 to 2016, LeBron James won two MVPs and three Finals MVPs. He reached the NBA Finals five times (with three wins), had one of the greatest single-season peaks in NBA history (2013), and he led the greatest Finals comeback in NBA history (2016). He also apparently had the best five year RAPM peak on record. Surprise.

From 2003 to 2007, Garnett won one MVP and was named to the All-NBA First Team twice. His Timberwolves even missed the playoffs thrice in this span with a sole WCF appearance in 2004. It’s one of the least “accomplished” five year peaks on this list. It’s a real shame that Garnett was not surrounded by better supporting casts at his peak like other players.

From 2001 to 2005, Tim Duncan won two MVPs, two Finals MVPs, and two NBA titles. He was named to five All-NBA First Teams and four All-Defensive First Teams. Duncan’s 2003 season was particularly impressive, as the league MVP carried the San Antonio Spurs to a Finals win despite lacking for help at times. Duncan’s dominant Game 6 in the 2003 Finals showcased his versatility and defensive dominance, putting up an insane line of 21/20/10 with eight blocks.

After a spot on the All-NBA Second Team in 2014, Steph Curry went on a historic four year stretch from 2015 to 2018 which included two MVPs, four Finals appearances, and three Finals wins. While I did not split this version of RAPM into offensive and defensive components, one would expect Steph’s offensive RAPM to top the charts.

Dwyane Wade’s five year stretch from 2006 to 2010 is actually higher than you might expect – right above CP3’s 2012-16 peak (albeit by a negligible margin). Wade started off this five year stretch with a dominant 2006 season, averaging 27 PPG in the regular season and carrying the Heat to a Finals win over the Mavericks. Wade averaged 35/8/4 in the 2006 NBA Finals and brought home Finals MVP. While that was his only championship during this run, Wade was named to his first All-NBA First Team in 2009 and did it again in 2010 after injury-riddled seasons in ’07 and ’08.

Chris Paul was named to three All-NBA First Teams and two All-NBA Second Teams during this stretch from 2012 to 2016, but never even reached the Western Conference Finals. While Paul was individually dominant, the Lob City Clippers could never find their mojo in the playoffs, often due to untimely injuries to either Paul or Griffin – or even both.

For Michael Jordan, his 1997-2001 peak is actually limited to just the 1997 and 1998 seasons because he retired following the 1998 Finals. Nonetheless, his two year stretch included two Finals wins, a league MVP, and two Finals MVPs. Not bad.

I’m pretty surprised that Dirk’s RAPM peak is considered a stretch from 2010 to 2014 (it’s basically tied with his 2008-12 stretch, but still). I’m assuming his legendary 2011 run has an impact on that. Still, Dirk was undoubtedly a great player who has arguably become underrated in recent years.

The early 2000s featured incredibly high level of play from both Duncan and Garnett, arguably the two greatest power forwards in the history of the game. Then LeBron took the throne as the best player in the league, a title he may have held longer than any player in the history of the sport. That’s ridiculous dominance.

I didn’t set a minimum limit for possessions played (maybe I should’ve) which is apparent when you see Jordan’s small red point at the start. But the second leading player from both ’97-’01 and ’98-’02 was Shaquille O’Neal, so shoutout to his dominant peak with the Los Angeles Lakers.

What about Kobe? Kobe’s best RAPM peak was from the 2006 season to the 2010 season. In this span, Kobe led the Lakers to two Finals wins and three Finals appearances along with an MVP win in 2008. Kobe’s 4.26 RAPM was the fifth highest during this span: well behind LeBron, Wade, and Garnett, but only narrowly behind Duncan.

Finally, here’s a full table of the results.

A few last observations I’d like to make:

As always, remember that this is not meant to be a player ranking – it’s more of a fun mathematics & statistics project.

I had initially planned on wrapping up this series with an article dedicated to 1997-2021 playoff RAPM. However, I didn’t think it warranted its own article or much discussion because of the high variance in the results. You can check out an interactive graph of the results here if you’re curious, though.

The post Quantifying the NBA’s Greatest Five Year Peaks Since 1997 appeared first on The Spax.

Background

Basketball analysts have searched for years for a viable all-in-one metric for quantifying the on-court impact of basketball players. We can always look at basic statistics like points and rebounds, but what about everything that doesn’t show up in the box score? Skills like setting effective screens, contesting shots, boxing out, and off-ball gravity can all have a huge impact on any given basketball play while not showing up in the box score. What if we could really assess player impact without needing to rely on these numbers?

A traditional way to represent player impact without box score stats is to just use base plus-minus. For example, Steph Curry had a +4.0 plus-minus per 100 possessions in the 2021 season. This number means that with Curry on the court, the Warriors outscored their opponents by four points per every 100 possessions. You can also compare this to his net plus-minus compared to when he’s off the floor. Steph had a +8.6 on-off plus-minus, meaning that the Warriors outscore their opponents by 8.6 more points when Steph is on the floor than when he is not.

While easy to understand, the traditional plus-minus metric is very flawed. If an inferior player’s minutes heavily aligned with Curry’s, their plus-minus would look far better than it should just because they get to play with Curry. In other words, base plus-minus does not adjust for the strength of your teammates. Furthermore, while a quick look at on-off plus-minus may let you know that a player is carrying their team, it tells you more about how strong a team’s bench is than anything else. James Harden posted an on-off plus-minus of +9.1 in 2020, which pales in comparison with his +0.2 mark in 2021 (albeit on a small sample size). Did he get that much better? Of course not – the Brooklyn Nets are just far more equipped to play at a high level without Harden on the floor than the Rockets were.

So, we need to adjust for the other players on the floor. That’s the idea of Adjusted Plus-Minus (APM) – solving the system of linear equations representing the players on a court and the associating plus-minus for their duration on the floor.

Suppose that we have a matrix called A representing the players on the floor (one column for each player, a value of 1 if they’re on the floor for that stint and a value of 0 otherwise) and a vector b representing the plus-minus per 100 possessions for each stint. We can then solve for x which is a vector of coefficients corresponding to each players representing their on-court value.

That’s the adjusted plus-minus solution. As you might anticipate, it has its own drawbacks. Most notably a high degree of variance. This problem can be alleviated with the addition of a filtering term that essentially acts as a penalty for outliers – it converges all values towards zero.

An optimal lambda value can be found which yields an approximate solution to the original Ax=b problem. This equation is the method used to calculate regularized adjusted plus-minus (RAPM).

Notice that at this point, the only stat that has been used is the stint plus-minus for each combination of players on the floor. No assists, rebounds, steals, blocks, etc. Or even points scored by a specific player – just the overall plus-minus in that duration of time.

Improvements upon RAPM like RPM and RAPTOR incorporate Bayesian priors with box score and tracking stats to give a better prior estimate of player value for the model. Instead of regressing to zero, you can regress to this prior value. This leaves us with two versions of RAPM: non-prior informed RAPM (NPI RAPM) which uses nothing but the lineup metrics, or prior informed RAPM (PI RAPM) which improves the accuracy of the model in small samples by incorporating box score numbers.

In most of its use cases, NPI RAPM has noticeable weaknesses. People usually want to see the numbers for a single season, which is a relatively small sample size for a regression without a suitable prior. There’s also a lot of variance in small samples because of factors like the three-point shot. A player shooting higher or lower than their average from three-point range in a small sample may have nothing to do with the lineup or the defense, but have a large impact on the result of a regression. Thus, alternatives like EPM and PIPM incorporate luck-adjustments that are make them much more adequate for smaller samples.

In larger samples, though, you’d expect most of these factors to mostly sort themselves out. Five year RAPM is often cited and yields more reasonable results than a one season sample. What if we go even further than that? Say, 25 years?

25 Year RAPM (1997-2021)

I began this project by scraping play-by-play data for every regular season and postseason game since 1997. Then I used the ideas in this tutorial (applying it to Python) to get lineup data for each possession in the play-by-play. I was successfully able to do this for every dataset except for the 1997 regular season, which contained a lot of missing information. The data used in final RAPM calculations is almost entirely complete from the 1997 postseason to Game 6 of the 2021 Finals.

In order to address the greater importance of the postseason, I doubled playoff possessions to increase their weight in calculations. At the end of the data collection process, I had compiled 859,049 stints across 5,972,736 possessions.

I also utilized a prior to improve the accuracy of the regression. I had initially planned not to do so, but it came to my attention that any long-term RAPM essentially requires some form of prior to account for player aging. Peak Shaquille O’Neal was one of the most unstoppable players in the history of the game. An old 38-year-old version of Shaq was far less of an intimidating force. Both players would be treated the same with NPI RAPM, meaning that 38-year-old Shaq’s teammates would be penalized for playing alongside him because of how great he was in the past. That doesn’t make any sense.

My initial plan was to incorporate a simple prior based on age. The problem is that all players don’t age on the same curve. Prior studies found that a Bayesian prior based on playtime & team strength is more reliable than age, so I went with that approach in this project. Thus, a player’s minutes per game and a team’s net rating were the only two external statistics used in the regression.

All that was left was to find an optimal lambda value and then run the ridge regression. Additional measures could certainly be taken to improve the accuracy of the model, such as a luck-adjustment or a different way to treat “garbage time” possessions. For now, I didn’t want to interfere too much unless it was required (like the aforementioned prior).

A quick disclaimer: this is not a player ranking, nor is it meant to be. If I was ranking the top ten players of the 21st century, I would undoubtedly include players like Kobe Bryant and Kevin Durant in my list. Anyone would. But the point of this article isn’t to give my personal rankings. It’s to observe the results of an objective regression.

I’ve plotted the results on a scatter plot with both total possessions and RAPM. There is obviously a large range of total possessions – the data includes both Dirk Nowitzki’s entire 20 year career along with LaMelo Ball’s injury-shortened rookie season. RAPM is, after all, a rate metric; volume shouldn’t be ignored. You can check out a full interactive graph here.

If someone with no prior knowledge of basketball was asked to guess who the best player in the NBA was over the past 25 years based on nothing but this data, they would probably pick LeBron James. And they would be right. Arguably the greatest player in the history of the sport, LeBron has the highest RAPM from 1997-2021 on top of playing the most possessions by a wide margin. Even if you disregard his four NBA titles, four Finals MVPs, four MVPs, 17 All-NBA selections, and 27/7/7 career averages, he comes out on top. His on-court impact is undeniable no matter how you look at it.

Tim Duncan and Kevin Garnett are two other legends of the game who are appreciated by impact metrics like RAPM. Despite the world of difference in their career achievements (four more rings and three more Finals MVPs for Duncan), one could argue that this has more to do with situation than anything else. Garnett’s often considered one of the more underrated players because of his transcendent on-court impact that isn’t reflected in his box score stats, on top of the fact that he spent much of his prime carrying a middling Timberwolves squad.

Right up there with Garnett and Duncan are two legendary point guards in Chris Paul and Steph Curry. Paul, the “Point God,” is one of the greatest floor generals in the history of the game. More of a traditional point guard, CP3 has called the shots for elite offenses his entire career while also playing great defense for his position. Meanwhile, Curry’s unprecedented shooting ability makes him one of the most impactful offensive players of all-time. The threat of his perimeter shooting along with his off-ball movement draws defenders away from his teammates and makes everyone’s job easier on the Warriors. On top of elite finishing and solid playmaking, Curry’s offensive impact is legendary.

Joel Embiid ranks a whopping 2nd in RAPM. While that’s certainly higher than I anticipated, Embiid is certainly a super special player and one of the most impactful players in the league currently. Unfortunately, his biggest problem is the inability to stay healthy. He just came off of an incredible season averaging 29/11 on 64% TS% while playing great defense – he likely would’ve been the league MVP if he hadn’t gotten hurt. Oh, Embiid also averaged 28/11 on 63% TS% in the playoffs while playing on a torn meniscus. He’s pretty good. Nonetheless, I don’t anticipate he’ll maintain a top-two ranking in the RAPM leaderboards as he plays more time. He’s great, but probably not at the level of guys like Steph, Garnett, and Duncan.

Kobe Bryant’s the guy who tends to be rated lower than expected by advanced metrics like RAPM. As one of the more polarizing players in league history, it’s definitely true that many people overrate his all-time standing. But ranking 59th overall from 1997-2021 is still insanity. That’s behind recent players like Dillon Brooks and Otto Porter Jr. I’m not entirely sure why the metric is underrating him so much. Perhaps his post-prime years have a large impact? The prior should account for that but I’ll look into the highest RAPM peaks in another article to see if it provides any answers.

Those are the main results that stand out, but here’s the full data consisting of 2267 players over the past 25 years.

The other players in the top 10 are Nikola Jokic, Manu Ginobili, Draymond Green, and Jayson Tatum. Draymond and Manu are other players frequently given a lot of love by impact metrics, so it’s not surprising to see them here. Jokic has also been a high impact player throughout his entire NBA career thus far, culminating in an extremely impressive MVP season in 2021. Tatum’s a fantastic young player but the top 10 is certainly higher than I expected to see him. I’d say the same thing I said about Embiid – he’s great, but probably not that great.

If we limit the rankings to players with at least 150,000 possessions to get rid of the Joel Embiids and Jayson Tatums in there (kukos to both of them, though), we get Dirk Nowitzki, James Harden, Shaquille O’Neal, Kevin Durant, Rasheed Wallace, and Paul Pierce rounding out the top 10 after James, Garnett, Paul, and Duncan. O’Neal is another player who I expected to rank higher. Among all players, his 3.78 RAPM is the 16th highest since 1997. He’s probably a bit hurt by the 1997 cutoff because of how great he was in Orlando.

Other observations:

There’s a few other things I’d like to do with this data, such as looking for the best five year individual peaks during this span. Maybe that would better illustrate the greatness of Shaquille O’Neal and Kobe Bryant. I could also separate the regular season and postseason results and observe the difference in each. For now, I think this 25 year outlook was enough for one article and a good start to the analysis. There were a few “problems” (it’s not really a problem because again, this isn’t meant to be a player ranking) like Kobe Bryant’s low ranking and the high ranking of Joel Embiid, but I’m satisfied with the project overall.

The post Calculating Regularized Adjusted Plus-Minus for 25 Years of NBA Basketball appeared first on The Spax.