Statistical Analysis. Humor. Knicks.

Friday, August 29, 2014

Using Stats to Gauge Player Ability

Let’s assume you’re the GM of an NBA franchise. It’s the offseason and you need to sign a free agent center. You have three options.

Name Ag PTS REB STL AST TO BLK
Player A 24 11.7 10.9 0.7 1.5 1.5 1.6
Player B 24 9.8 8.2 0.4 0.5 2.2 1.8
Player C 25 4.8 8.0 0.9 0.8 0.8 1.6

If these are the only stats we have, then it’s clear. Player A is a superior scorer and rebounder, and his defensive stats are about as good as the other two. On the other hand, Player C is a feeble scorer and the worst rebounder of the three. Player B is twice as good a scorer than C, and slightly better in rebounding and shot blocking. I would rank them Player A, Player B, then Player C.

Now what if your options were these three players:

Name Ag PTS REB STL AST TO BLK
Player A 24 13.5 12.5 0.8 1.7 1.8 1.8
Player B 24 12.6 10.5 0.6 0.6 2.8 2.2
Player C 25 8.0 13.3 1.5 1.4 1.4 2.7

In this example Player C is the best choice. He is superior to the others in 4 categories: rebounds, blocks, steals, and turnovers. Meanwhile Player B sinks to the bottom of the list, being too turnover prone and the worst rebounder of the three. This time I would rank them Player C, Player A, and Player B.

Now what if I revealed that the players in the first table are the same as the ones in the second table? How is it that a player can have two entirely different set of stats? Simple, the first table is the players’ per game stats, while the second is their per 40 minute stats. The stats changed so much from the first table to the next because per game stats are proportional to the number of minutes a player receives. And in this example, the players played varying amounts of minutes. Player A averaged 34.7 min/g, Player B 31.2 min/g, and Player C 24.1 min/g.

Playing time in the NBA is dependent on a few different factors. For younger players their talent, draft position, contract size, pre-draft hype, team depth, coach’s tendency, team record, and sneaker deal may alter their court time. A #2 overall pick playing for a rebuilding team with little depth (LaMarcus Aldridge) will see more playing time than a #4 pick playing for a playoff team with ample forwards/centers (Tyrus Thomas). Since per-game stats are proportional to playing time, and playing time is based on many different factors, then it makes sense that per-game stats are capturing some factors other than a player’s ability. In other words when Aldridge had more rebounds per game (5.0 rpg) last year than Thomas (3.7 rpg) it’s not due to Aldridge’s skill on the glass, but rather his higher draft position, team depth, team record, et al.

If we want to judge a player based on their talent alone, then we need to isolate a player’s talent from the rest of those variables. And that’s what per minute stats do. Once we remove a player’s minutes from his stats, then all the factors that go into playing time are removed as well. Per minute stats aren’t dependent on draft position, contract size, pre-draft hype, team depth, coach’s tendency, team record, or sneaker deal. When compared to per game stats, per minute stats come much closer to capturing a player’s ability.

Getting back at our tables above, it’s clear that Player C was hindered by his lack of playing time. Hence why he appeared to be inferior when using per game stats. But when we accounted for this lack of playing time with per minute stats, Player C was clearly superior to the other two. Player C, also known as Ben Wallace, would receive major minutes the next year in Detroit and win the first of his 4 Defensive Player of the Year award the season after. Player A, Dale Davis, was a fine player for 14 seasons, but was never considered great. Michael Olowokandi, Player B, never amounted to the hype of being the #1 overall pick, and despite being a year younger than Wallace, is barely holding on to his NBA career.

In the end, per game stats was unable to distinguish the perennial All Star (Ben Wallace) from the solid pro or the first round bust (Michael Olowokandi). However per minute stats identified the players correctly from most to least talented. Using per minute stats to compare players eliminates many of the unwanted factors that go into per game stats. Like sneaker contracts.


Extras:

  • Why do we use per 40 minutes stats? Ben Wallace averaged 2.3blk/40 and he also averaged 0.072blk/min. It’s easier to visualize 2.3 blocks instead of 0.072 blocks. You could use any number instead of 40, but we use 40 since it has become the most commonplace.
  • Using per 40 minute stats isn’t an endorsement for the player to receive that many minutes. Nor should you use per 40 minute stats for one player, and per game stats for another. (And yes I mention this because I’ve seen people do it).
  • You could use more advanced metrics than per-minute stats, but per minute stats are easily calculated and widely circulated.
  • Don’t think that per minute stats hold up over increased minutes? Check this out:

    I did a small study using player-seasons from 1978-2004. To be included in the study, a player had to (a) see an increase of at least 50% in minutes per game from one season to the next and (b) play at least 41 games in each season. These criteria gave me 465 player-seasons. In 346 of these seasons (74.41%), the player’s PER increased with an increase in playing time.

    And this:

    No, increased minutes do not seem to lead to decreased efficiency. In fact, the data indicates increased minutes lead to? increased efficiency. More than 70% of the players in the study (there were 251 in total) saw their PER (which is, by definition, a per-minute summary statistic) increase with the increase in minutes. Players whose minutes per game increased by five saw an average change of +1.38 in their PER.

    And then this:

    Players who receive 10 or more minutes per game are likely to keep the same per minute stats no matter what the increase in playing time is. Therefore per minute stats remains far superior to per game stats in terms of comparing and evaluating players.

42 comments on “Using Stats to Gauge Player Ability

  1. Mike

    Just another fantasy geek who probably never played the game wanting to think he knows more than coachs, gms and scouts.

    So a guy that plays 5 minutes per game and grabs 2 rebounds should automatically be expected to grab 16 rebounds per 40 minutes.

    So many factors not taken in to consideration:

    Were the minutes in garbage time?

    Were the minutes against starters or reserves?

    Was foul trouble a factor at all. Probably not for a guy playing 5 minutes per game.

    Does a guy playing 5 minutes per game get tired at all compared to a guy playing 40 minutes a game?

    Does the 5 minute per game guy play soley when teams are in the penalty leading to more free throws?

    Thats just some. I bet there are easy another 20 that could be mentioned

  2. teddd

    Judging by Mike’s response to this and many previous opinions, sadly, he seems to miss the crux of just about every article on this site.

  3. Khyle

    Has anyone looked at the negative case? What happens when a player’s minutes decline? What happens to his per minute status then?

    Everyone seems to be focusing on players who get more minutes, but isn’t it just as important to understand what happens when a player’s minutes decline?

  4. Mike K. (KnickerBlogger) Post author

    Khyle – I think when looking at fouls a few years ago, I found fouls went up when minutes decreased. That really seems to be the one stat that moves with minutes. Most likely bench players are more aggressive because they don’t have to worry about fouling out.

    I’m a bit skeptic on doing the study the opposite way, because there are more reasons a player would receive less minutes that would actually coincide with a decrease in production. Namely aging and injury. You could account for aging by looking at young players, but you might just get a subset of players coming off of injuries that haven’t fully recovered.

  5. Z

    “Most likely bench players are more aggressive because they don?t have to worry about fouling out.”

    Refs call fouls on reserves more than starters so they don’t get a call the next morning from David Stern. (Did Chris Dudley’s fouls per minute decrease when he started over Ewing in ’98? (If I was a betting man, the surest bet in town was that the second Ewing took a seat his sub would be called for a foul on the next possession. (Psychic coincidence???)))

  6. Abre Los Ojos

    Here’s a different scenario for you.

    You need a young power forward. Here are four 21 year old options:

    Player A averages 4.3 PPG, 3.7 RPG, 0.4 SPG, 0.3 APG, 0.8 TOPG, 0.3 BPG. Per 48M, 17.5 P, 15.3 R, 1.7 S, 1.4 A, 3.1 T, 1.2 B.

    Player B averages 3.9 PPG, 3.3 RPG, 0.2 SPG, 0.3 APG, 0.7 TOPG, 0.8 BPG. Per 48M, 15.2 P, 12.8 R, 0.6 S, 1.0 A, 2.6 T, 3.1 B.

    Player C averages 10.9 PPG, 7.4 RPG, 0.9 SPG, 1.5 APG, 1.9 TOPG, 0.7 BPG. Per 48M, 17.3 P, 11.8 R, 1.4 S, 2.4 A, 3.0 T, 1.1 B.

    Player D averages 8.4 PPG, 4.5 RPG, 0.5 SPG, 0.5 APG, 0.8 TOPG, 0.2 BPG. Per 48M, 24.0 P, 12.7 R, 1.5 S, 1.5 A, 2.3 T, 0.5 B.

    If this post isn?t censored, pick which one you would sign. Then I?ll return to name the principal actors.

  7. Mike K. (KnickerBlogger) Post author

    ALO:

    per game it’s easy to see that C is the best. Nearly double the rebounding. Then maybe B, D, A.

    per minute is tougher, esp. since you used per 48M. (I’m more accustomed to p40). C is the worst in per minute. Yeah he passes well, but his rebounding is awful, and the turnovers are a bit high too. Then you have to choose between B & D. D is the better scorer, but B is the better shot blocker (of the group.) I might choose B since the blk/min seems to be exceptional, whereas D is just a good scorer. The best seems to be A. Great rebounding. Decent shot blocking. Strong in steals. decent assist. Turnovers are high, but you expect that to decrease in a 21 year old. So from best to worst: A, B, D, C

  8. Abre Los Ojos

    TS% wasn’t part of the original example, but I’ll provide it anyway.

    Player A has a TS% of 54.5

    Player B has a TS% of 51.5

    Player C has a TS% of 54.7

    Player D has a TS% of 55.5

  9. Owen

    nope, ts% of 54.1 and 46.4 so far in his career.

    There is a feature over at basketball reference, player stats search, under the full court tab, if you need to know who these people are. I am happy to wait…

  10. JK47

    Well, it looks like Isiah has lost that court case. And so begins another ridiculous season in KnickLand.

  11. Devin

    Wow, that feature on basketball reference is pretty nifty. I hadn’t seen that before.

    I was able to find all four players in about 2 mins.

  12. brian quinnett's left nipple

    supposedly the jury is deliberating how many sexual innuendos isiah will induce per forty minutes.

  13. Abre Los Ojos

    Player A is Mike Sweetney, Player B is Jermaine O’Neal, Player C is Kwame Brown, and Player D is Zach Randolph.

  14. Mike K. (KnickerBlogger) Post author

    Interesting. To be fair I also gave the player’s heights. I’m not saying that knowing Player B is 6-11 and A was 6-8 would have changed my mind, but it might have played a role in it. Looking at their per-minute stats, Sweetney stayed relatively the same. His turnovers have ballooned (as well as his pants size). Meanwhile JO saw increases in his rebounding & scoring.

    At age 22, it’s clear that JO is the superior player by per-minute stats (JO-Zach-Swetney-Kwame). But by per game stats, Zach and Kwame look better than Jermaine (Zach-Kwame-JO-Sweetney.)

    http://www.basketball-reference.com/fc/pcm.cgi?req=1&cum=1&p1=sweetmi01&y1=2005&p2=onealje01&y2=2001&p3=randoza01&y3=2004&p4=brownkw01&y4=2005

  15. Owen

    Hmmm, don’t know if I ran the numbers exactly right, but here is how I make it.

    Winscore per 48

    Sweetney 11.75
    JO 11
    Randolph 11.55

    Sweetney and his weight problem are a bit of an anomaly. He was a very promising player. His ts% was actually 58% through age 22. it didn’t work out. It happens. There are exceptions to rules. Players get injured, players get fat. And the Bulls got stuck with Sweetney, Tyrus Thomas, and Joakim Noah. Such idiots…

    What’s your take ALO. I think you see this as in some way an indictment of per minute stats. Correct? I don’t think it’s particularly damning…

  16. KD

    If there’s one thing I’ve gotten from this site over the last three years, it’s that Knickerblogger sho do love his fantasy basketball!

  17. Abre Los Ojos

    Sweetney didn’t fail to develop because he gained a massive amount of weight. His weight has remained consistent throughout his career.

    I could have used plenty of other examples but I chose players I felt would be familiar.

    If you want to use centers, replace Ben Wallace with a 25 or 26 year old Dan Gadzuric in Mike K’s example. Gadzuric grades out as well, if not better, than Wallace in these terms.

  18. Abre Los Ojos

    I have Gadzuric as a WSP48M of 14.34 versus 16.47 for Wallace. Regardless, I’ll leave it you to explain the contributions of Dan Gadzuric.

  19. teddd

    Sweetney is one player with solid per minute stats early in his career that didn’t work out. That’s a given. He’s a black eye in the entire per minute argument. But that doesn’t mean that ALL per minutes stats should be thrown out because we found an exception.

    Nobody ever claimed it was a perfect measure. There are no perfect measures. If there was, Kwame Brown wouldn’t go #1 overall and Gilbert Arenas wouldn’t fall to the 2nd round of that same draft. Obviously, as with all statistical measures, you need a large sample size before you start to draw conclusions. And IMO, this already has been proven with per minute stats. I honestly don’t know why there are still people out there who refuse to see it’s usefulness?

  20. Owen

    I don’t have the answer to why Gadzuric played so much better his first three seasons than his last two. He had a good season his age 26 year, he was average the next year (.105), and he was below average (.046) last year, though still more productive than Curry. Perhaps injury had something to do with it? Perhaps they tried to change his role? Perhaps Bogut had something to do with it?

    I do know that Wins Produced shows Ben Wallace to be one of the most productive players in basketball over the last ten years. And I feel absolutely confident that Wins Produced would have told you that Wallace was much the better player to sign at age 26. His Win Score is higher. But also, Wins produced takes other factors into accounts, specifically team defense. Wallace would have garnered an advantage there. The Pistons were a top ten defense in 00-01. The Bucks were 27th I think in Gadzuric’s age 26 season.

    I don’t think anyone is saying that this is foolproof science. And you can certainly cherry pick strange seasons and anomalous results. My stance would be this:

    NBA Gm’s should look at the full breadth of evidence available. They should definitely think about whether even that constitutes an adequate sample size. They should think about the age of the player and his NBA experience. They should think about why stats might have been lower than expected, or higher. They should think about what the addition of a quality player at the same position will mean. They should think about injury propensity. They should NOT base their decision off of short term playoff performances, playing style (good dunking), college fame, name recognition, and most definitely scoring average.

    However, as it turns out, the biggest predictor of salary is scoring average.

    Basic case, an NBA Gm may still make mistakes, but on average he will do much better looking at a chart like this

    http://www.wagesofwins.com/FreeAgents80807.html

    than he would by relying on typical heuristics. Sometimes signings don’t work out. Sometimes players don’t live up to expectations. There are exceptions to rules, and it is a soft science. But Per minute stats and imho advanced metrics like WP should allow you to do a better job.

    With the Knicks for instance, looking at Wins Produced it would have pretty clear that Marbury was not the best way to spend 17 million dollars. He is a slightly above average point guard for his career, nothing more. And there was more than enough evidence to conclude that Eddy Curry was not worth two first round draft picks. Ditto for the fact that Tyson Chandler was a much better player than Curry. You couldn’t perhaps have predicted how much better Chandler would play this year than he ever has before, but he was always going to be the better player.

  21. teddd

    BTW, there’s another Mike Sweetney looming out there right now by the name of Sean May. He’s frightening similar actually. Great per minute stats as a rotation player (PER’s 15.3/19.1 first 2 seasons). Same issues with both his weight (which might be effecting his health as well) and the fact that he’s a bit short for a PF. Same high foul rates (which is likely related to the height and weight issues).

    It will be interesting to see where his career takes him. The conclusion just might end up being the most obvious one, that if you don’t get yourself into shape, you’re going to have trouble playing defense and your going to have trouble logging big minutes. Carlos Boozer also entered the NBA as a bit of a dough boy but he immediately got himself into top shape and turned himself into an all-star. On the other hand Robert Traylor never got in shape after his first 2 seasons either (17.0/15.8) and he failed to deliver as well.

    My prediction is that if May doesn’t get himself into shape, he goes the Sweetney/Traylor route rather than reaching his potential.

  22. Frank

    Sorry for the off-topic post but here is part of a story from today’s NY Times about Eddy Curry… can anyone say Eddy’s going to prove Owen wrong? (I’ll believe it when I see it).

    The news on the basketball court may provide some measure of relief, from both the trial and from last season?s dismal 33-49 campaign. Center Eddy Curry, who had a promising season, said he was 20 pounds lighter ? and proportionally quicker. Forward Zach Randolph, who averaged 23.6 points and 10.1 rebounds for Portland last season, is now playing next to Curry, forming perhaps the most powerful low-post tandem in the league.

    And the players whose injuries sank the Knicks last spring ? Jamal Crawford (right ankle surgery), David Lee (right leg stress injury) and Quentin Richardson (back surgery) ? said they were back to full strength. Indeed, Crawford is better than that, having added another 15 pounds of upper-body muscle to help absorb contact on the way to the rim.

    No one seemed more eager to get the season started than Curry. In late July, Curry and his wife were robbed at gunpoint in their suburban Chicago mansion.

    ?The scariest thing I?ve ever been through in my life,? Curry said, speaking about the incident for the first time. ?Guns in your face, guns in your chest, guns in your back. People screaming at you, cussing at you, ordering you around, cursing at your wife, guns on her. It?s crazy.?

    The incident prompted Curry and his family to return to New York almost immediately, which Curry said was beneficial to his game. He ended up spending more time at the Knicks? training center, and losing the most weight since he turned pro in 2001.

    Curry declined to list his weight but said that his performance in strength and quickness tests, when compared with this time last year, ?were just night and day.?

  23. Mike K. (KnickerBlogger) Post author

    I don’t think this is the intention (ALO, correct me if I’m wrong) but certainly people will examples like this to dispute per-minute stats importance. However it’s just as important to look at what this, and examples like this, actually prove.

    Do per-minute stats occasionally overrate players? Yes. However they do so at a much lower rate than per-game stats. And that’s all we’re talking about with these two stats. That per game stats can be sent to the glue factory, because their usefulness is superceded by per-minute stats. Per-game stats will never find the needle in the haystack (Redd, JO, Big Ben), while per-minute stats will find the needles and grab some hay with it (Sweetney, Gadzooks, Traylor). And I’d rather have the latter than the former.

  24. Nick

    Maybe Curry has turned a corner but stories like this crop all the time before the start of a season. Rarely do they mean much though.

    When I think of Curry, I see a player who is the equivalent of a mediocre DH in baseball. Someone who can hit for a decent average with decent power, but who can’t do anything else and then struggles mightily against good pitching. It’s preposterous that he’s a core member of the Knicks. All he does well is score but not at a rate that is elite and unfortunately his one lone strength can be effectively neutralized by double teams. As far as rebounding, shotblocking, passing, post-and-man defense goes, he’s a minus in all of them. Sigh.

  25. Owen

    That all sounds great to me Frank.

    Crawford’s ft’s jumped from 2.7 to 4.6 in 05-6. That is a big reason his ts% jumped to 54.4%. Last year, he got to the line a little less. He also shot much more from three and performed a little worse there. Having Jamal go to the rim more and shoot from deep less seems like a very sensible idea to me. Gis rebounding also fell off quite a bit, by .7 per 40, and hopefully the muscle will help him there.

    Crawford showed under Brown that he is capable of being an above average performer in the NBA. Hopefully, he gets back there. If Curry, Crawford, and Marbury can all be average next year, and if Lee, Randolph, Balkman, and Q can be above average, we will have a pretty good team.

    As for Curry, I think its wonderful to hear that in his third season in New York he has finally managed to get in shape for the first time in his career.

    I have a bottle of Cristal heading Jon Abbey’s way if he is above average in WP48 for the season (reasonable minutes played), and let me say I will be delighted if he is sipping bubbly in June, as we celebrate being in the playoffs. I don’t see it happening, but I hope it does.

    You have to think that losing weight will hurt Curry’s offensive game, which seems to mainly consist of bludgeoning opponents with his ass, backing them down till he is under the basket, then finishing. Overall though I definitely support the idea of in-shape, quick, Eddy Curry.

  26. Abre Los Ojos

    Shaquille O’Neal has enjoyed modest success in the NBA despite being perpetually overweight. And a short, fat man named Charles Barkley was reportedly a good basketball player.

    Dan Gadzuric and Mike Sweetney are very similar cases, despite completely different bodies and styles of play. Someone should soon arrive at the proper conclusion as to why both of these players failed to reach their potential.

    Would you use per-minute statistics to compare a 34 MPG player to a 37 MPG player?

    Do studies that conclude that per-minute rates remain static relative to playing time include players like Dan Gadzuric and Mike Sweetney? Or are players of this type excluded because they never quite managed to increase their minutes?

  27. Z

    “When I think of Curry, I see a player who is the equivalent of a mediocre DH in baseball.”

    Totally– he’s the Dave Kingman of the NBA.

    But baseball has a role for guys like that (an entire league even).

    “Crawford showed under Brown that he is capable of being an above average performer in the NBA. Hopefully, he gets back there.”

    Crawford has shown in fleeting moments that he is capable of doing some pretty damn amazing stuff with a ball and a hoop. Those moments continue to infuse hope into a career that is getting away from him. At this point, “an above average performer in the NBA” would be a realistic, helpful-to-the-team goal.

  28. Caleb

    This is an interesting discussion but ignores an elephant on the court – defense. That’s much harder to quantify, but I bet if you threw in some +/- ratings the true value of these players would be much clearer. Jermaine O’Neal has a lot of value even if his offensive game completely disappears (as it seems to be doing lately). Sweetney on the other hand, is and was a defensive joke.

    While there probably IS more variation in offensive ability, than defensive ability (making offensive stats more important), in general I think we undervalue the importance of defense – a difference of a block or two per game, doesn’t start to measure the different impact of these players.

    p.s. It’s foolish to think this undercuts the value of per-minute stats. In a league of hundreds of players, over many years, it’s not hard to find exceptions. The overall picture is clear, and has been well documented and discussed here.

  29. Deepak

    You can’t draw the conclusion that increased minutes leads to increased performance from that PER study. Common sense tells us that, generally speaking, increase in performance leads to increased minutes; not the other way around.

    To really predict whether a player’s stats will improve with more minutes, you should consider how that impacts the quality of the teammates he plays with and the opponents he faces. For instance, if he’s a bench player who generally only plays limited minutes with and against other reserves, increase in minutes will likely lead to a decrease in stats. If he’s a starter who happens to play very few minutes (mostly with and against other starters), than an increase in minutes may improve his stats.

    Another thing to consider is the player’s role on the team. If he’s an energy guy, for instance, he may be better in short spurts.

  30. Mike K. (KnickerBlogger) Post author

    “For instance, if he?s a bench player who generally only plays limited minutes with and against other reserves, increase in minutes will likely lead to a decrease in stats.”

    Yes but none of the studies have found this to be true. You should read the three links in the “extras” section that point to the different studies regarding this.

    “If he?s an energy guy, for instance, he may be better in short spurts.”

    All the players in this study were carbon based life forms. No energy beings were used.

  31. Ted Nelson

    “Common sense tells us that, generally speaking, increase in performance leads to increased minutes; not the other way around.”

    Common sense also tells me that often when a coach you hate sporatically gives you a few minutes on the court you’re more likely to be uncomfortable, jittery, and play poorly than when you’re an established started getting consistent minutes.

    Common sense once told people that the earth was the center of the universe, then we did some research and found out that this was very unlikely to be the case. I don’t think this is nearly as clear cut a case–and don’t know whether productivity increases or decreases with minutes played–but I think it’s worth it to do some research to find out what actually happens rather than guessing based on hypotheticals (“if he?s a bench player who generally only plays limited minutes with and against other reserves, increase in minutes will likely lead to a decrease in stats”).

    So far, I think the research suggests that if nothing else productivity doesn’t decline significantly with minutes played. This also seems to be common sense: a guy who plays 20 mpg and gets 10 reb/40 isn’t likely to get 6 reb if he plays 40 mpg. He might get 9 or 11, 8 or 12, and some factors like improving, aging, teammates, coach might come into play.

    What you do have to do is use some common sense when analyzing per min stats. The fact that Sweetney couldn’t get off the bench in Chicago doesn’t change the fact that he’s been a very efficient player. When he was a Knick I could have told you the odds were stacked against Sweetney ever being a quality starter even when looking at his per minute stats. I saw an undersized, fat, slow guy with lots of basketball skills, but very limited run-jump athleticism.

    I don’t think the point of this article was you can determine everything with per minute stats, just that per minute stats can paint a more accurate picture of a player’s ability than per game stats alone.
    I know the analogies are never dead on, but I’ll try anyway. Let’s say I tell you one guy had 50 hits this season and another had 100 and asked you which one’s a better hitter. You might say the guy with 100 hits.
    If I told you that one guy was 50 for 150 while the other guy went 100 for 600, you’d likely change your answer because you were looking at a more complete picture.

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