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So Who’s the MIP? (Episode II)

Posted by Justin Kubatko on April 1, 2011

About this time last year, I developed a method for identifying the leading candidates for the Most Improved Player (MIP) award. Since we are nearing the end of the 2010-11 season, I thought it might be interesting to revisit this topic. I made some minor tweaks to last year's method, so let me outline the process once again before reporting this season's results.

The first step, of course, is to select the players to include in the study. The player pool consisted of all players from 1980-81 through 2009-10 who met the following criteria:

  • Played at least 1000 minutes in the given season (610 for the lockout-shortened 1998-99 season).
  • Played at least 1000 minutes (cumulatively) in the three previous seasons.

That gave me a sample of 5905 player seasons, and for each of those seasons I did the following:

  1. Computed the player's Win Shares per 48 minutes (WS/48) in the given season.
  2. Computed a baseline value of WS/48 for the player going into the given season. The baseline vaue is a weighted average of the player's last three seasons, with last season receiving a weight of six, two seasons ago receiving a weight of three, and three seasons ago receving a weight of one. (Seasons in which the player has missing data are zeroed out.)
  3. Computed the difference between the player's actual and baseline WS/48.

Let me go through an example using Kevin Durant in 2009-10:

  1. Durant averaged 0.2384 WS/48 in 2009-10.
  2. The previous season, his second in the NBA, Durant finished with 7.9 Win Shares in 2885 minutes. In in his rookie season, Durant had 2.3 Win Shares in 2768 minutes. Thus, Durant's baseline value was 48 * (6 * 7.9 + 3 * 2.3) / (6 * 2885 + 3 * 2768) = 0.1018.
  3. Durant's actual average was 0.2384 - 0.1018 = 0.1366 WS/48 above his baseline.

I did this for all 5905 player seasons in the time period and examined the distribution of the differences. Here is a histogram of the results:

As you can see, the data are approximately Normal with mean 0 and standard deviation 0.037. We can then use this information to answer the following question: "What is the probability than a randomly selected player will beat his expectation by at least x WS/48?"

Let's return to the Durant example. In 2009-10, Durant beat his expectation by 0.1366 WS/48. We want to find:

P(X ≥ 0.1366)

where X is the difference between the player's actual and baseline WS/48. Since the data are approximately Normal, this calculation is straightforward:

P(X ≥ 0.1366) = P(X / 0.037 ≥ 0.1366 / 0.037) = P(Z ≥ 3.692)

Now, Z is a standard Normal random variable, so:

P(Z ≥ 3.692) = 0.0001

In other words, the difference between Durant's actual performance and his baseline performance was highly improbable: only about 1 out of every 10,000 players will beat their baseline by at least 0.1366 WS/48.

Here are the ten most improbable performances of the 2009-10 season, plus the MIP winner:

 Rk Player                      WS/48    Base    Diff   Prob
  1 Kevin Durant               0.2384  0.1018  0.1366 0.0001
  2 Luke Ridnour               0.1679  0.0683  0.0996 0.0036
  3 Quentin Richardson         0.1328  0.0448  0.0880 0.0087
  4 Jermaine O'Neal            0.1345  0.0595  0.0750 0.0213
  5 Jamal Crawford             0.1425  0.0689  0.0736 0.0233
  6 Zach Randolph              0.1526  0.0797  0.0729 0.0244
  7 J.J. Redick                0.1728  0.0999  0.0729 0.0244
  8 Beno Udrih                 0.1069  0.0361  0.0708 0.0278
  9 Russell Westbrook          0.1047  0.0348  0.0699 0.0294
 10 Channing Frye              0.1411  0.0717  0.0694 0.0303
105 Aaron Brooks*              0.0909  0.0897  0.0012 0.4871

 WS/48 = Actual WS/48
 Base  = Baseline WS/48
 Diff  = Actual WS/48 - Projected WS/48
 Prob  = Probability
 *     = MIP Award Winner

My opinion last year — an opinion I stil hold — was that Durant should have been the runaway winner of the award, but in reality he finished a distant second to Aaron Brooks.

OK, now let's take a look at the 2010-11 MIP race. Which players have shown the most improvement so far this season?

 Rk Player                      WS/48    Base    Diff   Prob
  1 Derrick Rose               0.2022  0.0925  0.1097 0.0015
  2 Tyson Chandler             0.2153  0.1283  0.0870 0.0094
  3 Elton Brand                0.1548  0.0688  0.0860 0.0101
  4 Kevin Love                 0.2148  0.1328  0.0820 0.0133
  5 Ryan Anderson              0.2078  0.1315  0.0763 0.0196
  6 Russell Westbrook          0.1576  0.0822  0.0754 0.0208
  7 Darrell Arthur             0.1205  0.0454  0.0751 0.0212
  8 DeShawn Stevenson          0.0720 -0.0006  0.0726 0.0249
  9 Thaddeus Young             0.1396  0.0729  0.0667 0.0357
 10 Jrue Holiday               0.0968  0.0325  0.0643 0.0411

Derrick Rose is at the center of every MVP discussion, but I have yet to see him mentioned as the leading candidate for the MIP award. This represents, in my opinion, a fatal flaw with the award. That is, players who are expected to become stars (e.g., Durant and Rose) are almost always passed over in favor of players whose performance "surprised" the voters. But the award is supposed to go to the most improved player, not the most surprising player, so voter expectations for the players should not be a factor.

Before I go, let me make it perfectly clear that I am not suggesting that the NBA actually use a formula to determine the MIP. I can think of quite a few reasons why a player who is, say, fifth using this method should be voted the MIP. However, I do think this is a good way to whittle down the list of candidates, and to separate players who have obviously improved from players whose improvement is questionable.

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29 Responses to “So Who’s the MIP? (Episode II)”

  1. AHL Says:

    It's not most surprising player that's the problem. It's that voters see the award as most increased scoring points in one season award. If you replaced WS/48 with PTS/g (yes, per game, I know), you'd probably get results that correlated stronger with what the voters were thinking.

  2. Matt Says:

    Guess we know why Philly overachieved

  3. Jason J Says:

    I'd like to see voter expectations for players and teams removed from the MVP voting as well. Just because we were all wrong about a team early on doesn't mean that we have to credit our collective mistake to one individual on the surprise team - unless there are other compelling reasons to believe he is in fact the reason for the team's success.

  4. Filippos Says:

    Good job! I like Chandler and Brand's name on that list. For some reason people think MIP should be a young/uprising player. That said, Rose is definitely this years MIP...

  5. Matt Johnson Says:

    This is excellent. MIP is an incredibly frustrating award because of the insistence on giving it to a play who isn't "too" good. I for one have had Rose at the top of my MIP list for a good long while (followed by Westbrook and Love).

    btw, I'm happy to see the Chandler's and the Brand's included in the calculation but I would be unlikely to include them in my MIP shortlist. imho, MIP is supposed to represent a player actually improving to a level he's never been before not simply being put in a better role or coming back from injury.

  6. Mike Goodman Says:

    "I have yet to see him mentioned as the leading candidate for the MIP award"
    It was right over
    here, as early as December -
    http://sonicscentral.com/apbrmetrics/viewtopic.php?t=2667&start=17

  7. Justin Kubatko Says:

    Matt Johnson wrote:

    btw, I'm happy to see the Chandler's and the Brand's included in the calculation but I would be unlikely to include them in my MIP shortlist. imho, MIP is supposed to represent a player actually improving to a level he's never been before not simply being put in a better role or coming back from injury.

    That's true in Brand's case, but not Chandler. This is easily Chandler's best season.

  8. Matt Johnson Says:

    @Justin

    Well first, let's also consider that WS/48 ignores the fact that Chandler's playing a lot less than he used to. His volume stats are certainly not at their peak. That right there is something that needs to be factored in, and it's hard for me to imagine an argument that he's improved in impact as much as Love or Westbrook just on that.

    Beyond that though, I just really question the notion of massive improvement in a 10th year player. Can he be put in a different role that makes him much more valuable a la Nash? Absolutely. To me though that's not ideally what the stat is about. To me it's about a player truly emerging as a far more capable general participant in the sport.

    I do recognize though that quantitatively, any notion that we can distinguish between what comes from actual new capabilities and what comes from role is pretty much hopeless. I would certainly not fault your metric for combining the two, and if you have a different philosophy than I do I can respect that.

  9. Joseph Says:

    Am I mistaken in thinking that your top candidate for this season is Jrue Holiday?

  10. ElGee Says:

    Justin, this is great. Even if one isn't married to win shares/classic box score values, this is such a nice exercise compared to the usual approach for MIP that #5 alluded to. I think Rose is clearly MIP, and I think of someone like Westbrook is also in the discussion. For some bizarre reason, the award has come to celebrate a shift from mediocrity (or worse) to decently good, despite real impact coming from improvement to all-star level players or better.

  11. Greyberger Says:

    Re:8, This is the fourth-most minutes Tyson Chandler has played in a season once you pro-rate it. His minutes per game are down (in part because he's on a good team with, I assume, more resting-the-starters fourth quarters than his previous teams) but he's been healthier to make up for it.

    It's definitely been his best year. I mean, good lord, he's got a .691 TS and a career low turnover rate. You can say that's thanks to his new role and teammates in Dallas, but he's been a big upgrade over any center the team's had in ages.

    But mainly, 69% TS. 64% FG%. Almost half as many turnovers per possession as last year, 25% less than his career average... quite the improvement.

  12. Matt Johnson Says:

    @Greyberger

    I'm not saying this isn't Chandler's best year, but I have a real tough time with the notion that MPG isn't a factor to be considered here. Obviously not playing big minutes doesn't necessarily mean you can't, but when a player is playing well enough to get into the all-star conversation while playing <30 MPG and 7 MPG less than his peak, it really begs the question of why wouldn't the coach be playing him as much as his other starters if he could have the same impact per minute in 7 more minutes.

  13. Greyberger Says:

    Re:12 "when a player is playing well enough to get into the all-star conversation while playing <30 MPG and 7 MPG less than his peak, it really begs the question of why wouldn't the coach be playing him as much as his other starters if he could have the same impact per minute in 7 more minutes."

    Can't say for sure but he has a history of missing games. Some players never play 82 in a season. Kidd and Nowitzki can do 80 or 82 games no problem, Chandler always ends up missing a few.

    Fewer minutes might be a way to manage that.

  14. Greyberger Says:

    Either that or they feel dumb paying Brendan Haywood all that money to sulk on the bench.

  15. Rashidi Says:

    It's Chandler's best year, but it's not markedly better than the year he had with Chris Paul before he got hit with injuries. He hasn't IMPROVED, he's just returned to health.

    I would be totally in favor of giving it to the Durants and Roses of the world. Better than giving it to the Don MacLean's and Alan Henderson's.

  16. Rashidi Says:

    Honestly though, there are quite a few big names among MIP winners, so I'm not going to argue with that.

    Boris Diaw and Bobby Simmons are the non-stars from the last decade (aside from Brooks), but they came from literally nowhere to have great seasons. They were 12th men on their previous teams and gave solid starter production for a full season with their new teams so I'm not going to complain much about that. Simmons' career was immediately wrecked by injury while Diaw's was wrecked by Amare Stoudemire's return from injury. In Diaw's case he was clearly the product of a system that produces big numbers, and voters should have taken that into account, but we didn't exactly anticpate him regressing the way he has the last few years either.

    Guys like MacLean and Henderson are easily bad picks but they are the exception and not the norm (We can probably throw Brooks into this group down the line). Danny Granger was a great pick as he became an all-star. Without checking his competitors, Hedo Turkoglu was probably a solid choice given his sudden importance to a new and improved Magic team. Monta and Arenas went from backups to big time scorers.

    I would have given Durant the MIP too, but it would also be nice to see some year by year data, as 2010 could easily have been a voter fluke.

  17. Mike Goodman Says:

    "But the award is supposed to go to the most improved player, not the most surprising player, "
    Eh, what's the difference between "most surprising" and "most improbable" ?

    Also,
    Matt and others are right that unless player (per minute) 'improvements' are weighed by player minutes, they're not so comparable.

  18. Sean Says:

    CLEARLY, it's Brian Scalabrine.

    Why? Because, to my knowledge, he hasn't forgotten to put his uniform top on underneath his warmups this year.

    Laugh all you want-----but my wife took us to a Nets game for Valentine's Day years ago and we were 5 rows back from the baseline. Byron Scott needed to give someone a blow for a few minutes and he pointed to Scalabrine. Brian got up, started to remove his warmup and........Ooooooooops!!!!----------he wasn't wearing a jersey!

    I kid you not. Scott was INFURIATED. Scalabrine ran top the lockeroom and Scott put somebody else in.

    It was like the Happy Days episode where Ralph Mauff (sp?) has his street clothes on under his warm ups-------the coach tried to put him in and Ralph was like 'I never play!'

    If Scalabrine fully dresses himself now-------he's made the most strides, IMO.

  19. Sean Says:

    If NOT Scalabrine, then I think Kevin Love jumps out at me.

  20. Larry Says:

    hey neil what about JJ Barea from the mavs, i saw him play last year but this season he has phenomenal often helping Dallas win close games. he has been just amazing, better than jason kidd this year oohh and playing just 20 minutes a game.

  21. Matt Johnson Says:

    @13 "Can't say for sure but he has a history of missing games. Some players never play 82 in a season. Kidd and Nowitzki can do 80 or 82 games no problem, Chandler always ends up missing a few.

    Fewer minutes might be a way to manage that."

    The need to conserve the player to maintain his high level of play is relevant to consider how valuable the player is, no?

  22. Phil Says:

    Your data, ie win shares, definitely is non-stationary and auto-correlated. If you wanted to find the most surprising player, wouldn't it make more sense to compare the error terms of an AR model's projection versus the actual to see what player actually had the most surprising improvement given his ascent/descent in recent years?

  23. Greyberger Says:

    Re:21, that was a response to the 'begs the question why Chandler doesn't get more minutes' part - He's assigned fewer minutes in the hopes of playing more games.

    In those minutes he's been very valuable - and if his minutes are managed to avoid injuries it stands to reason that his minutes are coming at more critical moments than bench players.

  24. lorrance Says:

    With a 6 point 4 rebound improvement and Improvement in all his shooting percentages, Kevin Love should win this award hands down. I think the MIP is usually for someone who either goes from being a mediocre or hardly contributing player to being someone who is producing on an all star level. An all star who becomes a superstar in his third or 4th season shouldn't get that award unless his improvement is so vast it far outweighs someone else. Kevin Love is the first 20 and 15 guy since moses malone if i'm not mistaken.

  25. khandor Says:

    Derrick Rose, Kyle Lowry, LaMarcus Aldridge, Dorell Wright and George Hill have each improved their play a considerable amount this season.

  26. Matt Johnson Says:

    @23. Just saying it's a negative factor to consider when looking at how truly useful the player is. If two players scored equally by the above metric, but one player had a massive minutes edge, obviously that player gets the nod, no? So then it's just a question of how much you should weight it, and there is just fierce competition this year with that kind of MPG edge.

  27. Basketball Brawl Says:

    Justin,

    Is there a negative correlation between WS/48 and either minutes per game or USG%? Obviously no matter how negative the correlation, Aaron Brooks probably should not have won last year, but the idea is this:

    If there is a negative correlation, then besides just weighting last 3 seasons' WS/48, we would also have to adjust by changes in minutes per game or USG% to come up with a "decreasing marginal productivity"-adjusted expected WS/48.

    Voters do have some ground to vote for players with much higher minutes, if they outperformed the expected loss of productivity from those higher minutes.

  28. Darren Says:

    This is incredible! All that math we learned in high school and college is finally coming in use. How much time did it take you to develop this formula, enter all the data, and come up with your results?

    I agree that the formula you used here to determine the MIP is interesting, but like you said, a formula may not be (and probably isn't) the best way of determining who should receive the honor of the most improved player.

  29. Yariv Says:

    Basketball Brawl, even if an increase in USG% leads to decrease in WS/48, I would not expect to see a negative correlation between the stats. The reason being, teams will try to adjust USG% so that marginal WS/48 will be equal among players, and this will probably mean higher avarage WS/48 for higher USG% players (this is pretty much hand waving, but this is what you'll see if the drop behaves similarily for different players, generally speaking). So in this case you'll see a general positive correlation.

    You might suggest looking for correlation for a player on different seasons, but this will be extremely noisy, with level of player changing, partners and positions changing, etc. And then, of course, is the problem of cause and effect (although in the case of negative correlation, it should be the obvious direction).