You Are Here > Basketball-Reference.com > BBR Blog > NBA and College Basketball Analysis

SITE NEWS: We are moving all of our site and company news into a single blog for Sports-Reference.com. We'll tag all Basketball-Reference content, so you can quickly and easily find the content you want.

Also, our existing Basketball-Reference blog rss feed will be redirected to the new site's feed.

Basketball-Reference.com // Sports Reference

For more from Neil, check out his new work at BasketballProspectus.com.

So Who’s the MIP?

Posted by Justin Kubatko on April 6, 2010

The other day I decided to check out the Most Improved Player (MIP) list on ESPN.com's NBA Awards Watch. Before visiting the page I figured that Kevin Durant would be at the top of the list, as Durant has made a stratospheric leap this season, going from at best an average player to one of the top five players in the NBA. Imagine my surprise when I saw Durant in the second spot on this list, behind Aaron Brooks of the Houston Rockets. In my mind I knew that this had to be wrong, that Durant's improvement was the most improbable performance of the season, but I needed a way to quantify it. The question is: How? Let's go to the data...

I started by determining which players would make up the pool of MIP candidates. I decided to use cutoffs of 70 games played or 1400 minutes played. Why those figures? Because in the last ten years, 104 of the 105 players who finished in the top ten of the MIP voting reached at least one of those minimums (the exception was Von Wafer in 2009). Then, using all players from 1985-86 through 2008-09 who met the criteria, I did the following:

  1. Computed the player's Win Shares per 48 minutes (WS/48).
  2. Using the Simple Projection System (SPS), computed a baseline WS/48 expectation for the player going into the given season. In short, the SPS will produce a projection for the player that takes into account the player's age and recent performance, with some regression to the mean factored in for good measure.
  3. Computed the difference between the player's actual and expected WS/48.

Let me go through an example using Boris Diaw in 2005-06:

  1. Diaw averaged 0.1490 WS/48.
  2. Based on his previous seasons, a reasonable expectation for Diaw would have been an average of 0.0192 WS/48.
  3. Diaw's actual average was 0.1490 - 0.0192 = 0.1298 WS/48 better than expected.

I did this for all 4645 players in the player pool 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 0.04. 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 Boris Diaw example. In 2005-06 Diaw beat his expectation by 0.1298 WS/48. We want to find:

P(X ≥ 0.1298)

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

P(X ≥ 0.1298) = P(X / 0.04 ≥ 0.1298 / 0.04) = P(Z ≥ 3.245)

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

P(Z ≥ 3.245) = 0.0006

In other words, the difference between Diaw's actual performance and his expected performance was highly improbable: only about 6 out of every 10,000 players will beat their expectation by at least 0.1298 WS/48. Now, 2005-06 happens to be the only season where the player with the most improbable performance was also the MIP. Here are the ten most improbable performances of that season:

 Rk Player                      WS/48    Proj    Diff   Prob
  1 Boris Diaw*                0.1490  0.0192  0.1298 0.0006
  2 Gerald Wallace             0.1630  0.0576  0.1054 0.0042
  3 Kevin Martin               0.1375  0.0384  0.0991 0.0066
  4 DeSagana Diop              0.1299  0.0336  0.0963 0.0080
  5 Dwyane Wade                0.2388  0.1536  0.0852 0.0166
  6 Andres Nocioni             0.1437  0.0624  0.0813 0.0211
  7 LeBron James               0.2322  0.1536  0.0786 0.0247
  8 Smush Parker               0.1005  0.0240  0.0765 0.0279
  9 Chris Kaman                0.1139  0.0432  0.0707 0.0386
 10 Elton Brand                0.2294  0.1632  0.0662 0.0490

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

OK, now let's get back to the 2009-10 MIP race. What have been the most improbable performances so far this season?

 Rk Player                      WS/48    Proj    Diff   Prob
  1 Kevin Durant               0.2328  0.1008  0.1320 0.0005
  2 Luke Ridnour               0.1651  0.0720  0.0931 0.0100
  3 Quentin Richardson         0.1278  0.0480  0.0798 0.0230
  4 Jermaine O'Neal            0.1418  0.0624  0.0794 0.0236
  5 Donte Greene               0.0400 -0.0384  0.0784 0.0250
  6 Zach Randolph              0.1594  0.0816  0.0778 0.0259
  7 Russell Westbrook          0.1157  0.0384  0.0773 0.0266
  8 J.J. Redick                0.1699  0.0960  0.0739 0.0323
  9 Josh Smith                 0.1614  0.0912  0.0702 0.0396
 10 Channing Frye              0.1389  0.0720  0.0669 0.0472

While Luke Ridnour's season has been impressive, Durant's improvement is clearly the most improbable of the season. Where is Aaron Brooks?

 Rk Player                      WS/48    Proj    Diff   Prob
106 Aaron Brooks               0.0898  0.0912 -0.0014 0.5140

Believe it or not, Brooks has actually played a bit below his expectation. Now, I know the argument: Brooks has managed to maintain his efficiency while increasing his minutes by about 10 per game. That's true, but that does not mean that Brooks has actually improved. There are two possibilities:

  1. Brooks should have seen a decrease in efficiency given an increase in his minutes, and the fact that he has been able to maintain that efficiency is evidence of improvement.
  2. Brooks has not improved beyond what we would expect from a player his age, and his per game numbers are up simply because of an increase in minutes played.

Quite frankly, there is no way to prove whether (1) or (2) is correct. I tend to believe that the answer is a combination of the two, but more (2) than (1). Regardless, the fact that we can argue this point should make it clear that Durant should be the winner, as we are certain that Durant has shown remarkable improvement.

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, 5th 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.

ShareThis

31 Responses to “So Who’s the MIP?”

  1. sp6r=underrated Says:

    On another website I frequent, a poster pointed out that ppg is by far the most important stat in predicting who will win the award.Brooks has made the biggest leap by far in ppg, and that's why he'll win it.

    Also, my own observation, is that the Most Improved Player doesn't go to players who were figured for stardom like Durant.

  2. Mike G Says:

    I had Brooks at #19 a couple weeks ago.
    http://sonicscentral.com/apbrmetrics/viewtopic.php?t=2407&start=45

    QRich at #3 ?
    I've got him around #100.

    And Ridnour just 3rd on his team, after Ilyasova and Bogut.

  3. Harry Says:

    Gotta agree with sp6r=underrated's observation that MIP awards usually don't go to superstar caliber players. McGrady won it in 2000-2001, but by and large it doesn't go to future superstars. Some top-tier players have won it, like Gilbert Arenas for 02-03 and Kevin Johnson for 88-89, but by and large it's given to lower achieving players.

    Anybody know why?

  4. keelanious Says:

    I think that it is because high profile, superstar caliber/futre supertars are supposed to be good and get better, while players like Boris Diaw/Aaron Brooks are not 'supposed' to put up the numbers that they did

  5. Luke Says:

    I think it's much more likely for people to vote for players who went from "bad" to "good" or "irrelevant" to "relevant," rather than players who went from "good" to "great."

  6. Alvy Says:

    In the Wages of Win journal the author noted, "After 71 games, Aaron Brooks had a 0.038 WP48. I do not think he would rank as one of the 15 best PG in the league ... Brooks is below average with respect to assists, rebounds, and steals."

    More or less, everyone outside the NBA seems to understand Brooks isn't MIP, or even that good.

  7. Mike G Says:

    Justin, where does Jamal Crawford rank among your MIP's?

    Last year, he averaged .064 WS/48, and this year he's at .138 .
    In 2358 minutes, he's gotten 3.7 WS more than he'd have with last year's WS/min.
    Among your top 10, only Durant and Westbrook have bigger increases.

  8. Mike G Says:

    Also, why is Durant's "Projected WS/48" only .1008, when last year he was .131 ?

  9. Justin Kubatko Says:

    Mike G wrote:

    Justin, where does Jamal Crawford rank among your MIP's?

    He ranks 13th:

     Rk Player                      WS/48    Proj    Diff   Prob
     13 Jamal Crawford             0.1361  0.0720  0.0641 0.0545
    

    Also, why is Durant's "Projected WS/48" only .1008, when last year he was .131?

    Because the projection uses a weighted average of Durant's first two seasons, and he was terrible in his rookie year.

  10. Mike G Says:

    OK, so if Durant's WS/48 in his first 2 years are .040 and .131, shouldn't we project his 3rd year to be higher again, rather than lower?

  11. Justin Kubatko Says:

    Mike G wrote:

    OK, so if Durant's WS/48 in his first 2 years are .040 and .131, shouldn't we project his 3rd year to be higher again, rather than lower?

    Why should we assume that? I looked at all third year players from 1979-80 through 2008-09 who played at least 1000 minutes in each of their first three seasons. Overall, 293 of these players saw their WS/48 improve from their first year to their second year. Of these 293 players, 153 improved in their third season and 140 declined.

    If we restrict our attention to players who made big improvements from their first year to their second year (let's say a change of at least +0.04 WS/48), we find 115 players. Of these 115 players, 54 improved in their third season and 61 declined.

  12. Mike G Says:

    That's very enlightening; thanks.

    Disregarding that in Durant's case, many expected him to improve; I'm still surprised that your projection has him regressing 30% from last year (in WS/min).

  13. Jordan Says:

    Is there a list of the players that you did this for? I wanted to see how George Hill did.

  14. Igor Says:

    Curious about years other than 2005-06. What rank in improbability were the actual MIP winners for a few recent years?

    Nice analysis.

  15. Air France Says:

    I would like to see the bottom of the list.

  16. Thezzaruz Says:

    Have to agree that the full list would be interesting to see, I would have figured M Gasol to be pretty high on the list tbh.

    Great (and interesting) work I have to say.

  17. Gabe Says:

    A few things I wanted to mention...

    1) Why use difference in WS, rather than ratio? If you look at the ratio, Durant will more than double his expected WS/48, but so will Ridnour. Q-Rich is about triple what would be expected, and Russell Westbrook is about 4x.

    2) What about pace? It's probably hard to account for it, but I would think pace adjustment may have an effect in some of this, especially since some of the numbers in the Difference column are so close together.

    3) Fundamentally, I'm not sure your numbers are looking at things the way they are intended. About Aaron Brooks, you write "Brooks has not improved beyond what we would expect from a player his age". While this may be true, looking at who is Most Improved wouldn't take into account what they *should* be doing, just what they *are* doing, in my opinion. In other words, it shouldn't matter what we would expect to happen based on last year, just what does happen. So, rather than comparing their project vs actual WS/48 from this year, how about comparing their actual 2009 WS/48 to their actual 2010 WS/48?

  18. Justin Kubatko Says:

    Gabe wrote:

    Why use difference in WS, rather than ratio?

    Why not? The ratio approach is not perfect. For example, is an improvement from 0.010 WS/48 to 0.020 WS/48 more impressive than an improvement from 0.100 WS/48 to 0.150 WS/48? By the ratio approach it is, but I certainly wouldn't agree with that. You would also have a problem with players with WS/48 figures that are less than or equal to zero.

    What about pace?

    The Win Shares system already accounts for pace (details can be found here and here).

    [I]t shouldn't matter what we would expect to happen based on last year, just what does happen. So, rather than comparing their project vs actual WS/48 from this year, how about comparing their actual 2009 WS/48 to their actual 2010 WS/48?

    I can think of a couple of reasons. First, when we're talking about the MIP, we should be talking about a player who has shown significant improvement. In my opinion, a player who has improved by an amount that would be typical for most players his age should not be considered for the MIP award. Second, if we just compare players to their previous season then we are going to pick up many more cases where a player did not actually improve (e.g., a veteran who had a down year the previous season and then bounced back the following season).

  19. Justin Kubatko Says:

    Mike G wrote:

    Disregarding that in Durant's case, many expected him to improve; I'm still surprised that your projection has him regressing 30% from last year (in WS/min).

    First, it's not a 30% drop, it's a 23% drop:

    (0.101 - 0.131) / 0.131 = -0.23

    Second, it's not all that unusual for a player who made such a tremendous improvement from his first year to his second year to then regress by a fair amount in his third year. I'm sorry, but I don't have time to run the numbers, so you'll have to trust me on this one.

  20. Joe Schaller Says:

    I have suggested for many years that the mainstream voters are totally clueless about Most Improved and to a lesser extent Sixth Man award. Primary reason is increased playing time translating to increased "per game" stats- productivity per minute should be the indicator.
    Zach Randolph did not improve at all on a per minute scale the year he won and it appears Aaron Brooks may be in the same boat.
    Sophs should not be allowed in the vote since improvement is naturally common and expected. Veteran stars should often be in the running yet are hardly considered.
    Durant should easily be Most Improved followed by Ridnour.

  21. Justin Kubatko Says:

    Jordan wrote:

    I wanted to see how George Hill did.

    I'll throw in Marc Gasol for Thezzaruz as well:

     Rk Player                      WS/48    Proj    Diff   Prob
     17 George Hill                0.1417  0.0816  0.0601 0.0665
     23 Marc Gasol                 0.1672  0.1200  0.0472 0.1190
    

    Air France wrote:

    I would like to see the bottom of the list.

    The bottom ten:

     Rk Player                      WS/48    Proj    Diff   Prob
    186 J.R. Smith                 0.0599  0.1200 -0.0601 0.9335
    187 Monta Ellis                0.0248  0.0864 -0.0616 0.9382
    188 Jason Maxiell              0.0792  0.1440 -0.0648 0.9474
    189 Chris Paul                 0.2037  0.2688 -0.0651 0.9482
    190 Ben Gordon                 0.0432  0.1104 -0.0672 0.9535
    191 Richard Hamilton           0.0440  0.1200 -0.0760 0.9713
    192 Devin Harris               0.0597  0.1392 -0.0795 0.9766
    193 Ramon Sessions             0.0292  0.1152 -0.0860 0.9842
    194 Trevor Ariza               0.0494  0.1392 -0.0898 0.9876
    195 Rafer Alston              -0.0135  0.1008 -0.1143 0.9979
    
  22. Gabe Says:

    Justin - thanks for the responses. Regarding the ratio, your point is well taken. Regarding pace, I didn't know that, so thank you. For the third item, I had a couple of things I wanted to mention, in response.

    "when we're talking about the MIP, we should be talking about a player who has shown significant improvement. In my opinion, a player who has improved by an amount that would be typical for most players his age should not be considered for the MIP award."
    Given that age/performance curves aren't perfectly known, I think it's tough to really gauge what is typical, especially when you lump all the positions together. I guess we just can agree to disagree here.

    "Second, if we just compare players to their previous season then we are going to pick up many more cases where a player did not actually improve (e.g., a veteran who had a down year the previous season and then bounced back the following season)."
    You mean sort of like Quentin Richardson (0.104 WS/48 in 2007) or Jermaine O'Neal (0.177 WS/48 in 2003, 0.155 in 2004), both of whom are on your Top 10 list? Besides, doesn't SPS take into account the previous years' values?

  23. Justin Kubatko Says:

    Gabe wrote:

    Given that age/performance curves aren't perfectly known, I think it's tough to really gauge what is typical, especially when you lump all the positions together.

    The SPS age adjustment is very conservative, so I don't feel like it would bias the results.

    You mean sort of like Quentin Richardson (0.104 WS/48 in 2007) or Jermaine O'Neal (0.177 WS/48 in 2003, 0.155 in 2004), both of whom are on your Top 10 list?

    First, I said by using just one season we would "pick up many more cases where a player did not actually improve." Notice that I did not say that my approach eliminates these cases; I just think it produces fewer of them.

    Second, no, not like Quentin Richardson or Jermaine O'Neal. Take Richardson, for example. Look at what he did from 2003-2009:

    +-------+------+------+-------+
    | MP    | ORtg | DRtg | WS/48 |
    +-------+------+------+-------+
    | 13343 |  103 |  110 | 0.057 | 
    +-------+------+------+-------+
    

    His WS/48 was less than the league average in six of those seven seasons, and overall his WS/48 was 43% below the league average. Compare that to what he has done this year:

    +------+------+------+-------+
    | MP   | ORtg | DRtg | WS/48 |
    +------+------+------+-------+
    | 1980 |  113 |  104 | 0.131 | 
    +------+------+------+-------+
    

    He's producing wins at a rate 31% above the league average. Is this a fluke or real improvement? We can't say for sure, but this is clearly not an example of a player who had one down season and then bounced back to his career norms.

    Besides, doesn't SPS take into account the previous years' values?

    You can read all about it here.

  24. Gabe Says:

    My point with Q-Rich was that he's put up WS/48 numbers similar to this before.

    And I did go there to read about SPS, that's where I got the idea from.

  25. Justin Kubatko Says:

    Gabe wrote:

    My point with Q-Rich was that he's put up WS/48 numbers similar to this before.

    Check out his player page: he's only had one season close to this one, and that came eight years ago with the Clippers. Once again, this is not an example of a player who is bouncing back to previous career norms. Coming into this season, Richardson's career WS/48 rate was 0.070, but he's almost doubling that this season. The vision you have of Richardson might not match what the numbers say, but statistically he's been a below average performer for a majority of his career.

  26. Gabe Says:

    Fair enough.

  27. AYC Says:

    In absolute terms, Brooks has seen a huge improvement in his stats, of course; but even on a per-min basis his unadulterated stats have improved:

    16.1 ppg, 4.3 apg, .404 fg%, .366 3pt-fg% per 36 min in 2009
    19.9 ppg, 5.4 apg, .432 fg%, .397 3pt-fg% per 36 min in 2010

    The rise in scoring,assists, fg% and 3pt% are all significant; the only notable regression I see over the past year is in TO's ( from 2.3/36m to 2.9/36m)

  28. Mike G Says:

    "16.1 ppg, 4.3 apg, .404 fg%, .366 3pt-fg% per 36 min in 2009
    19.9 ppg, 5.4 apg, .432 fg%, .397 3pt-fg% per 36 min in 2010"

    What in all of this is a per 36 min rate?

  29. OBH Says:

    I know this probably looks like a typical douchie comment, but just wanna say I think it's wicked that you give reasonable responses to comments, and obviously give a bit of thought to them. Really respect that, a lot of bloggers either ignore the comments or reply with lame atttempts to make the commenter look like a fool.

  30. Justin Kubatko Says:

    @29: Thanks, much appreciated.

  31. Context Says:

    WinShares has a lot of team defense in it. The team defense for the Thunder really improved and Durant was a big part of that improvement. The team defense for the Rockets went way down without Yao. Adjust for that to some degree and Brooks would look better on WS this season.