# Choosing the MVP, geometrically

To begin, here are is my pick/prediction for the 2008 NBA MVP award: Chris Paul of the New Orleans Hornets. Second most valuable is Kobe Bryant, followed by LeBron James and Paul Pierce. How did I decide this? Read on…

I have discussed the concept of Winshares previously in this space, and I believe that this measure is the most parsimonious and theoretically satisfying way to estimate player value. If you are unfamiliar with the construction, here is the formula:

• valuable contributions = pts + as*2 + tr + st + bk – to
• winshares = (valuable contributions / team valuable contributions) * team wins

The very simple motivating theory is that each player is responsible for some fraction of his team’s success (and here I define success as winning, plain and simple–value is a separate concept from quality or talent, and value in athletics is commonly gauged by game outcomes and the contribution of individuals thereto). The better the player doing the contributing, the more successful the team, and so contributions should be weighted by team success to reward those players whose efforts result in winning.

Picture a team with one player who contributes substantially more than his teammates (say, Minnesota with Al Jefferson, or Cleveland with LeBron James). It stands to reason that win or lose, that player deserves a large share of the credit for that team’s outcomes. Now picture a team for which valuable contributions are more evenly made (say, Chicago, Sacramento, or Boston). It similarly stands to reason that credit for the success of those teams ought to be more evenly attributed to the several players who contribute.

This means that a great player doing all the work for an otherwise very poor team should be worth about the same amount, in terms of wins, as a great player doing a smaller part of the work for an otherwise very good team. This makes sense, both are great players, so both should be able to generate similar levels of success. LeBron James should be approximately as valuable as Kevin Garnett, since although the quality of their teammates is different, so is the amount they are required to contribute to their teams’ success.

So this is how I arrived at my formulation of player value: essentially add up all the good things a player has done for his team, and divide that by the total number of good things his team did. Multiply this percentage by the number of team wins, and there you have it–a per-player number of Winshares.

Now, there are several downsides to this operationalization. It takes no account of intangibles, or anything besides basic boxscore statistics. Kevin Garnett’s incredible intensity defensive leadership doesn’t count in this formulation (except as they are expressed in the boxscore–no doubt they contributed to team wins), so Paul Pierce comes through as slightly more valuable. Keep in mind, however, that this (Pierce for MVP) is what Garnett himself has told us all year long, and also keep in mind that this is not a per-minute or per-possession measure. Garnett played 2329 minutes to Pierce’s 2873, a substantial difference. Garnett had less time to add wins, even though he may have been more valuable per-minute than Pierce. However, for the MVP award, the focus ought to be on total value over the season, not player quality or efficiency. I am as big a Garnett fan as anyone, but no one would argue that injured Gilbert Arenas has been more valuable to the Wizards this year than Jamison or Butler, even if he is more valuable in some per-minute sense (though this is questionable).

The other problem with Winshares is that it does not take into account the specific possessions, minutes or games in which the valuable contributions came. I’m working on this, but in the meantime, you’ll want to use something like plus/minus figures if this is what you’re looking for. This disadvantage is most marked in attempting to measure the value of players traded during the season, but let’s face it–it is unlikely that an MVP-level player will be traded in the midst of an MVP-type season, and it’s even more unlikely that a player who was traded in the midst of the season would be in the running for MVP.

Any questions or critiques on this methodology are welcome, please feel free to leave a comment, but I submit that as far as elegance, parsimony, accessibility, and theoretical validity, Winshares as measured here are an optimal conceptualization of value.

After all that, here is the payoff: I’ve constructed a visualization depicting each player’s value in Winshares: their percent of valuable contributions is depicted on the vertical axis, and team success along the horizontal. Multiplying these two figures together results in Winshares, and each player is listed with their Winshare value and represented as a rectangle, the area of which is exactly proportional to his value. (Color is derived from my favorite way to capture playing type–the RGB scorer/perimeter/interior quasi-trichotomy.)

In a new twist, I’ve got it set up in a Google-Maps-style interface, so you can get as big a picture or as much detail as you’d like. Enjoy! (You’ll probably want to zoom in when the page first loads…)

If that’s not the coolest, most straightforward way to envision basketball value, I don’t know what is!

### 26 responses to “Choosing the MVP, geometrically”

1. very very cool, I’d like to see a lot more creative graphs like this

2. Logic

Trying to get at “individual statistics” is like trying to turn matter into discrete particles. In the end, the individual statistics are more like waves, or strings.

3. Logic

Another interesting observation is how the map reflects perception in the case of Paul vs Bryant: Pauls overall contribution to the team is higher than Bryant’s, but the second, third, and fourth ranked contributing players for Paul have bigger “chunks”, while there are more players following Bryant in smaller “chunks”.

Would be really interesting to see what patterns were held for previous years’ MVP candidates.

Nice work, by the way.

4. J.

just wondering why winshares don’t reflect turnovers.

J: Thanks for reminding me. The formula actually includes turnovers, I just forgot to include that in my post. I’ve corrected my mistake. Also, I’d wonder what everyone’s thoughts are on the measure itself? It’s not per-game or per-minute, and it ties directly to team success, which I think is a useful thing for a value metric to do… how does this compare with PER and Wins Produced/Win Score, etc? Any thoughts are appreciated.

Logic: I’ll eventually put up a series of graphs like this for every year going back at least to 79-80, and maybe further…

6. Joe

one thing to note is that gasols contribution is super low on both teams, he may not have been MVP candidate but how much did the graphs for the lakers change between with gasol and without gasol?

it is intersting to see each teams makeup. The pistons are all pretty even in the top 4 and seem to have a pretty linear decrease. But the spurs have 3 big contributors and then a sharp dropoff to smaller contributors

Joe: Winshares are designed to be additive across teams, so Gasol was worth a total of about 5.0 wins, which ranks him fairly highly, especially given that he played only 66 games total.

8. JJ

This is beautiful… along with your scatterplot of all players, set against the black background.

What software did you use to create this? It sure doesn’t look like Excel.

Extremely good work.

9. JJ

Doh, I wasn’t paying attention… you used Google Maps.

JJ: Thanks for the compliments… check back Monday for a real killer graph I’m working on now.

Actually, I didn’t use Google Maps at all. There’s a service called GmapsUploader which I’m using to present the graphics in a scalable, pannable way, but the software I use for everything you see on this blog is called R. It’s free and relatively easy to use. I would recommend it to everyone.

11. Nick

Assists * 2 is a dramatic overweight to me. I’d use a weight 1/4th to 1/8th that amount.

12. steev

I would multiply assists by 1.5 instead of 2, because passing to someone to score a basket is not the same as actually scoring it. But multiplying assists by 1.5 does take into account the passer and scorer working together.
I would also like to see the 05-06 MVP chart to see how Kobe and LeBron compared to Nash that year, because I’m pretty sure it will end up like this: 1 Kobe, 2 Lebron, 3 Nash, and 4 Wade.

13. What about defense?

14. JR

Just an observation:
Horford is by far above Durant, (+50%)
Does it mean something?

15. garethlewin

Cool work, but I do have one comment, I realise this will border on starting a big argument, but I would like to bring it up.

Winshare doesn’t take shot attempts into account, missed shots end up as rebounds for your team (which is already reflected in winshare) or a turnover (rebound for the opposing team).

A player that shoots a lot but misses a lot is basically turning the ball over, but a metric like winshare will basically encourage him to keep shooting, because a player that goes 3-14 contributes just as much as a player that goes 3-4.

That said, really nice work! Visualizing statistics is something I am very passionate about, and you did a great job!

Str8hoops: Defense is included in the form of steals and blocks.

JR: It does mean something that Horford > Durant. It also means something that Luis Scola > both. I say Scola for Rookie of the Year.

garethlewin (and everybody else with weighting suggestions): I agree that the formula might need some tweaking–I’m working on it as we speak, and I think we need to make it part of the national conversation, so to speak. One problem with taking away from the 2x assist multiplier is that without some sort of assist multiplier, point guards tend to fall of hugely. I know this is subjectivity invading my analysis, but I’m not comfortable with just one PG in the top 20 all-time.

Also, I’m glad you like the work. Visualizing statistics is what we do around here.

The author here– I’m wondering if there would be any interest for either a desktop-wallpaper sized version of this for people to put on their computers, or if there would be any interest in producing this as a print you could purchase for your actual wall? Let me know in the comments, here…

18. kenc

I think to get a better perspective of winshares, maybe include FGmade and FGmissed, FTmade FT missed. I like the smallworld scoring system a while back. -.5 missed FG, -1 missed FT, +1 points, +1.5 rebs, +2 assists, +2.5 steals, +2.5 blcks, -1 TO. I’m wondering if you decide to make these adjustments the results would be different.

19. Joe

Turnovers should be weighted more strongly. I don’t have stats to support this, but I suspect that teams score more than 50% of the time off a turnover.

20. Nick

I’d compare PGs only to PGs.
Wings to wings, bigs to bigs.

21. Nick

I understand in your winshare system everyone is together. The large size of the assist boost is hard to justify on immediate value (quality of unassisted shooting vs assisted) but
running the team does have value beyond the surface. If it is to be a simple linear weight system your assist weight may be a decent subjective choice. PER uses a very modest weight supported by regression but maybe it isn’t “fair” to PGs.

But as said above missed shots affects value of contribution and should be included in my mind.

Shot defense and other +/- impact beyond that directly attributable to individuals are also a part of value not usually included in an individual stat linear weight system. In Rosenbaum’s overall +/- it gets tacked on via the pure +/- weight.
system. You can do something like that too if you want to try to capture those elements.

22. EmmaWK

I’d be interested in a wallpaper (virtual – easier to change every year) — I really like the colors.

And the stats, too.

23. BobR

as*2, if being used to account for total points responsible for, is incorrect since some assists are for three pointers and others are for two. To diminish the value of setting up three pointers is a flaw in the calculations. To be precise, you would have to know how many assists, on average, result in threes made and how many result in twos made. Oh, and how about assists blown, e.g., a perfect lead pass to someone going in for an uncontested layup who then misses? Does that nothing because no points were scored or does it count more because your teammate is useless?

The idea of some responders that it should be as*1.5 is also flawed as it is an artificial multiplier. you might as well pick as*1/4 or *1/3 or *10.

24. Justin

One thing I’d be cautious about with Winshares is based on something Hollinger pointed out: a team’s future success is better predicted by cumulative point differential than their win-loss record. So… if Winshares doesn’t differentiate between BIG wins and little ones (as well as between BIG losses and little ones), you might end up giving undue credit to a guy whose team pulled out a disproportionate number of lucky wins in a given regular season. Maybe there’s some way of including point differential in there that’d improve the measure’s validity?

(Winshares is still new to me, so forgive me if I’ve noobed all over it just now.)

25. Justin

Another thought on adding in missed shots as a negative factor – coaches seem to hate missed 3-pointers because they are more likely to lead to fast breaks. If this was true, it would bring down the value of a high-volume three-point shooter if the extra credit from his makes are counteracted by an increased penalty due to his misses. The data would be hard to put together, especially since it may turn out a team’s transition defense and offensive rebounding would play into it a lot.

Kinda reminds me of how drug efficacy and side effects are starting to be tailored to our genes.

26. Justin

Joe – I’m guessing that you’re differentiating between “I dribbled out of bounds” turnovers where the ball has to be inbounded and “I passed to the other team” turnovers where they get to run. Then there’s the shameful “Lamar Odom forgets to inbound the ball under his own basket” turnover. I bet some coach has made an assistant figure out the stats for how bad each of those are.