Monday, July 9, 2012

A Long Primer on Marginal Win Score: A Basketball Metric

Q: What is Marginal Win Score per 48 (MWS48)?

Marginal Win Score per 48 is the basketball metric I use to attribute wins and losses to individual players on any given basketball team.  It is based upon the Win Score metric created by economics Professor David Berri and his colleagues who wrote the excellent book The Wages of Wins.  Their work uncovered how traditional basketball statistics correlate with wins.  Win Score is simply an expression of their findings, and Marginal Win Score is derived from that.

Now, always bear in mind when considering the value of MWS that Berri’s Win Score is the original work and is the only variation of the metric that has been rigorously tested, researched, and reviewed.  Marginal Win Score on the other hand is just a derivative idea hatched in the mind of a basketball fan and submitted for the approval of other interested basketball fans, and I wouldn’t ever represent it as anything more than that.  To the extent I’ve tested it, sure it works, but nevertheless take it for what it is.


Q: How is Win Score calculated?

A: Points + Rebounds + Steals + .5Assists + .5Blocks – Field Goal Attempts – Turnovers – .5Free Throw Attempts – .5Personal Fouls


Q: Why do you like Win Score better than other metrics?

A: Because, unlike John Hollinger’s PER metric, and the NBA’s Efficiency metric, the Win Score metric actually tells you which players are producing wins. The others have no relationship to wins.  The key finding that Win Score made that the others seem to overlook is the importance of effectively using and creating possessions in basketball.  This difference shows up in two main ways.  First, Win Score deducts for every field goal attempt taken by the player, the others only deduct for missed field goal attempts.  Thus the other metrics reward players for the simple act of shooting the basketball, an act that has no value in and of itself.  Win Score requires players to turn field  goal attempts into points, and penalizes them if they do not.

Second, Win Score values rebounds and steals (possession creating acts) more heavily than assists and blocked shots, NBA Efficiency does not (PER does).  Assists and blocked shots are helpful acts, certainly, but they are not as important as Rebounds and Steals when it comes to producing wins, and Win Score recognizes this.


Q: How does Marginal Win Score differ from Win Score?

Its basically a comparative difference.

Win Score attributes wins to players by comparing their Win Score per 48 (WS48) to the NBA average WS48 at the player’s position.  Marginal Win Score attributes wins produced on the basis of the Player’s Win Score and the Win Score he and his team allow opponents who play the same position to produce.
The reason I prefer this method is simple.  No team and no individual player ever competes against “the average”.  They compete against actual opponents.  And in the game of basketball, one can impact the level of efficiency one’s opponents are able to achieve (I am loosely referring, of course, to “defense”).  That fact has to be recognized, I believe, in any win calculation.

Think of it this way.  Lets say you have a team that produces, at all five positions, the average NBA Win Score per 48 minutes.  Under the traditional Win Score calculation, you would expect that team to finish the season with as many wins as losses, a .500 team.

But lets add a ridiculous element to illustrate an important point.  Lets say that “.500 team” wishes to protest against their frugal owner and lets say they elect to do so by collectively refusing to cross half court to play defense. Under those circumstances, one would expect their opponents to produce  Win Scores against them at every single position that are much higher than the NBA average.

If that is the case then traditional Win Score is in a logical bind.  How can that team still be considered a .500 team?  If “Win Score” statistics correlate with basketball wins, and they do, then the fact that the team’s “Opponents” are producing Win Score statistics that are far beyond the average would suggest that the team itself must ALSO produce Win Score statistics far beyond the average if they themselves are to win?

Right? The obvious answer is yes.

That means a team’s level of defense can affect the amount of “Win Score” they must produce to win games.  And if “defense” or more precisely “Opposition Win Score average” can be affected by the team itself, and our little thought scenario shows that it can, then that “defense” has to be recognized in any win calculation.  That is precisely what Marginal Win Score does.

I bring up one additional point to help prove my case.  If you calculate Team Win Score averages for every NBA team, and then try to translate them into wins, you will find that you MUST account for Opposition Win Score or you will not accurately calculate the team’s wins produced.  That also suggests you must use the Marginal Win Score comparison (For instance, go back to 2007-08.  As a team, the Celtics Team Win Score average was much lower than the Team Win Score average produced by the Phoenix Suns.  So, if you are strictly comparing against the average, as Win Score does, then Phoenix should have more wins.

But that wasn’t the case.  But, once you factor in Opponent Win Score, you solve the problem.  Once you account for the fact that the average Celtic Opponent Win Score was much, much lower than the NBA average, and that the average Suns Opponent Win Score average was slightly higher, then you get the proper win calculation.  The Celtics and Suns, in other words, created different “win atmospheres” for themselves.

The Celtics didn’t have to produce as efficiently to win games because they did not allow their opponents to produce efficiently.  That is Marginal Win Score in a nutshell).


Q: So Marginal Win Score is Win Score with defense?

Yes and no.  First of all,  traditional Win Score, as expressed by "Wins Produced" has a defensive adjustment built in.  It simply spreads defensive responsibility across the entire team. Marginal Win Score attempts, right or wrong, to individualize defensive responsibility, in a sense.

But basketball defense is so intertwined between the individual and  the team, its impossible to precisely value each player’s defense.  That’s not what I’m claiming to do.  Instead what I like to say is “With Marginal Win Score each team and each player on that team produces wins based upon a comparison between his positional Win Score and the Win Score average that he and his team allow at his given position“.  Is defense part of that?  Yes.  Can individual defensive effort effect that?  Yes.  But are there elements of that defense that are not in each player’s control?  Yes.

That’s why I don’t claim that “Marginal Win Score” is necessarily about defense per se.  Because basketball defense is partially an individual act, and partially a team act.  And since its really a poorly compensated act, it relies somewhat on the cooperation and collective morale of the entire team.

Therefore a player’s Marginal Win Score will be effected by elements out of his control.  A player on a hopeless team whose teammates play no defense has little to no incentive to play defense himself.  And even if he does, how is he going to stop his counterparts alone?  So you have that element.

But I’m comfortable with that, because, really, that is what winning in sports is all about.  You’re not always faced with ideal circumstances or circumstances that are 100% under your control. Producing wins, or more precisely, performing the acts that produce wins, is often circumstantial.  That’s just sports.


So how is Marginal Win Score calculated?

Marginal Win Score per 48:  (Player’s Win Score – his collective “same position” Opponent Win Score / 2) / his minutes played * 48


How does MWS48 translate into wins?

There is a formula that uses the player’s MWS48 and his minutes and plugging those individual numbers into that formula you get the number of wins  produced by each player.


How accurate is Marginal Win Score?

I’ve done about 5 full NBA seasons, and I’ve found that each team’s total Marginal Win Score wins explain, on average, 95% of each team’s Pythagorean wins (its almost identical for actual wins, but I use Pythagorean wins for historical purposes).  Normally the explanation is in the 93 to 99 percent rant, but you will occasionally find it varying, never by anymore than 88% of Pythagorean wins.


Do you have any examples of MWS48 in use?

Yes, here is a page attributing wins and losses to every player on every team from the 2008-09 NBA season.

And here is a page that uses what I call “Historical Marginal Win Score” to attribute wins to every player on every team from the 1964-65 NBA season.  I will explain Historical Marginal Win Score on another page.  Its just Marginal Win Score that relies on inductive reasoning to fill in the necessary but missing statistics.  You might find that interesting.  My dream is to someday complete every NBA season and then publish my findings.

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