## “Marginal Win Score per 48″ (MWS48) explained

“Tell me how you come to your conclusions and I’ll decide if they are intelligent or horsecrap” — An astute commenter

### 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.  Basketball defense is so intertwined between the individual and  the team, its impossible to precisely value each player’s defense.  So 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.

### 21 Responses to ““Marginal Win Score per 48″ (MWS48) explained”

1. Why the Chicago Bulls have declined « The Courtside Analyst Says:

[...] started, I was trying to guess how many wins the Chicago Bulls would end up with based upon the Marginal Win Score per 48 averages of their roster over the last two seasons.  I think I came up with around 38 wins.  Not [...]

2. Jerry Bridgman Says:

“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.”

Why??? An assist implies at least two points scored. A rebound or steal doesn’t imply any points at all. What’s the reasoning here?

• tywill33 Says:

The assist is part of the act of scoring, but not the act itself. So though it does imply that a score took place, it isn’t a score in and of itself.

Remember that basketball is also not only about points, its also about possessions. Rebounds and steals both directly return and/or continue possession of the basketball.

Its harder to appreciate the value of possession in the sport of basketball because there is so much scoring and so many changes of possession. But that doesn’t make the value of every possession any less. It merely makes it less visible. In many ways the act of creating a possession for your team in basketball is just as important as recovering a fumble or procuring an interception is in football. It ends one teams scoring chance.

Actually I like to compare the act of “possession creation” in basketball with the same act in the sport of volleyball. No one would argue that a volleyball act that regained service for one’s team (but which of course results in zero points scored for that team) was nevertheless every bit as valuable an act as one that created a point for one’s team. But in volleyball the value of possession creation is manifest because of the rules, whereas in basketball it is just as valuable an act but is more “hidden”.

Here’s one other way to help you with the concept: You ever played the schoolyard game of “hustle”, or seen guys playing it? Its blood on the pavement going for a rebound and/or digging for a steal. That’s because in “hustle” the rules are “you make it, you take it” and therefore no one is guaranteed possession after an opponent’s score, so instead of being “hidden”, the value of possession — which is the very same as in the regular game of basketball — is suddenly made very, very clear.

3. Jerry Bridgman Says:

So late replying to this because wasn’t notified by e-mail as (I thought) I had requested.

I think I played Hustle once- one of my unpleasant basketball memories. No one told me the rules, for one thing.

Sorry to say, but I don’t agree with your answer about the value of assists. For one thing you gave a qualitative answer to a quantitative question. Maybe someone could go with your explanation for why assists are worth less than a made shot, but why just 1/4 of a 2-pointer? Why not 1/2- or 1/10, for that matter?

You’ll say the value of an assist was determined by Prof. Berri’s regression analysis. I have a theory (guess!) about that: The NBA doesn’t collect all the correct stats. Thus when the good Prof does his analysis, his coefficient on the assists variable is distorted to compensate for the “missing stats” variables.

Examples:

Suppose a shooter cleverly gets free, receives an easy pass, and makes an easy basket. The shooter gets credit for the easy basket, the passer gets credit for the assist, but the shooter gets no credit for the skilled part- the getting free.

Michael Jordan brings the ball up, calls his own number, beats a triple team and scores. -Again, credit for scoring but not for setting up your own score. [Getting an assist (or whatever) on your own shot will seem sacrilegious to many, but the ability to get your own shot is, IMO, undervalued in the stats. Such auto-assists being undervalued maybe requires regular assists to also be undervalued to bring them in line.]

Passer throws a brilliant pass to a team mate at the basket. The shooter is immediately wrapped up, but makes both free throws. -Two points, but no assist.

All these examples (and others that could be given) suggest that passing is incorrectly valued in the stats.

• tywill33 Says:

Sorry it took me so long to answer… and sorry about the “qualitative” answer… that’s all I’m “qualified” to provide.. yuk,yuk.

Anyways, I think you’re absolutely right. I think real assists, or what I sometimes call “but for” assists are highly valuable, much more so than my rinky dink formula indicates. (by “but for” I mean “but for” the pass, no score). I’ve always said that.

But if notice, the things the statisticians consider assists are often not really “assisting” the scorer at all. For instance, if you pass to the wing and the guy merely shoots and scores…. “assist”. If you do the same and the guy DRIVES to the hoop and scores… “assist”. The pass need not in any way add to the likelihood of a score, it often merely has to precede the score.

The problem with changing the way they keep assists is (a) I’ll bet you’d have a revolt on your hands from the NBA’s statisticians, and (b) now all past assists become oranges to the future assists apples.

But again, you’re right on your general point. I guess I didn’t read your original comment closely enough. (I barely have time to write on this blog anymore… I do the best I can).

Go Bucks!

4. Analyzing the slow start of the Detroit Pistons « The Courtside Analyst Says:

[...] of the Detroit Pistons By tywill33 Before the All-Star break I’d like to calculate the Marginal Win Score and the consequent wins and losses produced by each player on every NBA team.   When I am finished [...]

5. tywill33 Says:

Wait a second, I still didn’t answer your question. You specifically asked why I value an assist as 1/4th of a two pointer? For the same reason I count a free throw possession as minus 1/2 when in fact its actually something like 47%… its a balancing act between simplicity, precision, and reliability.

If I had information that would allow me to consistently distinguish between higher and lower value assists, and if I thought doing so would make a meaningful difference in the relative win values given to individual players, I might use a different number or a varying number. But I can’t, and over time its not worth the trouble.

As a sidenote, I once out of curiosity charted “high value” assists over a month of professional basketball viewing. There were only really a handful I thought would qualify as creating the points, and if memory serves almost 80% of them were lob passes or the like. Otherwise the vast majority of assists were only marginally helpful in facilitating points. And 1/4th of 2 seems to reflect that well enough.

Thanks!

PS — with regard to Berri’s model. I’m using a simplified version of the model, and Berri’s full blown model (as well as the simplified version) doesn’t really “value” assists, per se, it gives them a weight that reflects how they correlate with team wins relative to the other statistics kept in a box score. That’s all. And it just so happens that assists, probably for all the reasons you mentioned, do not correlate as strongly with wins produced as points or rebounds do. So the ideas of “value” is kind of a misnomer.

PSPS — What do you mean no one told you the rules? Were they hustling you?

6. The MVP Race (using Win Contribution) « Hardcourt Mayhem – Where Basketball Is Truly Magical Says:

[...] on that player’s efficient statistical production compared to his counterparts (measured by Marginal Win Score) and that player’s minutes on the court.  (the formula for “Win Contribution” is [...]

7. The NBA’s 20 Most Harmful Players in 2009-10 « Courtside Analyst Says:

[...] today.  This is the third season I have used my derivation of the Win Score metric, which I call Marginal Win Score (because it calculates individual player wins produced according to each player’s statistical [...]

8. NBA’s 20 most valuable players in 2009-10 « Courtside Analyst Says:

[...] a couple  of days ago, I just completed my win production calculations for every NBA team (using Marginal Win Score per 48).  I have also transposed them onto win charts for every single team and will post the link to all [...]

9. NBA Wins and Losses attributed to every player « Courtside Analyst Says:

[...] The two month project is over.  I have produced, before the end of the postseason, NBA Team Win Charts attributing each team’s wins and losses recorded during the 2009-10 season to the individual players who created them through their marginal statistical production, as measured by the metric known as Marginal Win Score. [...]

10. Who to credit/blame for Game 2 of the NBA Finals « Courtside Analyst Says:

[...] a statistic I call “Win Contribution“, which is based upon a player’s Marginal Win Score, I am charting the impact made on the outcome of each game by every participant in the 2010 NBA [...]

11. How big was the Big Baby in Game 4? « Courtside Analyst Says:

[...] morning watching SportsCenter the praise was always going toward the Big Baby.  Big Baby is not a Marginal Win Score hero (check the Celtics Win Chart extracted from my NBA Win Chart Page) but he has been recording [...]

12. R Says:

This is a good project.

I like the counterpart comparison a bit more than the team adjustment to Wins Produced, though maybe a combination of the two would be a worthwhile product to try to get at help defense.

But this is based on boxscores not play by play right? I understand that play by play is a lot more work. I’ll use play by play based counterpart ratings at 82 games and a few other places more heavily than boxscore based ratings.

Still, nice work moving forward with this logical next step.

13. Summer League Analysis from Ty Willihnganz (the Courtside Analyst) « The Wages of Wins Journal Says:

[...] I only calculated the numbers for rookies and others whom I was interested in evaluating.  I adjusted each player’s WS to his projected position and then estimated how that number would translate to Marginal Win Score per 48 (this measure is explained by Ty HERE). [...]

14. Milwaukee Bucks Win Chart (7 games) « Courtside Analyst Says:

[...] reading the chart, the first number next to each player is the player’s Marginal Win Score per 48 minutes of action, the second number is  the number of wins I credit him with producing so far this season, and the [...]

15. Miami Heat Win Chart through 9 games « Courtside Analyst Says:

[...] I broke down each Heat player’s marginal statistical production and their corresponding Marginal Win Score per 48 to find [...]

16. Surprising early candidates for NBA MVP « Courtside Analyst Says:

[...] Marginal Win Score, the metric that believes that individual basketball performance can and should be measured on both [...]

17. How long will the LINsanity last?? « COURTSIDE ANALYST Says:

[...] upon Marginal Win Score, Lin is off to a superb start to his NBA career.  The majority of his time has still been his time [...]

18. steve-from tpburg Says:

I’m not a serious basketball fan, but I think I see a major flaw in the way Win Score is calculated. A field goal attempt is counted -1 and a succesful 2 point field goal counted as 2 (points scored). That means any player who shoots less than 50% on 2 point attempts loses credit (on average) every time he shoots a 2.. I believe many (most?) of the top scorers average less than 50%. Doesn’t that mean that according to Win Score those players would help their teams more (i.e. get higher Win Scores) by simply never shooting 2 point attempts?

• Ty Willihnganz Says:

That’s an EXACTLY correct observation… but slightly incorrect conclusion

The reason you are deducted -1 on a field goal attempt is because of the opportunity cost… you have, essentially, given up possession of the basketball.

Now, I believe you are correct in stating that most NBA players shoot below 50% on pure field goal attempts, BUT most NBA players produce positive points for every “scoring” attempt they try. That’s because players can score points in ways other than just two point field goals. They can also score on 3 pointers and free throws.

For example, let’s say LeBron makes 7 out of 16 field goal attempts, with 2 of his makes being 3 point shots, and let’s say he also makes 8 of 11 free throws, with 10 of his throws coming in pairs. In that scenario, LeBron’s combined scoring attempts equal 22 (the 16 shots from the field, plus the 6 trips to the line — remember 5 of his trips to the line were 2 shot trips). In those 22 scoring attempts, he produced 24 points, which is +2 more points than attempts, even though he shot less than 50% from the field.