The New Game Metric

Editor’s Note: Yes, I know, you have questions. Why Am I posting here? Well, all I can say is that life happens. I will write a fuller post on future plans once I’m actually back fully from the Holidays but the short of it is, I will be posting more out of here in the near future. Never fear though, I have plans to keep writing until they pry the keyboard from my cold dead hands (or someone writes a large check!). Now, I give you a long delayed post, how does the new metric I used for the season previews work exactly?

“It is common sense to take a method and try it: If it fails, admit it frankly and try another. But above all, try something.”

-Franklin Delano Roosevelt, Oglethorpe University Commencement Address (22 May 1932)

We did worse last year at predictions than we have in previous years. I can freely admit it. Now, I could have taken my spreadsheets and gone on home or I could have rebuilt everything from the ground up stronger and better than before.

Much like the Spurs last season, failure just served as fuel for this offseason.

The results of that effort are collected here for your easy reference:

Let’s talk a bit about the journey though.

One of the more interesting about models is that a descriptive metric is not necessarily a predictive metric. This point was analysed at length by Alex Konkel. Wins Produced was designed as a descriptive metric and not a predictive one. It is very good at doing what it was designed for and that is determining what the players actually did in a season and their relative value. However when it comes to predictive ability it tends to lag behind as constructed.

2012-13 Prediction Results

2013-14 Prediction Results

That’s the list of internet wide predictions on Win Totals for the past two NBA seasons. You’ll note that the Wins Produced predictive models I put together come out with an RSME of 7.6 for 2013 and 10.65 in 2014 versus a best of 5.9 and 8.1 respectively.

What this basically told me, Is that I needed to build a new predictive metric.

Luckily, I already had the outline of one in my mind. Let’s go on a tangent for a bit. Don’t worry though, it’s important to the story.

One of the recurring ideas of my writing on the internet has been the goal of continuing to grow the existing boxscore based models. I’ve always wanted to be able to look at game to game and even play by play data using the same concepts and base equation that Prof. Berri outlined in his work:

Here is the specific model linking winning percentage to offensive and defensive efficiency.

  • The model was estimated with data from 1987-88 to 2010-11
  • Data taken from Basketball Reference
  • Dependent Variable is Winning Percentage
Independent Variable Coefficient t-statistic
Offensive Efficiency 3.152 82.110
Defensive Efficiency -3.134 -73.348
Constant term 0.481 8.702

Adjusted R2 = 0.94


  • Offensive Efficiency = Points Scored divided by Possessions Employed (PE)
  • Defensive Efficiency = Points Surrendered divided by Possessions Acquired (PA)
  • PE = FGA + 0.45*FTA + TO – REBO
  • PA = DFGM + 0.45*DFTM + REBD + DTO + REBTM
FGA = Field Goal Attempts FTA = Free Throw Attempts
TO = Turnovers REBO = Offensive Rebounds
DFGM = Opponent’s Field Goals Made DFTM = Opponent’s Free Throws Made
REBD = Defensive Rebounds DTO = Opponent’s Turnovers
REBTM = Team Rebounds

The formulation for PE and PA is explained in Berri (2008).

The value for FTA and DFTM is explained in Berri (2008)

REBTM refers to Team Rebounds that change possession.  This calculation is detailed in Berri (2008)

Dave took this model and used the season total data to build a robust explanatory model. However, because of the way it was built there was data that was lost in the translation. There was granularity that was simply not readily available at the time. Using season as opposed to game data forced some compromises. Defense outside of the boxscore was considered wholly as a team activity.The detail of where the actual value was coming from was a submerged in the one number. Team adjustments were required for defense and other activities and while mathematically sound, reasonable and backed by the actual empirical data, they led to countless discussions because of their complexity.

I had decided early this offseason that this was the summer I build my game metric. I wanted to build something simple, based on sound principles and intuitive. To that end, I based everything around Win Score.  What I was surrendering in mathemathical complexity, I was expecting to gain back in the order of magnitude increase in granularity by going from season totals to a game to game tally. I was not disappointed.

Win Score is the simplified version of Wins Produced. It’s a measure of net positive things happening on court as a function of a player’s boxscore statistics.  The calculation is as follows:
  • Win Score =  Points + Steal + Offensive Rebounds + 0.5*(Defensive Rebounds +Assists + Blocks) – Turnovers – Field Goal Attempts  – 0.5*(Free Throw Attemps + Personal Fouls)
Now this is a good shorthand but it’s actually incomplete. We don’t actually consider what the player’s opponent does we can solve that by using Opponent Adjusted Win Score. Since Basketball is a team sport, An opponent adjusted version of Win Score provides a simple and robust measure of Player Value on a game to game basis. The calculation is done by working out the Win Score by position of a team’s opponents on a game to game basis and adjusting a Player’s Win Score accordingly. For example:
  • if player A has a Win Score of 10 in 40 minutes played at center and the opposing team’s Centers produce a Win Score of 8 for the game, Player A’s Opponent Adjusted Win Score per 48 (OAWS P48) is equal to : 10*(48/40) – 8= 4.

As an example for a player playing multiple positions in a single game (e.g. 50% PF and 50% C)  the calculation would look something like this :

OAWS/48 = [Win Score] * (48/[Minutes Played]) – [Opponent Win Score at Position 1] * [Time at Position 1]/48 – [Opponent Win Score at Position 2] * [Time at Position 2]/48

I am not the first to blaze down this path. Much of the credit for what follows lies at the feet of Ty Willinganz who first came up with the framework and concepts behind the metric that follows (he called it Marginal Win Score) . His explanation is here. This game metric is built around the same principles (but not exactly the same). Let’s quote some passages that are relevant (the highlights are mine):

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.


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.


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.

Please keep in mind that, I don’t really see this metric as a replacement for wins produced. It’s a different approach that has a few advantages. It’s simpler to calculate and explain. We can easily look at individual components of a player’s game. We can forego any complicated adjustments. It also treats defense much more as a player activity than a team activity. I agree with Ty in that neither approach for defense is truly right in my opinion but both have merit and should looked at.  One of the avenues of research that this method opens up is the possibility of actually comparing and contrasting both methods of working out defense.
It does also seem like defensive roles are slightly different than traditional positional roles. We have primary post defender (think Bogut, KG, Duncan, Hibbert) and secondary post defender (just stand over there and prevent cuts David Lee/Big Baby) and Primary wing defender (Iguodala or Kawhi) and secondary wing defenders (Curry, Klay thompson, Harden, etc.). Somehow digging this out is something i’d love to do. Let’s get back on topic though.

A few more bits of math are needed. The correlation (r-square) between OAWS and actual point margin on a game to game basis is 92% from the 1986 to 1987 season. This is functionally the same as the result if we did the same for the full wins produced model.

Next, I have to work out the correlation of OWAS per game to actual point margin per game. I did this on a season to season basis. The conversion factor from OWAS to Point Margin is listed in the table below:

Season Conversion from OAWS to Point Margin Produced
1987 59.2%
1988 59.0%
1989 59.7%
1990 60.8%
1991 60.0%
1992 60.0%
1993 59.6%
1994 59.4%
1995 60.0%
1996 61.4%
1997 60.5%
1998 61.0%
1999 60.3%
2000 60.9%
2001 61.1%
2002 62.6%
2003 62.4%
2004 60.2%
2005 61.2%
2006 61.9%
2007 61.7%
2008 62.2%
2009 61.8%
2010 61.5%
2011 61.0%
2012 63.7%
2013 62.4%
2014 62.5%

Using this conversion factor I can create Point Margin Produced (PMP) simply as OAWS times 62.5% for 2014 for example. I can then map that to a few familiar formats:

  • Game Wins Produced per 48 (GWP48) = PMP per 48/31.1 + 48*1230/(Minutes for season)
  • Game Wins Produced= Game Wins Pruduced per 48 times Player MP /48

At this point the basic model is done. However, due to the nature of scorekeeping in the NBA we have certain events that are not directly attributed to actual players but to the teams themselves, team rebounds and team turnovers. These are actually fairly hard to dig out and almost impossible to asign to any one player. Not accounting for them causes error between the projected point margin in a game and the actual point margin. This is easy enough to calculate. That difference, which is coming from the team assigned stats, forms the basis of the team adjustment ( take the difference in the point margin tabulated for each game and divide it up by minutes). Adding that in gives us correlation similar to what I’ve previously observed from doing Wins Produced on a game to game basis. However, it’s not an adjustment that we strictly need.

The end result looks like this:

Wins Produced versus Games Wins Produced for 2014

You’ll note that some players that are recurring sources of arguments here, such as Melo and Aldridge, benefit from the change. We will be talking about this more during the season. A few more notes:

  • The more minutes a player plays, the more accurate the number is. A player playing point guard for 400 minutes next to Chris Paul will see a significant benefit to his defensive and offensive numbers. The next level (play by play) will address that in the future.
  • The metric can be divided into the following components:

1. Scorer Point Margin per 48: ((Points  – Field Goal Attempts  – 0.5*(Free Throw Attemps ) – Average at Position) times the conversion factor : Simple measure of how good/bad a player is at scoring

2. Handle Point Margin per 48: ((.5*Assists– Turnovers )- Average at Position) times the conversion factor: Simple measure of how good/bad a player is at handling the ball.

3. Rebounding Point Margin per 48: ((Offensive Rebounds + 0.5*Defensive Rebounds) – Average at Position) times the conversion factor: Simple measure of how good/bad a player is at getting rebounds.

4. Defensive Point Margin per 48: ((Steal + 0.5*Blocks – .5*Personal Fouls + Opponent_Difference_from_Average_WS_Production)- Average at Position) times the conversion factor: Simple measure of how good/bad a player is at Defense. Two components here:  Box Score Defensive Point Margin per 48 or defense as measured in the Boxscore and Opponent based Defensive Point Margin or how much more or less production we see from the player’s average opponent.

5. Finally the team component which is just the differential on a game to game basis divided on a per minute basis.

Here’s a look at the R-Square for different components of the metric to actual team point margin per game:

You’ll note that the team adjustment is mostly unnecessary. Just the player attributed boxscore stats give you an R-squared of 97%. Interestingly, the just scoring and boxscore defense gives you around 90% of all the information you need.

Let’s get back on track. With the new metric in hand,I did some testing (yes it’s show my work time).

I did four main test models:
  • Wins Produced and Wins Produced per 48
  • Raw Wins Produced and ADJP48 (i.e Wins Produced with no position adjustment)
  • Game based wins produced without any team adjustment. Basically, I just used the player boxscore and opponent stats and ignored everything else.
  • Game based wins produced with the team adjustment. .
And I did 5 tests:
  • Total model Wins for each model versus actual wins for the year (descriptive)
  • Retrodiction test for teams. Predicted wins based on Prod per 48 for players the previous season and actual minutes for that season. I put a minute floor of 400 for the previous and current season. Player’s below that floor just saw their actual win totals. (Predictive)
  • Year to Year variation in productivity per 48 with the same minute cap. All players.
  • Year to Year variation in productivity per 48 with the same minute cap. Players who did not change teams.
  • Year to Year variation in productivity per 48 with the same minute cap. Players who did change teams
The results are:

All the models are functionally the same in terms of descriptive ability. The simple Game model without the Team adjustment loses some descriptive ability and predictive ability but it’s really not significant.
The two game based models are significantly more predictive and more consistent for individual players. This holds true whether or not a player changes teams year to year.
Does this result make sense? Yes. I followed the same methodology but increased my sample by an order of magnitude. Where a typical Wins Produced Calculation has about 5000 pieces of data for a season, the Game Wins Produced has 250K. Basically increased sampling is providing a more representative sample. I would estimate a play by play version for a season would be at around 250 million pieces of data and a SportsVU version would be at 250 billion datum. Yikes.
I will say that based on the positive effect on predictiveness from going to season level to game level for the metric calculation going to a play by play version would seem to be indicated at some point (and the application of ridge regression might be useful as well). I do need an off-season project for next season.
Full disclosure, in parallel to this I also looked at Win Shares and various versions of RAPM but these were either incomplete while predictive (see here) or not as predictive. I also tested blended models but didn’t see any significant increase in predictive accuracy.
In the end, for predictive purposes, the Game Wins Produced model with the team adjustment was the best. The team adjustment makes zero difference on a player level but it does move the needle slightly for prediction. For players though? The simple Game Wins Produced with no adjustments is what you’ll see from me outside of prediction posts.

Let’s recap:

  • I built a new game metric (OAWS, PMP, Game Wins Produced) based on Wins Produced principles and it was good.
  • I rebuild the projection model from the ground up. I tested multiple metrics and the new game metric was the best. There is a simple version of the Age model and a game to game team correction included in the metric.
  • For rookies and euro’s I used and adapted the existing draft models (see here).

So all the projection articles for this season when talking about Wins Produced and WP48 are talking about Game Wins Produced and Game WP48 using the team adjustment as defined in this article.

With the metric in hand, I went to do the season simulation or as the Andres calls it: the minute projection death trap. Again, I was up to facing the impossible challenge. The key was this little tidbit:

Minute Map Depth Chart Current Season Depth Chart Current Season Depth Chart Current Season
Age Group Depth Chart Previous Season 1 to 5 6 to 10 11 & Up
18 to 22 1 to 5 62% 25% 13%
18 to 22 6 to 10 23% 46% 31%
18 to 22 11 & Up 5% 21% 74%
23 to 25 1 to 5 64% 26% 10%
23 to 25 6 to 10 26% 43% 31%
23 to 25 11 & Up 9% 23% 68%
26 to 29 1 to 5 69% 25% 6%
26 to 29 6 to 10 37% 41% 22%
26 to 29 11 & Up 15% 39% 46%
30 and up 1 to 5 74% 20% 6%
30 and up 6 to 10 31% 46% 23%
30 and up 11 & Up 16% 39% 45%

That table represents a map of a players motion on the depth chart as a function of age and their place in the depth chart the previous season. Using this, the players average minutes over the last three season, their minute variability, their projected place on the depth charts, teams minute allocation patterns and a lot of random functions, I was able to build a minute allocation simulation for each team. I then combined that with expected average production for each player as well as the error for each projections (and of course more random number generator functions).

Finally, I identified the typical error introduced by the schedule and Home Court (it’s around 2.1 wins and completely random season to season) and threw that in together with corrections to make sure that the wins for the league add up to 1230 for each simulation.

The result of course, is your season projections for each team.

As you have already seen.

Still here? It occurs to me that the rosters have changed a tiny bit since 10/17 when I locked in the simulation. In particular, Steve Nash is out.

Are you ready for some basketball?





2 Responses “The New Game Metric” →

  1. David Cox


    Just saw this link at the top of the site, but didn’t find it in the blog… Amazing work (not that I understand most of it :).

    How hard is it to re-run your O/U sim periodically? Could you run an update based on records at the All-Star break or something?


  2. davegcox


    Sorry, just realised you’re already doing this.


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