Introducing WORP (Wins over Replacement Player)

“Surely some revelation is at hand;
Surely the Second Coming is at hand.
The Second Coming! Hardly are those words out
When a vast image out of Spiritus Mundi
Troubles my sight: somewhere in sands of the desert” -Yeats, The second Coming

Over the course of the last week I have been troubled by an idea that needed to get out. It wouldn’t let me be. It wouldn’t let me sleep. It demanded my attention. The genesis of this idea come from the idea that  the scarcity of particular resource (for example the short supply of tall people) can drive up the value of an asset (i.e. an NBA player). There is compelling data recommending a  difference in valuation for big men in particular, their weight against gross productivity and the increased risk versus a talent dropoff at that position.

This of course led to my pieces on estimating the Replacement Level for the NBA (here and here, I’m assuming everyone’s read this and understands how we got to the replacement level definition).

The key driver for all these pieces is that the value of the average player is by position can be influenced based on the scarcity of those players. Now our standard approach assumes equal value at the baseline at each position which is perfectly valid. Our alternative approach (which I’m calling Wins over Replacement Player or WORP for short) goes from the assumption that the population of talent available at each position is not homogenous.

Calculating Wins over Replacement Player (WORP)

For understanding how to calculate Wins over Replacement Player (WORP) you need to have an understanding of Wins Produced (explained here, are you back? Good, let’s continue.)

Wins Produced is based on the marginal productivity for each team. If I tweak the equations for Wins Produced to look at the math in a slightly different way:

Wins Produced Team=

Sum_for_all_your_Players (Prod_by_min*Minutes_Played) –

Avg_for _all_teams (Prod_by_min*Minutes_Played) +

The 41 games you would win with an average team

Wins Produced Player=     Players _Prod_by_min*Minutes_Played –

Avg.Oppnent_Prod_by_min*Minutes_Played +

.100*Minutes Played

The .100 term means that if you break even on average you’ll win half your games.

For Wins over Replacement Player (WORP) we will be tweaking the terms for the equations. They will still add up to the same numbers overall and the correlation will remain the same (trust me I checked) but the individual value by player will change. So the equations will look like:

Wins over Replacement Player Team=

Sum_for_all_your_Players (Prod_by_min*Minutes_Played) –

Productivity_for_a_team_of_avg._replacement_players  (Prod_by_min*Minutes_Played) +

The games you would win with a replacement team

Wins over Replacement PlayerPlayer=

Players _Prod_by_min*Minutes_Played –

Avg._Replacement_Player at Position_Prod_by_min*Minutes_Played +

NetWinProductivityByReplacementPlayerAtPosition*Minutes Played

There are two key changes in the second equation. First, I’m using the Replacement Level Player as the zero point for marginal value but the second change is equally as important. I am calculating the third term as the net win productivity by a replacement player who plays the same position. This means that rather than assuming an equal share across all positions I am calculation what percentage of the baseline production is on average allocates to C,PF,SF,SG & PG.

But enough buildup,   I ‘d like to see what the numbers say.

Introducing WORP

I calculated WORP for every year since the merger. But I will be publishing the data from 2006 on. I am including Minute Allocations, Raw ADJP48, WP48 and Wins Produced from 2006 on as a nice bonus (you too can play along at home, we here believe in modeling by open source).  The data set is here.

Let’s look at some charts.

The first is how wins are reshuffled by position (W1 to W5 are Wins Produced ,WR1 to WR5 are WORP):

Wins moved from SG and SF to C and slightly to PF. PG suffered because of low baseline productivity but made it up with the scarcity of their skill set

Here’s a view of Wins Produced vs WORP for those Years:

Of note is that the shape of the curve did not change and that exceptional players remain for the most part exceptional.

If I look at the Change vs Wins Produced:

Most of the action goes on in the middle as spending priorities are re-arranged by position. SG & SF move down, PG and PF remain about the same and Centers get a boost.

So what does it mean?

Not what you expected. It's called a swerve.

Let’s clarify something first, I actually don’t think there’s one unique/optimum strategy to determine the value of a basketball player. I think using the average (as in the Wins Produced model)  is a valid strategy for success.  But I think adjusting the point of comparison from the average to the replacement (a la WORP) would just provide a different strategy to allocate resources that would also lead to success.

Our first value model recommends accruing assets that are exceptional when compared to their position averages (and we know this works see all the half baked theory stuff I’ve written for this blog). The alternative recommended approach would emphasize accruing assets that are exceptional in a limited pool. I think this could be succesful as well (and weirdly this seems to be what my beloved celtics  are doing :-)).

Simply put if  average Centers (or even Point Guards) are in general more scarce resources than Shooting Guards then skilled labor at that position should command a higher premium. Let’s put this in manufacturing terms. Shooting guards are base line operators, point guards are skilled operators/group leads and centers are something like technician/operators. The baseline value of the labor is different based on the role and is a function of the actual labor pool (which is were the replacement level comes in).

I think the logic behind the second approach to me goes back to the scarcity of a resource. What the analysis is telling me is that average Centers and PG are in general more scarce resources than SG and so skilled labor at those positions should command a higher premium.

In manufacturing terms shooting guards are base line operators, point guards are skilled operators/group leads and centers are something like technician/operators. The baseline value of the labor is different based on the role and is a function of the actual labor pool (which is were the replacement level comes in).  It really becomes like looking at different medical specialties and figuring out their value( (and centers seem to be the orthopedic surgeons of the NBA).

Arturo Galletti Written by:


  1. BPS
    August 19

    This is good stuff; the point guard result in particular wasn’t predicted ahead of time but starts to make sense when you look at it. I think it’s very interesting that PG and SG tend to have very similar levels of average production (Adjp48 / position offset), but that the replacement level of the PG is so much lower. Variance is not increasing 1:1 with production, there really are different skill sets.

    This is still using the automated positional assignments as well, correct? I seem to remember there being some questionable PG/SG distinctions in there, which didn’t matter for WP48 but would start to matter a lot more here.

    I’m not sure what the best way to account for injured players would be. Injured star level players definitely skew the averages. With the baseline jumping around so much, that’s probably an important effect.

    But those are refinements. The more important bit is making sure the basic framework is doing what it is supposed to. You want to be able to make the refinements without worrying too much about whether the underlying assumptions are causing problems.

    • August 19

      Actually, I used Prof. Berri’s data set for 2006 to 2010. The PG/SG makes practical sense actually. They’re physically similar positions but it’s a lot harder to play point effectively.Ball handling, court vision and passing seem to be rarer than just straigh on shooting .
      I’ve been thinking of using minutes per game played as a corrective factor but I found myself agreeing in principle with where the line fell. The big question marks all came up at center and Point Guard.
      I’m fairly happy with the result. The real fun is that now I have two ways to look at the data for analysis. I suspect that combining this with my half baked-notion and see if it help’s with some of the notable anomalies.

  2. R
    September 1

    WORP might be slightly better than WP for judging coaching impacts or GM roster change impacts.

    “combining this with my half baked-notion…” would be a good idea because you have to get such a high percentage of your winning impacts in the playoffs from the first 5-6 players. If you designate certain pieces as ‘keeper” you could estimate what you have to find or what level of “development / improvement” you probably need from the “open” slots to get to playoffs, final 4 level or championship level.

    • September 1

      Actually a lot of this work came about because of a research article I had the chance to review on models that made some judgements on coaching impacts and GM roster changes (A RE-EXAMINATION OF PRODUCTION FUNCTIONS AND EFFICIENCY ESTIMATES FOR THE NATIONAL
      BASKETBALL ASSOCIATION Hoon- Berri 2008). The conclusion pointed to big men having a greater impact on team wins than small forwards or Guards (again short supply of tall people). The surprising thing is that handling the ball is on the level with size.

      At the end of the day you want oversized players who handle the ball well at every position and shoot efficiently. This makes Pat Riley look like a freaking genius.

  3. R
    September 1

    Over-sized players who handle the ball well and shoot efficiently at 2-3 positions certainly seems very helpful- if they rebound proportionate to height and choose to use their handle for passes and drives proportionate to their talent and above league average.

    To have such players at every position might be nice but you might have a greater need to balance these offensive leaders with talented defensive players (hopefully above average on offense even if not over-sized and above average on handle or at least near average) and player with other offensive skills (screens, offensive rebounds, scoring from deep for spacing) to win it all much of the time.

    Wade-James-Bosh is very nice but they will need to get enough from PG and C too to fulfill expectations. They “might” not this season but they will have the ability to improve in future seasons with the MLE, trades and some draft picks.

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