Individualized Win-Loss Records

Sabermetrician Tom Tango introduced the concept of individualized win-loss records (“The Indis”) for MLB players on his old blog back in 2010. I actually didn’t see Tom’s post until January 2015, but I really liked the idea and thought it could easily be extended to the NBA. Below I will outline how to calculate “The Indis” for the NBA. Throughout the process I will use Kevin Durant’s 2013-14 season as an example.

In order to calculate “The Indis” for a given player, two things are needed:

  1. The player’s game space.
  2. The player’s wins above average.

I will describe out how to calculate both of those things below.

I. Game Space

A player’s game space is calculated as follows:

Gm_Space = 0.5 * Tm_GP * ((MIN / Tm_MIN) + (Poss / Tm_Poss))

A player’s individual possessions (Poss) and the team’s possessions (Tm_Poss) are calculated as described on the page Individual Offensive and Defensive Ratings.

Kevin Durant’s game space is:

Gm_Space = 0.5 * 82 * ((3122 / 19805) + (1988 / 7876)) = 16.8

II. Wins Above Average

Wins above average are made up of two things: offensive wins above average and defensive wins above average.

A. Offensive Wins Above Average

In order to calculate a player’s offensive wins above average, we first calculate the offensive rating of an average team with the player added:

Avg_Tm_ORtg = ((Poss / Tm_Poss) * ORtg) + ((1 - (Poss / Tm_Poss)) * Lg_ORtg)

A player’s individual offensive rating (ORtg) is calculated as described on the page Individual Offensive and Defensive Ratings.

The offense rating of an average team with Durant added is:

Avg_Tm_ORtg = ((1988 / 7876) * 122.55) + ((1 - (1988 / 7876)) * 107.23) = 111.10

* Note that 107.23 is not actually the league’s offensive rating (which was 106.65). Rather, it is the weighted average of all of the individual offensive ratings for players in that league.

The average team’s offensive rating is then adjusted based on the player’s possession percentage:

Adj_Avg_Tm_ORtg = Tm_ORtg + (15 * MIN% * (Poss% - 0.20))

where:

MIN% = 5 * (MIN / Tm_MIN)
Poss% = Poss / (MIN% * Tm_Poss)

For Durant this is:

MIN% = 5 * (3122 / 19805) = 0.7882
Poss% = 1988 / (0.7882 * 7876) = 0.3202
Adj_Tm_ORtg = 111.10 + (15 * 0.7882 * (0.3202 - 0.20)) = 112.52

Offensive wins above average are then calculated as follows:

OWAA = (Avg_Tm_Poss * ((Adj_Tm_ORtg - Lg_ORtg) / 100)) / PTS_Per_W

where:

Avg_Tm_Poss = Tm_GP * (Lg_Poss / (2 * Lg_GP))
PTS_Per_W = 0.3 * (Lg_PTS / (2 * Lg_GP))

For Durant these figures are:

Avg_Tm_Poss = 82 * (232987 / (2 * 1230)) = 7766
PTS_Per_W  = 0.3 * (248482 / (2 * 1230)) = 30.3
OWAA = (7766 * ((112.52 - 107.23) / 100)) / 30.3 = 13.6

Durant is credited with 13.6 offensive wins above average.

B. Defensive Wins Above Average

In order to calculate a player’s defensive wins above average, we first calculate the defensive rating of an average team with the player added:

Avg_Tm_DRtg = ((MIN / Tm_MIN) * DRtg) + ((1 - (MIN / Tm_MIN)) * Lg_DRtg)

A player’s individual defensive rating (DRtg) is calculated as described on the page Individual Offensive and Defensive Ratings.

The defense rating of an average team with Durant added is:

Avg_Tm_DRtg = ((3122 / 19805) * 103.42) + ((1 - (3122 / 19805)) * 106.79) = 106.26

* Note that 106.79 is not actually the league’s defensive rating (which was 106.65, the same as the league’s offensive rating). Rather, it is the weighted average of all of the individual defensive ratings for players in that league.

Defensive wins above average are then calculated as follows:

DWAA = (Avg_Tm_Poss * ((Lg_DRtg - Avg_Tm_DRtg) / 100)) / PTS_Per_W

For Durant this is:

DWAA = (7766 * ((106.79 - 106.26) / 100)) / 30.3 = 1.4

Durant is credited with 1.4 defensive wins above average.

C. Wins Above Average

Wins above average are the sum of offensive and defensive wins above average:

WAA = OWAA + DWAA

For Durant this is equal to:

WAA = 13.6 + 1.4 = 15.0

III. Individualized Wins and Losses

Individualized wins and losses are initially calculated as follows:

iW = (0.5 * Gm_Space) + WAA
iL = Gm_Space - iW

For Durant we get:

iW = (0.5 * 16.8) + 15.0 = 23.4
iL = 16.8 - 23.4 = -6.6

* Wait a second — negative losses?!? Yes, negative losses. I know negative losses can be hard to reconcile, but here’s the way I like to think about it: Durant was so good in his allotted game space that he negated some of the losses created by his teammates.

After individualized win and losses are calculated for each player, those values are adjusted upward or downward such that the sum of the player individualized wins and losses matches team wins and losses.

Below are “The Indis” for the 2013-14 Thunder. I’ve chosen to round everything to the nearest one for presentation purposes, so the player totals might not exactly match the team totals.

Name GP MIN iW-iL
Kevin Durant 81 3122 23+6
Serge Ibaka 81 2666 10-1
Russell Westbrook 46 1412 7-1
Reggie Jackson 80 2277 5-5
Jeremy Lamb 78 1538 3-3
Nick Collison 81 1353 3-2
Derek Fisher 81 1428 2-3
Steven Adams 81 1197 2-2
Thabo Sefolosha 61 1584 2-4
Caron Butler 22 598 1-1
Perry Jones 62 765 1-2
Andre Roberson 40 399 0-1
Reggie Williams 3 17 0-0
Royal Ivey 2 5 0-0
Ryan Gomes 5 34 0-0
Mustafa Shakur 3 11 0-0
Hasheem Thabeet 23 192 0-1
Kendrick Perkins 62 1207 0-4

Note that Durant’s record is presented as “23+6” rather than something like “23--6” or “23-(6)”. I think the first style is preferable to the others.

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4 thoughts on “Individualized Win-Loss Records

  1. Is there anywhere you have published either the yearly league weighted ORtg and DRtg’s to save us nerds some heavy math, or if you have published yearly results anywhere. I know your win shares method is now popularized by bbr.com, but I find this intriguing. I’d like to do a Jordan- LeBron- Kobe comparison, a Magic- Bird comparison, and perhaps a Curry, A.Davis, Durant, Harden, Westbrook comparison as well. What was your minute or possessor cutoff or did you literally use EVERY player from that particular season? Actually, the way your weighting the Offensive and Defensive Ratings, is it by minutes or possessions? I’ve thought perhaps a quick “on the fly” way would be to do it by team, say one team is 103.29 and makes up 3.4% of the league minutes and another is 102.88 and makes up 3.1% of the league’s minutes, another 101.62 and makes up 3.8% of league minutes, would (103.29×.034)+(102.88×.031)+(101.62×.038), etc, get me close or where I need to be?

    1. No, those aren’t published anywhere. To get the league offensive rating I weighted by individual possessions and to get the league defensive rating I weighted by minutes played.

  2. @jkubatko I have a question, I posted it under your Individualized W-L post on Statitudes as far as whether it’s weighted by MIN or POSS, and whether you have to calculate each team season w each individual player or just teams w/ their % of MIN or POSS ? Please help! I want to play w it..

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