Translating Win Contribution into Projected Wins

Here's how Win Contribution translates into wins.

You take a team's cumulative Win Contribution (which is the sum of each player's Position Adjusted Win Score per 48 minutes x each player's percentage of overall playing time).

For example, at the end of the 2006-07 season, the Milwaukee Bucks cumulative WC was
-0.959. Here's how it translates:

1. You take that number, -0.959, and divide it by 48.

2. Then you take the resulting number and multiply it by 1.621.

3. Then you take that number and add 0.104.

4. Then you take that number and divide it again by 48.

5. Then you multiply that number by the total number of player minutes (games played x 48 x 5). At the end of the season, that is around 19680.

If you do that calculation for the 2006-07 Bucks, you come up with 29.63, which is very close to their actual victory total: 28.

What do the numbers mean?

WIN SCORE

The concept of the Win Score I'm using is the brainchild of some Stanford economists who spent an inordinate amount of time and resources figuring out exactly which statistics correlate with winning and losing in basketball. From that research they created this algorithm:

Win Score/48: Points + rebounds + steals + 1/2 assists + 1/2 blocks - field goal attempts - turnovers - 1/2 personal fouls - 1/2 free throw attempts / minutes played * 48

SIDENOTE: If you notice, their research determined that the two most important factors in winning and losing are: Scoring efficiency (the number of points you can make per possession of the basketball), and the ability to maintain or gain possession of the basketball. Thus points, rebounds, and steals count as a full Win Score point, while turnovers and field goal attempts count as a full negative Win Score point. The other statistics, such as blocked shots, assists, and personal fouls are more peripheral... they are important but to a lesser degree. Thus they are only counted as 1/2.

The economists then calculated the average "Win Score" points/48 minutes amassed by each player at each of the 5 positions on the basketball floor. From that they can compute each player's "position adjusted" Win Score. And once they've computed each player's "Position Adjusted Win Score", they can compute a team's "Expected Win Total" within one or two games. It works incredibly well.

Example:

Michael Redd's Win Score computes to 10.3 per 48 minutes. Shooting guards have the lowest Win Score Averages on the court at 6.1 per 48, so Redd's Position Adjusted Win Score is +4.2. That's really good. Here's how it translates into Wins:

WIN CONTRIBUTION

Lets say Michael Redd played 38 minutes a game for all 82 games, and his PAWS was the aforementioned +4.2. To figure out his Win Contribution, I take his total number of court minutes, 3116, divide that by the total number of court minutes available for the entire team for the entire season (5 players play 48 minutes each for 82 games), and that is 19680 minutes, which means Redd used up 15.83% of the Bucks available court time.

I then multiply 15.83 times his PAWS of +4.2 and I get +0.664, a very high Win Contribution. To put it in perspective, let's say you put Redd on a team comprised entirely of average players (PAWS = +0.00). The team's aggregate Win Contribution is then entirely Redd's contribution of +.664. Here's the algorithm for determining the number of wins that team would expect:

Expected Wins= (Aggregate Win Contribution/48 * 1.621 +.104) / 48 * Total Team Courttime

Thus in an entire season, a team consisting of Michael Redd and a bunch of average players would be expected to win:

.664/48 * 1.621 + .104 /48 * 19680 minutes = 51.83 games

Now let's look at Charlie Bell, who has the Win Contribution of -.366. If Bell were surrounded by average players, that would mean the team could expect to win only 37.3 games. So Bell is effectively costing the Bucks 4+ games (I like expressing it in terms of production versus the average replacement, because that better captures the negative contribution).

Bucks Diary Relative Power Ranking

Here is the PVOA Relative Power Ranking updated through games played on December 12, 2007.

1. Boston Celtics...+13.23
2. San Antonio Spurs...+7.98
3. Los Angeles Lakers...+7.36
4. Detroit Pistons...+6.03
5. Orlando Magic...+5.88
6. Toronto Raptors...+5.34
7. Phoenix Suns...+4.23
8. Golden State Warriors...+4.10
9. Houston Rockets...+3.11
10. Utah Jazz...+3.01
11. Dallas Mavericks...+2.43
12. New Orleans Hornets...+2.35
13. Washington Bullets...+1.73
14. Denver Nuggets...+1.72
15. Indiana Pacers...-0.46
16. Atlanta Hawks...-0.74
17. Sacramento Kings...-1.06
18. Portland Trailblazers...-1.26
19. Philadelphia Sixers...-1.32
20. Memphis Grizzlies...-1.38
21. Miami Heat...-1.97
22. Cleveland Cavaliers...-2.52
23. Chicago Bulls...-3.04
24. Charlotte Bobcats...-5.07
25. Milwaukee Bucks...-5.87
26. New Jersey Nets...-5.99
27. Los Angeles Clippers...-6.15
28. Seattle Supersonics...-8.29
29. Minnesota Timberwolves...-8.82
30. New York Knickerbockers...-12.57

What is Eff48?

Eff48 is a statistic that has been compiled by the NBA since 2002. It measures the sum of all of the player's positive production stats (points + rebounds + assists + blocks + steals) subtracts them from the sum of all of the player's negative production stats (field goals missed + free throws missed + turnovers), then divides that by the minutes the player played, and then multiplies that number by 48.

This statistic provides a much, much better... albeit still not perfect... measure of a player's performance than you would traditionally get just by looking at the player's points and rebounds. Unlike those stats, Eff48 rewards all-around production, while it penalizes "volume scorers" -- guys who score a lot of points but cost their teams by missing a lot of shots.

I also like it because it is comprehensive yet very easy to understand, unlike some other more mathematically inclined "performance" statistics (see Hollinger, John.. "Per" stats).

Here's how to read the Eff48 numbers:

Eff48 Easy Translator

40+: All-World

35+: All-Star

27+: Elite

23+: Pretty good

20+: Average

< 20: Below Average

< 15: Crappy

< 10: NBDL Reservations being made

What is PVOA

PVOA, or "point value over average" is a concept based upon the thinking behind footballoutsiders.com's DVOA, or "defense adjusted value over average". What it tries to capture is how a team performed based upon how the average NBA team would have performed given the same opponent and the same number of possessions.

Here's how its calculated. You take the opponent's established offensive and defensive efficiency numbers for the season (which are pts * poss/100 and pts allowed * poss/100, respectively), then you calculate the number of possessions in the game for each team (FGA + .44FTA + TOs - Offensive rebounds), and you multiply. Then you compare it against the actual number of points scored and points allowed for the team you are evaluating.

Example: Detroit plays the LA Clippers. Detroit won the game, 103 to 79. But I want to evaluate how Detroit performed against the average. So I look up LA's offensive and defensive efficiency numbers at this point in the season. They are 108.52 and 97.72. Then I calculate the number of possessions. That turns out to be 93.92 for Detroit and 91.32 for LA.

So, to evaluate Detroit's offensive performance I multiply their number of possessions 93.29 by the number of points LA has been giving up per possession, .9772. I come up with 91.78 -- that's what the average team has been scoring against LA in that number of possessions. But Detroit scored 103, so their "point value over average" is +11.22. Then you do the same for Detroit's defense, and it turns out they gave up 20.12 points less than the Clippers average number of points in that many possessions, so Detroit's defensive PVOA is -20.12, for an outstanding overall PVOA for Detroit of +31.34 (the defensive numbers, if negative, are considered positive when calculating Detroit's overall PVOA, and vice versa for offense).