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.
Monday, December 31, 2007
Friday, December 21, 2007
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).
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).
Thursday, December 13, 2007
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
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
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