APBRmetrics

[freeportkid]

Hey Guys,

I've never posted on this board, but have been a long-time reader. Anyhow, my main research interest is college/ACC basketball. I use a Wins Over Replacement Player (WORP) formula that I created to rank ACC players from 1981 to 2007 (since complete data has been available on minutes played and TO's).

This WORP formula is, of course, a work-in-progress, so I thought I'd present it here to get some feedback.

First, the formula is couched in terms of Hollinger's PER-- so any problems with the PER are inherent in my WORP calculation. Replacement values are based on a historical study of ACC players (1981-2006) in which I found "replacement-value" (i.e., non-rotation) players to have PER's that ranged from 55-60% of average ACC starters (bench/rotation players had PER's ranging from 80-85% of starters' PER's). So, based on this finding, PG's and C's have a "replacement-level of 55%. SG's, SF's, and PF's have a replacement-level of 60%.

PER is calculated per Hollinger. It is then adjusted for historical pace, historical strength of conference, and seasonal team defense. Historical strength of conference measures the strength of the ACC as compared to the rest of NCAA (using things like % of ACC teams making the Tournament, non-conference winning %, etc.)-- it doesn't account for the general strength of college basketball (which is assumed to be constant over the period 1981-2007). The team defense adjustment treats each of a team's players identically (except by allocating more credit/blame to those defenders who play more minutes). That is, if a team's defensive efficiency is 10% better than the ACC average for that season, each of that team's players get a 10% bump in PER. Basically, the PER itself accounts for individual defense (via steals, blocks, and DR's) while the team defensive adjustment accounts for the overall strength of a defense. Solid positional defenders (who don't accumulate many steal/blocks) are again a little underrated-- but what else is new?

To calculate WORP, a player's adjusted, pre-normalized (before it is set to an average of 15) PER is compared to the replacement-level PER for his postition. This difference is multiplied by his MPG in order to get Value Over Replacement Player (VORP). The VORP is translate into a WORP by using the relationship between Defensive-Adjusted PER and Winning % in the ACC from 1981-2007. This regression looks like:

Winn. % = -0.127 + 2.444 (Def-Adj. PER), with an r-squared of 0.75.

Def.-Adj PER is again not normalized to 15 (meaning the ACC average is 0.306-- not 15).

So to get WORP: (player's PER - replacement-level PER) * (player's MPG / 200) * 2.444.

Basically, this formula answers (or tries to answer) the question: how would replacing a player's x MPG with x MPG from a "replacement-level" player impact a team's ability to win games?

If a player's PER is .3 (say, .454 to .154) better than his theoretical replacement-level substitute, and he plays 35 MPG, the team's PER will be increased by 0.0525 (35/200 * .3) by having that player on the floor. To calculate that player's impact in wins, we can multiply 0.0525 * 2.444 * games played (say, 35) to get a WORP of 4.49 (or the difference between 19-16 (NIT) and 23-12 or 24-11 (NCAA Tournament).

Since 1981-82, the 20 highest WORP / 35 games in the ACC have been:

1. Tim Duncan (1997--SR): 8.57
2. TIm Duncan (1996--JR): 6.60
3. Ralph Sampson (1982-- JR): 6.32
4. Tim Duncan (1995-- SO): 6.31
5. Ralph Sampson (1983- SR): 6.29
6. Kenny Anderson (1991--SO): 6.29
7. Danny Ferry (1989--SR): 6.05
8. Joe SMith (1995--SO): 6.04
9. Christian Laettner (1991--JR): 6.04
10. Horace Grant (1987--SR): 5.78
11. Christian Laettner (1992--SR) 5.75
12. Rodney Rogers (1992--SO): 5.64
13. Grant Hill (1993--JR): 5.56
14. Bobby Hurley (1993--SR): 5.54
15. Brad Daugherty (1986--SR): 5.44
16. Derrick Lewis (1987--JR): 5.43
17. Shane Battier (2001--SR): 5.33
18. Kenny Anderson (1990--FR): 5.31
19. Sam Perkins (1984--SR): 5.29
20. Jason Williams (2001--SO): 5.25

So any thoughts on this metric? What am I forgetting? What can be improved? What should be kept, revised, or flat-out thrown away?

[basketballvalue]

Very interesting work, I like it. One question:

[freeportkid]

By position:

PG: 8.1
SG: 9.8
SF: 9.4
PF: 10.1
C: 8.3

Avg.: 9.2

[Ben]

I like it. As an ACC fan, I'd interested to see more of the values too. Would you be willing to share your spreadsheet?

I'm particularly interested in UNC players...

[freeportkid]

Sure, I can send you a copy of the spreadsheet if you give me an e-mail address.

I'm a Carolina fan too, by the way.

Here are UNC's top 20 in WORP / 35 since 1981-82:

1. Daugherty (1986--SR): 5.44
2. Perkins (1984--SR): 5.29
3. Jamison (1998--JR): 5.11
4. Montross (1993--JR): 4.73
5. Daugherty (1985--JR): 4.63
6. May (2005--JR): 4.63
7. Fox (1991-SR): 4.62
8. Jordan (1984--JR): 4.53
9. Wallace (1995--SO): 4.52
10. Perkins (1982--SO): 4.43
11. Jordan (1983--SO): 4.35
12. Perkins (1982--SO): 4.33
13. Lynch (1993--SR): 4.27
14. Stackhouse (1995--SO): 4.26
15. Worthy (1982--JR): 4.06
16. Forte (2001--SO): 4.00
17. Carter (1998--JR): 4.00
18. Sh. Williams (1998--SR): 3.79
19. H. Davis (1992--SR): 3.76
20. McCants (2004--SO): 3.75

And its 5 worst WORP / 35 seasons:

1. Morrison (2002--SO): -0.63
2. M.Scott (2002--FR): -0.59
3. Sanders (2003--FR): -0.51
4. Manuel (2002--FR): -0.34
5. Will Johnson (2002--JR): -0.29

[DLew]

Where did you get all that historical ACC data?

[freeportkid]

The historical data is available at:

http://www.sportsstats.com/ACC/

This site only goes through 2003-- but the 2004-07 stuff is more readily availble, of course.

[Statman]

NM
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