The TORTS System

An Experimental Method for Measuring Player Efficiency


In thread after thread here at GSoM, statheads such as jae and others discuss the relative merits of players using statistics. The stats that seem to come up time and again are rebounds, turnovers, and shooting efficiency, as these have the highest correlation with winning than any others. I thought it would illustrative to develop a “quick and dirty” measurement to use for comparing players which account for these stats and these only.

The first question, then, becomes, “what stats do we use for each of those?” There are many ways of measuring a player’s rebounding prowess: total rebounds, rebounds per game, rebounds per 36 minutes, offensive/defensive rebounding splits, and my personal favorite, total rebound percentage (TRB%). You can probably tell which way I am going to with this, but I chose total rebound percentage because it measured a player’s rebounding ability, independent of minutes played and pace. For turnovers, I used the analog of TRB% which is turnover percentage (TO%), or the number of turnovers committed by the player per 100 possessions. Finally, for shooting efficiency I chose true shooting percentage (TS%), which factors in free throw shooting, 2-point and 3-point field goals.

Using the Hollinger NBA stats at, I was able to put together a database of 328 players who were eligible from last season (minimum 6 minutes played per game). I then determined the average and standard deviation of all players’ TRB%, TO%, and TS%. To normalize the value for each player, I determined the distance from the mean for each statistic in terms of standard deviations. For example, the average TS% was 53.7%. The standard deviation was 4.6%. Therefore, a player with a TS% of 58.3 would have an adjusted value of 1.0 since their contribution was one standard deviation above the mean.

This calculation was done on all stats for all players and the three values combined (with the turnover value subtracted from the sum of the other two, since turnovers are negative contributions whereas the other two improve as they get higher).  I call this the “TORTS System” because it stands for T(urn)O(vers)R(ebounds)TS(%) and because I will sue the pants off of you if you steal it from me to make a profit. Think of it as an analog to OPS in baseball, which is a useful tool to measure a player’s contribution, yet ignores certain measurable which have a positive correlation to winning (OPS does not account for stolen bases or defense), and of course ignores unmeasurables. This is roughly comparable to Hollinger’s PER formula, but is much easier to calculate and is a bit more intuitive. A player below league average would have a negative value, and a player over league average a positive one. This is true for all 3 categories.

One thing I noticed immediately when I compared the values of all players were that centers generally came out on top and point guards on the bottom. This makes sense since rebounds are generally accrued at a higher rate by post players than perimeter ones, whereas turnovers and shooting percentages are relatively position-neutral. To remove this bias I grouped players by position so they are compared against their peers; position assignments were done using

Without further ado, I prevent the top 10 and bottom 10 at each position with occasional comments, followed by the relative ranks of YOUR GOLDEN STATE WARRIORS in their positional groups.

Top 10 Centers
1. Marcin Gortat (ORL)
2. Pau Gasol (LAL)
3. David Lee (NYK)
4. Joel Przybilla (POR)
5. Erick Dampier (DAL)
6. Dwight Howard (ORL)
7. Al Jefferson (MIN)
8. Shaquille O’Neal (PHO)
9. Tim Duncan (SAS)
10. Andris Biedrins (GSW)

This is why I think the Gortat signing is going to be outstanding value for the Mavericks. Also, I’m quite surprised to see Dampier on this list.

Bottom 10 Centers
63. J. J. Hickson (CLE)
64. Chris Kaman (LAC)
65. Sean Marks (NO)
66. Malik Allen (MIL)
67. Johan Petro (DEN)
68. Francisco Elson (MIL)
69. Hilton Armstrong (NO)
70. DeSagana Diop (CHA)
71. Chuck Hayes (HOU)
72. Joel Anthony (MIA)

One of these guys is getting paid $10m per season. Ouch.

Top 10 Power Forwards
1. Troy Murphy (IND)
2. Matt Bonner (SAS)
3. Antonio McDyess (DET)
4. Carl Landry (HOU)
5. Kevin Garnett (BOS)
6. Steve Novak (LAC)
7. James Singleton (DAL)
8. Antawn Jamison (WAS)
9. Brandan Wright (GSW)
10. Dirk Nowitzki (DAL)

Bonner and Novak’s surprising presence on this list will be explained further later.

Bottom 10 Power Forwards:
49. Yi Jianlian (NJN)
50. Shelden Williams (MIN)
51. Luc Richard Mbah a Moute (MIL)
52. Elton Brand (PHI)
53. Boris Diaw (CHA)
54. Ben Wallace (CLE)
55. Reggie Evans (PHI)
56. Brian Skinner (LAC)
57. Josh Powell (LAL)
58. Brian Cardinal (MIN)

Poor Elton Brand. First the season-ending shoulder injury, then making this “Bottom 10” list! Seriously though, he probably makes the top 10 list most years, but he shot extremely poorly in limited action last year.

Top 10 Small Forwards:
1. LeBron James (CLE)
2. Jamario Moon (MIA)
3. Marvin Williams (ATL)
4. Gerald Wallace (CHA)
5. Bobby Simmons (NJN)
6. Maurice Evans (ATL)
7. Wally Szczerbiak (CLE)
8. Danny Granger (IND)
9. Peja Stojakovic (NO)
10. Kelenna Azubuike (GSW)

All hail the King.

Bottom 10 Small Forwards:
59. Trenton Hassell (NJN)
60. Luke Walton (LAL)
61. Quinton Ross (MEM)
62. Dominic McGuire (WAS)
63. Joe Alexander (MIL)
64. Adam Morrison (LAL)
65. Jared Jeffries (NYK)
66. Ricky Davis (LAC)
67. Greg Buckner (MEM)
68. Donte Greene (SAC)

No real surprises here.

Top 10 Shooting Guards:
1. Anthony Morrow (GSW)
2. Ray Allen (BOS)
3. Brandon Roy (POR)
4. Jason Richardson (PHO)
5. Manu Ginobili (SAS)
6. Shane Battier (HOU)
7. Kobe Bryant (LAL)
8. Michael Redd (MIL)
9. Rudy Fernandez (POR)
10. Dwyane Wade (MIA)

Surprised to see the #1 guy here? I’m not. As it turns out, this system is basically tailor-made for a player like Anthony Morrow, a good rebounder (for his position) and dead-eye shooter.

Bottom 10 Shooting Guards:
57. Kyle Weaver (OKC)
59. Devin Brown (NO)
60. Tony Allen (BOS)
61. Damien Wilkins (OKC)
62. Desmond Mason (OKC)
63. DeShawn Stevenson (WAS)
64. Bobby Brown (MIN)
65. Goran Dragic (PHO)
66. Matt Carroll (DAL)
67. Marko Jaric (MEM)

Two comments: First, what the hell is Adriana Lima thinking? Second, no wonder the former Sonics played Sefolosha so much after his acquisition; just look at their other options!

Top 10 Point Guards:
1. Chris Paul (NO)
2. Eddie House (BOS)
3. Jameer Nelson (ORL)
4. Travis Diener (IND)
5. Leandro Barbosa (PHO)
6. Jose Calderon (TOR)
7. Chauncey Billups (DEN)
8. Derek Fisher (LAL)
9. Nate Robinson (NYK)
10. Mo Williams (CLE)

An obvious bias towards shooting/slashing PGs here. It’s a real testament to just how good Chris Paul is that he tops the list despite being a pass-first (and thus relatively turnover-prone) PG.

Bottom 10 Point Guards:
54. Jordan Farmar (LAL)
55. Sergio Rodriguez (POR)
56. Roko Ukic (TOR)
57. Mike Taylor (LAC)
58. Jerryd Bayless (POR)
59. Anthony Carter (DEN)
60. Juan Dixon (WAS)
61. Ronnie Price (UTA)
62. Earl Watson (OKC)
63. Brevin Knight (UTA)

And finally, your Golden State Warriors, with their ranks within their positional group:
Monta Ellis-SG-51/66
Acie Law IV-PG-42/63
Anthony Morrow-SG-1/66
Marco Belinelli-SG-52/66
Stephen Jackson-SF-57/68
Kelenna Azubuike-SF-10/68
Corey Maggette-PF-36/58
Anthony Randolph-PF-42/58
Brandan Wright-PF-9/58
Ronny Turiaf-C-37/72
Andris Biedrins-C- 10/72

This is unfair to Monta as normally he’s more efficient from the floor than he was last year. Jackson commits tons of turnovers, shoots poorly, and rebounds poorly for a SF; this system is almost tailor made to punish him. Corey Maggette would score much higher (23rd out of 69) if he were placed at his normal SF position instead of PF. Turiaf is basically an average center (something that makes sense).

This system has some merits but also numerous flaws. It appears to highly reward spot up shooters such as Matt Bonner, Anthony Morrow, and Eddie House. These players do not handle the ball with much frequency; many of their touches result in immediate shots, cutting their capability for turnovers relative to other players who dribble the ball. These players are also rewarded since 3-point marksmen tend to have a high TS%.

It also tends to ignore other measurable that have a positive (but diminished) correlation with winning. Passing PGs such as Nash and Deron Williams are hurt by a lack of an AST component. Energy guys like David Lee and Anderson Varejao (15th among PFs) are rewarded for rebounding, but not punished for a lack of shot-blocking ability. Of course, having a center who can send back a couple shots a game (and alter numerous others) is of value. Also, the TS% of players is considered without relation to the volume of shots taken. A player with a TS% of 58% on 20 attempts per game would be of much higher value than one with a TS% of 59% on 6 shots a game. Finally, this formula treats all three of its components equally, while I’m sure they are of differing importance. Perhaps there are easy ways to fix these flaws, but considering my aim was to develop a simple method for player efficiency, any correction would likely make the math a lot more complicated.

I applaud anyone who actually waded through this sea of information. It was as much a thought experiment as anything else, and I hope we all learned something from it.

This FanPost is a submission from a member of the mighty Golden State of Mind community. While we're all here to throw up that W, these words do not necessarily reflect the views of the GSoM Crew. Still, chances are the preceding post is Unstoppable Baby!

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