Permaximum Ratings and Rankings (Updated Often)

[permaximum]

Since there is no pure empirical box-score ratings for players (probably because of assist weights) I wanted to make one and called it PTR(Player Total Rating). Used 1997/1998 - 2011/2012 data. I chose 97/98 as the starting point because of 3-point line rule change in 97 summer. I'm especially curious about how PTR will compare to PER when it comes to player effect on team success.

Also, since there is no complete team ranking system, I made one which takes MOV, SOS, HCA, B2B and PACE into account. It's a team-level ranking system as you probably guessed so it doesn't care about injuries.

First; PTR of top 30 players in NBA.

PLAYER TOTAL RATINGS

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      Player             PTR
1. LeBron James         30.63
2. Kevin Durant         29.92
3. Tim Duncan           29.21
4. Andre Drummond       28.41
5. Tyson Chandler       28.20
6. JaVale McGee         27.81
7. Andray Blatche       27.09
8. Carmelo Anthony      26.94
9. Blake Griffin        26.74
10.Anderson Varejao     26.73
11.J.J. Hickson         26.34
12.Robin Lopez          25.79
13.Kobe Bryant          25.33
14.Chris Bosh           25.12
15.Larry Sanders        25.07
16.Serge Ibaka          24.97
17.Chris Paul           24.83
18.Ed Davis             24.83
19.Kenneth Faried       24.77
20.Zach Randolph        24.49
21.Tiago Splitter       24.32
22.Dwight Howard        24.23
23.Al Jefferson         23.80
24.David Lee            23.61
25.Ryan Anderson        23.26
26.Kosta Koufos         23.10
27.Amir Johnson         22.94
28.Derrick Favors       22.81
29.Paul Millsap         22.72
30.James Harden         22.55

Box-Score stats do not represent players' defensive effect other than block and steal (e.g contesting shots, indirectly causing turnovers etc.), superstars' ability to draw double-teams and make contested shots, guards' ability to bring the ball, run plays for the team and create chances. Because of these reasons, you won't really see guards and bruce bowen, ron artest type of defenders at top. Notice Chris Paul at 17 and Kobe at 13. In the same time PTR doesn't like assists as much as PER does too. I have data for past years and I can confirm that there hasn't been any point guard or small players in top 5 except Chris Paul and Dwyane Wade. Only Allen Iverson got into top 10 in a season besides those two although PTR penalises more for misses than PER. IMO it's more about the fact that Iverson was a high-efficiency player in reality (although he has 43% career fg) when it comes to +30% usage players.

Second; team-total PTR of NBA teams and their PTR positions' comparison to MOV positions.

TEAM-TOTAL PTR AND MOV COMPARISON

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Team      PTR   PTR-MOV P

1. LAC	95.92     0
2. OKC	94.53     0
3. MIA	91.74    -1
4. NYK	90.62    -1
5. SAS	89.79    +2
6. DEN	86.07    -6
7. LAL	84.85     0
8. HOU	84.57     0
9. UTA	84.02    -8
10.MEM	82.43    +4
11.GSW	81.05     0
12.ATL	80.70    +3
13.BRK	80.66    -2
14.PHO	80.02   -10
15.BOS	79.92    -1
16.MIN	78.89    +3
17.PHI	78.46    -5
18.POR	77.95    -3
19.MIL	77.29    +1
20.CHI	76.88    +6
21.DAL	75.91    -2
22.CHA	75.59    -8
23.TOR	75.23    -2
24.SAC	74.56    -2
25.NOH	74.06    -3
26.IND	73.98    +16
27.DET	73.74    +7
28.ORL	71.87    +9
29.CLE	68.82    +2
30.WAS	64.30    +1

PTR fails at explaining the MOV positions of 10 teams. DEN, IND, ORL, DET, CHA, UTA, PHO, PHI, MEM and CHI (Misplaced by more than 3). It looks they are either very good or very bad defensive teams compared to their PTR position. Especially Pacers must have top-class bruce bowen, ron artest type defenders. I wonder how PTR compares to PER in this regard. Bear in mind PTR adjust for 100 poss while PER adjust for the league average poss (91.85 atm).

TEAM-TOTAL PER AND MOV COMPARISON

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TEAM      PER   PER-MOV P

1. LAC	86.57     0
2. OKC	86.56     0
3. MIA	84.96    -1
4. NYK	84.25    -1
5. SAS	82.92    +2
6. DEN	79.90    -6
7. LAL	79.28     0
8. HOU	78.88     0
9. UTA	77.60    -8
10.MEM	76.36    +4
11.BRK	75.72    -4
12.GSW	75.65    +1
13.ATL	75.39    +4
14.PHO	74.92    -10
15.BOS	74.23    -1
16.POR	73.66    -5
17.PHI	73.63    -5
18.MIN	73.30    +5
19.MIL	72.32    +1
20.CHI	71.88    +6
21.DAL	71.65    -2
22.CHA	71.34    -8
23.SAC	70.97    -3
24.DET	70.24    +4
25.NOH	70.04    -3
26.TOR	70.00    +1
27.IND	69.49    +17
28.ORL	68.31    +9
29.CLE	65.84    +2
30.WAS	61.13    +1

It looks very similar to PTR. PER fails at explaining the positions of 14 teams (misplaced by more than 3). Overall PER performs 7.55% worse than PTR. No surprise for Pacers. Misplaced by 17 positions. I thought the big difference in assist weights between two metrics would give considerably different results but it seems it's nearly evened out by the difference in other weights.

Last, team rankings. MOV adjusted by SOS, HCA, B2B and Pace. HCA is different for each team. Pace adjustment made for 100 possessions. I think this can be the best and most accurate metric for quickly analyzing team performances in NBA. NoPaceA is the rank without pace adjustment.

TEAM COMPLETE RANKINGS

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   Team C.Rank  NoPaceA
1. LAC  10.72   9.85
2. OKC  9.23    8.56
3. SAS  8.44    8.00
4. NYK  5.90    5.38
5. MIA  5.52    5.09
6. MEM  5.45    4.92
7. ATL  3.51    3.22
8. LAL  2.59    2.44
9. DEN  2.58    2.42
10.CHI  2.08    1.87
11.HOU  2.05    1.99
12.GSW  2.03    1.90
13.IND  1.54    1.39
14.BRK  1.48    1.30
15.MIN  1.33    1.23
16.BOS  0.06    0.06
17.MIL  -0.95   -0.89
18.DET  -1.18   -1.06
19.UTA  -1.74   -1.59
20.PHI  -3.13   -2.82
21.POR  -3.20   -2.92
22.ORL  -3.76   -3.46
23.DAL  -4.23   -3.99
24.TOR  -4.54   -4.11
25.PHO  -4.63   -4.28
26.CLE  -5.10   -4.67
27.NOH  -5.92   -5.20
28.SAC  -7.19   -6.63
29.CHA  -9.16   -8.45
30.WAS  -10.48  -9.56

I think 12-13 NBA champions will be one of the top 5 teams. Clippers, Thunder, Spurs, Heat and Knicks. Memphis would be a big surprise. Lakers... very little chance.

[Mike G]

The team rankings are unchanged whether or not you adjust for pace.
It's often been noted that PER for players do not yield an accurate summary for the teams: offense is rewarded, and defense is not.

I get a pretty large weight on assists by a few adjustments:
-- adjusting players' scoring by their (estimated) % of points which are unassisted; this gives more credit to players who create shots (like point guards) and less to players who are assist-dependent.
-- adjusting to home/away disparity. Basically, a team or player's away assist rate is his real assist rate.
-- adjusting to the team ratio of Pts/FG. A 3FG is 1.5 times the contribution as a 2FG, so an assisted 3FG should be worth more. A lot of team FT also suppresses Assists, so that may get bumped up.

Also I get better correlation between teams and their players' rates when adjustment is made for starters and bench players. A formula estimates the % of opponents who are starters, and this gives the biggest boost to starters who play modest minutes; discounts bench guys who play few minutes.

This factor applies to all production stats equally. PerMax has Javale McGee, Andre Drummond, and Andray Blatche among the top 7 players.
Blatche has started about 1/4 of games and goes 21 mpg. I estimate just 56% of his opponents have been starters, and his totals are factored by .96
The others have not started and avg 19 mpg. At about 46% vs starters, I factor their rates by .90 .

Without such a starter/sub adjustment, you have to use an arbitrary minutes cutoff when you list 'top players'. And you still get not-ready-for-primetime players sneaking in.
Carry on.

[permaximum]

Actually I agree with all the things you said. In fact, at one point I was going to make a more reliable metric which would contain "estimated" (more error) advanced stats like, assisted fg etc.

But in the end, I thought that you or someone else who does this work more seriously, must already have a good metric for that. So that I decided to only go with "point, offensive rebound, defensive rebound, assist, block, steal, turnover, personal foul, 2p miss, 3p miss, ft miss", simply pure box-score stats. I know those other advanced stats could be estimated by using these stats, but I didn't want to make a complex metric with more error margin. If you go down that route, only RAPM will satisfy you.

Result, it's 7.55% better than PER so far and it's enough for me.

As for your claim about pace effect on team rankings, I want you to explain it to me.

Team A : +11 Pace: 90
Team B: +12 Pace 110

Which one is better? I fear I miss something here.

[Mike G]

As for your claim about pace effect on team rankings, I want you to explain it to me.

In the last list in your opening post, teams with and without pace adjustment, the teams are ranked in the same order, top to bottom. There are just a couple which come close to being different, but no.

Result, it's 7.55% better than PER so far and it's enough for me.

I think you're talking about players' minutes-weighted rates summing to team rates.
This could also be achieved by the simple metric (player pts/48)/(opponent team pts/48).
This would sum to (team pts)/(opponent pts), which is precisely equal to team strength.

However, you would be far off on fairly assigning credit to the individual members of a team. You have to give credit for rebounds, assists, etc. That's the tricky part.

Most people, whether they're statistically adept or numerically challenged, will not look at a metric very deeply, when they see subs from bad teams ranked among the top 10 NBA players, and well above known superstars.

Being "better than PER" in some esoteric correlation, while it says something, it is still dubious.

[permaximum]

In the last list in your opening post, teams with and without pace adjustment, the teams are ranked in the same order, top to bottom. There are just a couple which come close to being different, but no.

Actually Dallas and Philadelphia's positions are different with the pace adjustment. I thought you were pointing out a rule like "pace doesn't matter when it comes to team rankings".

I think you're talking about players' minutes-weighted rates summing to team rates.
This could also be achieved by the simple metric (player pts/48)/(opponent team pts/48).
This would sum to (team pts)/(opponent pts), which is precisely equal to team strength.

PTR= Value/min*48 + team pace adjustment.

I was talking about total player Value (in the formula above) of teams (total Value pace adjusted at last). Only to see how it performs. OFC (team pts)/(opponent pts) would be a lot better metric but the goal is not to calculate "team" strength but "player" strength by looking at simple box score stats. Players don't have exact opponents and their averages.

I mean it was a validation method. I am not trying to calculate team strength by using PER or PTR. How do you think a pure box-score metric like PER or PTR's accuracy should be tested then?

If you have a player-metric that takes advanced stats into account, I would test it "this way" again... Actually if you have one, I would like to test it this way to compare Estimation Error of Advanced Stats vs the Reliability of your formula. It would be good to see using advanced stats like assisted FG would worth the error of estimation.

Most people, whether they're statistically adept or numerically challenged, will not look at a metric very deeply, when they see subs from bad teams ranked among the top 10 NBA players, and well above known superstars.

Superstars to who? Check PER and you'll see a lot of subs at top too... This is what you'll get with per minute pure box-score metrics, I can't deny that. But that doesn't mean these type of metrics are invalid. Still you have to show me a proof that supposed superstar is actually better than that sub...

Edit: To make those people happy, I could base the metric on per-game instead of per minute stats and suddenly you would see those "superstars" at top. Then it makes me think coach decisions make superstars...

[v-zero]

Per-minute is fine, the best way to deal with the problem of low-minute subs is to treat the problem in a bayesian rather than frequentist way, and, if you like (though it's not a really big deal) do as Mike suggested and adjust player values by estimating percentage of time spent facing starter-level players rather than replacement-level. The combination of these two will, for the most part, keep your ratings reasonable with few obvious outliers.

[Mike G]

Check PER and you'll see a lot of subs at top too... This is what you'll get with per minute pure box-score metrics, I can't deny that. But that doesn't mean these type of metrics are invalid. Still you have to show me a proof that supposed superstar is actually better than that sub...

Right -- when you go with a pure per-minute stat, you get this kind of stuff.
A "proof" would be debatable at best. But you might poll head coaches, GM's, NBA players, or anyone else and see whether they'd pay more for Chris Paul or for Ed Davis.

I don't even know who Ed Davis is.

[EvanZ]

I use WARP just because it's easy and gives you the "total" productivity of players. (A Bayesian WARP would be even better.)

Is MVP given to the "best" player (e.g. best per possession) or the one who contributed the most total value to his team (e.g. by playing X number of minutes at a high level)?

[DSMok1]

Per-minute is fine, the best way to deal with the problem of low-minute subs is to treat the problem in a bayesian rather than frequentist way, and, if you like (though it's not a really big deal) do as Mike suggested and adjust player values by estimating percentage of time spent facing starter-level players rather than replacement-level. The combination of these two will, for the most part, keep your ratings reasonable with few obvious outliers.

Starter level defenders = replacement level defenders, for all intents and purposes. It's only on the offensive side that the differences arise.

[Mike G]

I am pretty sure that most players get more offensive rebounds when they're coming off the bench.

[v-zero]

Starter level defenders = replacement level defenders, for all intents and purposes. It's only on the offensive side that the differences arise.

Evidence? In any case it's still important to control for opposition strength in general.

[DSMok1]

Starter level defenders = replacement level defenders, for all intents and purposes. It's only on the offensive side that the differences arise.

Evidence? In any case it's still important to control for opposition strength in general.

http://godismyjudgeok.com/DStats/2012/n ... ent-level/

[Bobbofitos]

Check PER and you'll see a lot of subs at top too... This is what you'll get with per minute pure box-score metrics, I can't deny that. But that doesn't mean these type of metrics are invalid. Still you have to show me a proof that supposed superstar is actually better than that sub...

Right -- when you go with a pure per-minute stat, you get this kind of stuff.
A "proof" would be debatable at best. But you might poll head coaches, GM's, NBA players, or anyone else and see whether they'd pay more for Chris Paul or for Ed Davis.

I don't even know who Ed Davis is.

That's an Ed Davis

[permaximum]

Per-minute is fine, the best way to deal with the problem of low-minute subs is to treat the problem in a bayesian rather than frequentist way, and, if you like (though it's not a really big deal) do as Mike suggested and adjust player values by estimating percentage of time spent facing starter-level players rather than replacement-level. The combination of these two will, for the most part, keep your ratings reasonable with few obvious outliers.

Thanks for the suggestion but as I said before, this should be only the simple box-score stat metric like PER. Only difference is PER goes with theoritical approach while PTR goes with empirical approach. I don't want to get into the field of estimation because I would rather use RAPM if I can risk error margin. BTW while we're talking about RAPM do you know which cross validation method is used to find the lambda? I hope it's loocv but I doubt it since it would take "days" for a decent PC to calculate.

@Mike G

Ed Davis can be any NBA player who shoots 55%, grabs a lot of rebounds and turns the ball over 2 times or less per 48 minutes.

Anyway, Chris Paul is at number 13 now and passed our friend Ed. Meanwhile LeBron passed Durant and Kobe climbed up to 16. Here are the updated PTR for players and CRank (saying it again it's simply MOV adjusted by SOS, HCA, B2B and Pace) for teams.

Code: Select all

      Player         PTR

1. LeBron James     30.24
2. Kevin Durant     30.04
3. Tim Duncan       29.19
4. Andre Drummond   28.30
5. JaVale McGee     27.90
6. Tyson Chandler   27.87
7. Andray Blatche   27.79
8. Carmelo Anthony  26.92
9. Anderson Varejao 26.72
10.Blake Griffin    26.72
11.J.J. Hickson     26.53
12.Robin Lopez      26.33
13.Chris Paul       25.13
14.Ed Davis         25.06
15.Chris Bosh       24.98
16.Kobe Bryant      24.97
17.Serge Ibaka      24.85
18.Zach Randolph    24.77
19.Kenneth Faried   24.66
20.Tiago Splitter   24.50
21.Larry Sanders    24.44
22.Dwight Howard    23.90
23.David Lee        23.85
24.Derrick Favors   23.85
25.Kosta Koufos     23.60
26.Al Jefferson     23.59
27.Amir Johnson     23.43
28.Paul Millsap     23.00
29.James Harden     22.89
30.Ryan Anderson    22.89

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   TEAM    C.Rank  NoPaceA

1. LAC     10.16   9.32
2. SAS     8.75    8.27
3. OKC     8.68    7.99
4. MIA     7.03    6.50
5. NYK     6.12    5.59
6. MEM     5.24    4.74
7. HOU     3.42    3.29
8. ATL     2.94    2.70
9. DEN     2.29    2.15
10.LAL     2.09    1.97
11.CHI     1.79    1.61
12.BOS     1.70    1.56
13.IND     1.59    1.43
14.GSW     1.34    1.26
15.MIN     1.28    1.18
16.BRK     0.97    0.86
17.MIL    -1.62   -1.51
18.DET    -1.62   -1.46
19.UTA    -1.87   -1.70
20.ORL    -2.58   -2.37
21.POR    -2.72   -2.48
22.PHI    -2.99   -2.68
23.DAL    -3.58   -3.38
24.PHO    -4.61   -4.26
25.CLE    -5.11   -4.68
26.NOH    -5.91   -5.19
27.TOR    -5.91   -5.37
28.SAC    -7.62   -7.03
29.CHA    -9.17   -8.49
30.WAS    -10.76  -9.81

[EvanZ]

Can you explain how the ratings are "empirically determined"? Also, what does a rating of 30 mean in terms of wins/losses?