Expected Performance and The Four Factors
Old 11-26-2013, 11:01 AM   #1 (permalink)
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Hi all,

Another long and complicated post with lots of stats fun.

I peruse a lot of hockey and baseball stats posts, because I'm interested in that sort of stuff. Now, baseball is the king of advanced stats, but it is hard to translate any of that stuff to basketball due to the different and more fluid nature of the game (as well as the effects of teammates on a player's performance). Hockey on the other hand is making great strides in finding simple statistics to measure important aspects of the game. Corsi is a great example (simply, number of shots on net, as well as missed and blocked for each team). It is a countable measure that represents possession, which has been shown to predict success for a team.

Now, someone over at Pension Plan Puppets developed a statistic that looks at how a player should be expected to perform based on his teammates play, and whether they under and over achieve (dCorsi I think he called it). I'm going to try something similar here, with a twist. There's no Corsi for basketball, but there are the 4 factors. So I'm going to use those, and then project the impacts onto an average team to see the sort of players we have.

-----

Now, exactly how do I do this? I used the awesome database at nbaWOWY.com to put together these stats. I started with a list of each teammate a player has played with this year. I compiled how many possessions they've played together, and how many away from the player of interest. Then I pulled the team's performance in the 4 factors (offensively and defensively) for each teammate while NOT playing with the player. So that gives me 10 numbers for each teammate (possessions with, possessions without, 4 factors without, defensive 4 factors without).

Now, I compile those into a weighted average (weighted by possessions played WITH the player) to get 8 expected performance values. This is how the player's teammates would perform, in theory, if they were playing with a perfectly average (for the team) player.

Now, I had some hesitation about whether the performances of the starters would be dragged down, since the bench players would obviously face easier competition. But looking at it, I decided there should be limited effect there. The possession-weighted average means that by far the biggest impact on these numbers comes from the players they play with most - for example, DeRozan is most impacted by Gay, Lowry, Amir and Jonas, with a total of 2686 possessions with them. He spends 1048 possessions combined with the entire rest of the team, so you can see that about 75% of this stat comes from those 4 teammates.

So, for a player like DeRozan, you get an expected performance as follows (note that these are TEAM numbers, not individual numbers):

Value: Team | Opponent
eFG%: 46.8% | 45.8%
ORB%: 28.1% | 21.8%
FT/100: 20.0 | 18.3
TOV%: 13.3% | 16.4%

So, now we look at his actual performance, to see how he did relative to expectations.

Value: Team | Opponent
eFG%: 46.4% | 50.2%
ORB%: 30.2% | 24.7%
FT/100: 21.3 | 17.8
TOV%: 12.9% | 14.8%

And, the difference between the two in percentage of expected performance:

Value: Team | Opponent
eFG%: -0.8% | +9.6%
ORB%: +7.4% | +13.3%
FT/100: +6.8% | -2.7%
TOV%: -2.7% | -9.8%

So, quick takeaways. He's not killing the eFG%, so he's not the biggest problem in terms of the chucking we've seen (spoiler alert, Gay is up next). He also allows the other team to have their way in terms of eFG%. Another indicator that his defense is still lacking. Similarly, he allows way too much offensive rebounding (possibly because of his perimeter defense needing a lot of help from the bigs, drawing them off their own man). We also see that the team forces less turnovers while he's on the court. He does help the team draw fouls, one of his strengths.

Now, all that is very interesting and I'd be glad to dig up that info just for those numbers. But there's some more math I want to do. And once I finish the whole team and can compare my results to reality, I'll be able to confirm if this is a good approach. But for now, let's take a look at those 4 factors. By the original definition of the 4 factors, they are of differing importance. eFG% is by far the most important of the 4, and is assigned by Dean Oliver a weight of 0.4. The weights are as follow:

eFG%: 40%
TOV%: 25%
ORB%: 20%
FT/100: 15%

Applying these weights to the differences above in each of the 8 categories (4 offensive, 4 defensive) gives us a total percent difference on offense and on defense. I then apply that percent difference to a 100 ORTG and 100 DRTG fictional team, based on the assumption that the 4 offensive factors impact offense and the 4 defensive factors impact defense. The resulting ORTG and DRTG are combined via pythagorean win prediction.

WIN%(PYTH) = ORTG^14 / (ORTG^14 + DRTG^14)

So, using DeRozan's numbers, his offensive impact comes to 2.9%, and his defensive impact comes to 8.6% (remember that in DRTG, an increase is a bad thing). So applying those to a 100 RTG team gives an ORTG of 102.9 and a DRTG of 108.6. These calculate to a pythagorean win% of 32%, or 26 wins in an 82 games season. So by my method, we can say that DeRozan is a 26 win player. This is not good. I'm not going to jump to any conclusions yet based on this figure, as I want to see where the rest of the team lands using this methodology. Not promising though.

Please let me know if you see any holes in this method, or a better way to integrate the 4 factors, or just if you have comments on a player's impact numbers.

I'll keep updating as I go. Rudy Gay next.
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Old 11-26-2013, 11:54 AM   #2 (permalink)
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Very interesting read, thanks Danh. Can't wait to see how other players compare
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Old 11-26-2013, 12:56 PM   #3 (permalink)
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Rudy Gay:

Expected Performance:

Value: Team | Opponent
eFG%: 48.8% | 47.0%
ORB%: 29.0% | 25.3%
FT/100: 24.8 | 19.3
TOV%: 12.6% | 16.9%

Actual Performance:

Value: Team | Opponent
eFG%: 46.0% | 50.2%
ORB%: 30.3% | 23.5%
FT/100: 20.0 | 17.5
TOV%: 13.6% | 14.7%

Difference:

Value: Team | Opponent
eFG%: -5.7% | +6.8%
ORB%: +4.7% | -7.1%
FT/100: -19.5% | -9.6%
TOV%: +8.0% | -12.8%

ORTG: 93.7
DRTG: 103.0
Wins: 17

Ouch.
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Old 11-26-2013, 01:20 PM   #4 (permalink)
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Kyle Lowry:

Expected Performance:

Value: Team | Opponent
eFG%: 46.1% | 46.4%
ORB%: 31.8% | 24.6%
FT/100: 21.9 | 18.9
TOV%: 14.1% | 13.6%

Actual Performance:

Value: Team | Opponent
eFG%: 46.7% | 50.1%
ORB%: 29.3% | 23.8%
FT/100: 21.0 | 17.7
TOV%: 12.7% | 15.3%

Difference:

Value: Team | Opponent
eFG%: +1.3% | +8.0%
ORB%: -7.9% | -3.4%
FT/100: -4.3% | -6.5%
TOV%: -10.1% | +12.5%

ORTG: 100.8
DRTG: 98.4
Wins: 48
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Old 11-26-2013, 01:26 PM   #5 (permalink)
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Amir Johnson:

Expected Performance:

Value: Team | Opponent
eFG%: 45.1% | 49.3%
ORB%: 28.0% | 23.2%
FT/100: 26.0 | 22.8
TOV%: 14.2% | 14.4%

Actual Performance:

Value: Team | Opponent
eFG%: 47.5% | 49.5%
ORB%: 30.8% | 23.6%
FT/100: 18.1 | 14.5
TOV%: 12.4% | 15.8%

Difference:

Value: Team | Opponent
eFG%: +5.3% | +0.4%
ORB%: +10.0% | +1.8%
FT/100: -30.3% | -36.7%
TOV%: -13.0% | +10.0%

ORTG: 102.8
DRTG: 92.5
Wins: 67

Wow. It's been noted that Amir has not been drawing fouls at all, but here it shows that the entire team is suppressing both fouls committed AND drawn while he's on the floor. Anyway, Amir gonna Amir, as usual.
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Old 11-26-2013, 01:50 PM   #6 (permalink)
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Hurry up with JV!
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Old 11-26-2013, 02:12 PM   #7 (permalink)
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And people said talked s**t about me saying that Amir + KL are more important than DD and RG.
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Old 11-26-2013, 02:14 PM   #8 (permalink)
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Jonas Valanciunas:

Expected Performance:

Value: Team | Opponent
eFG%: 46.2% | 46.4%
ORB%: 30.3% | 22.8%
FT/100: 25.7 | 22.9
TOV%: 11.2% | 14.1%

Actual Performance:

Value: Team | Opponent
eFG%: 46.3% | 50.8%
ORB%: 29.3% | 24.6%
FT/100: 18.5 | 14.6
TOV%: 14.1% | 15.6%

Difference:

Value: Team | Opponent
eFG%: +0.3% | +9.6%
ORB%: -3.2% | +7.7%
FT/100: -28.2% | -36.2%
TOV%: +26.4% | +10.6%

ORTG: 88.7
DRTG: 97.3
Wins: 18

Well that's surprising. I'm definitely starting to think that my calculation is making the ORTG and DRTG too extreme. Still, with the huge turnover impact he has, and the fact that the free throws go way down when he plays, there doesn't seem any way around the fact that he's had a rough start to the season.

Any suggestions on how else to go from the impact numbers to ORTG and DRTG? I can't come up with any reasonable alternatives.
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Old 11-26-2013, 03:11 PM   #9 (permalink)
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Terrence Ross:

Expected Performance:

Value: Team | Opponent
eFG%: 45.2% | 51.8%
ORB%: 28.9% | 24.6%
FT/100: 21.1 | 17.1
TOV%: 12.4% | 14.5%

Actual Performance:

Value: Team | Opponent
eFG%: 47.5% | 45.9%
ORB%: 30.4% | 23.5%
FT/100: 25.5 | 21.1
TOV%: 13.7% | 15.7%

Difference:

Value: Team | Opponent
eFG%: +5.1% | -11.3%
ORB%: +5.1% | -4.6%
FT/100: +20.9% | +23.3%
TOV%: +10.8% | +8.6%

ORTG: 103.5
DRTG: 95.9
Wins: 61

T-Ross the superstar. This shows just how much he's meant to the bench this year - his expected performance is pretty terrible (based on the terrible players he plays with) and so since he actually performs pretty solidly (read: actually pretty awesome eFG% suppression), he just rocks this stat. He gives back a bit with increased fouls, but considering the low eFG% against, high eFG%, and high TOV% for the opposition, this high mark looks well earned.
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Old 11-26-2013, 04:08 PM   #10 (permalink)
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Tyler Hansbrough:

Expected Performance:

Value: Team | Opponent
eFG%: 46.7% | 48.7%
ORB%: 28.8% | 22.6%
FT/100: 18.9 | 20.0
TOV%: 11.3% | 14.1%

Actual Performance:

Value: Team | Opponent
eFG%: 46.8% | 48.6%
ORB%: 30.6% | 25.1%
FT/100: 24.7 | 18.6
TOV%: 14.3% | 15.4%

Difference:

Value: Team | Opponent
eFG%: +0.1% | -0.2%
ORB%: +6.3% | +11.0%
FT/100: +30.5% | -6.9%
TOV%: +26.8% | +9.5%

ORTG: 99.2
DRTG: 98.7
Wins: 42

Great offensive rebounder and awesome at drawing fouls, gives it all back via turnovers and being weak on the defensive glass. Still, very average, which exceeds my expectations of him.
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Old 11-26-2013, 04:15 PM   #11 (permalink)
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Trade em all, build around albaTROSS
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Old 11-26-2013, 04:18 PM   #12 (permalink)
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I'll be the first to call small sample size

Guys, dont forget these ratings only show player performance relative to expected, not absolute
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Old 11-26-2013, 04:18 PM   #13 (permalink)
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Quote:
Originally Posted by DanH View Post
Well that's surprising. I'm definitely starting to think that my calculation is making the ORTG and DRTG too extreme. Still, with the huge turnover impact he has, and the fact that the free throws go way down when he plays, there doesn't seem any way around the fact that he's had a rough start to the season.
I don't know that it is.

I would think that free throws are very much impacted by the time a player plays in the quarter and whether either team is in the bonus. Not sure how you can account for a player that plays the first 8 minutes of 3 quarters this way.
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Old 11-26-2013, 04:31 PM   #14 (permalink)
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Quote:
Originally Posted by JoeyJoJo Shabbadu View Post
I don't know that it is.

I would think that free throws are very much impacted by the time a player plays in the quarter and whether either team is in the bonus. Not sure how you can account for a player that plays the first 8 minutes of 3 quarters this way.
This is a great point. Very good point. However, FT is the weakest correlation with wins and he's actually gaining on the defensive end the same as he's losing on the offensive end. Removing FT's from the calculation actually yields a slightly lower win value. It's the turnovers that are killer for Jonas, as well as the opponent eFG%. I should have spotted the FT discrepancy though, even though it turns out not to matter.
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Old 11-26-2013, 04:33 PM   #15 (permalink)
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Quote:
Originally Posted by Shifty.py View Post
I'll be the first to call small sample size

Guys, dont forget these ratings only show player performance relative to expected, not absolute
Yes, important to remember - it just shows who is excelling IN THEIR ROLE - doesn't show whether they would be any good placed in different circumstances.

And of course small sample sizes are unavoidable at this stage of the season, so keep that in mind. But on a possession basis, the samples mostly are not all that small, and the smallest samples factor into the calculation the least due to the weighted averages.
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Old 11-26-2013, 04:48 PM   #16 (permalink)
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To paraphrase Rasheed " The numbers don't lie!!!" The win rate for Amir and Rudy and Jonas seem to correlate with eye test data. Jonas is struggling and seems to be forcing his offense while defense is a little better. I was really surprised at T Ross result. He looks on occasion to be the real deal but often coasts...
His effective field goal percentage is way up . In the land of the blind the one eyed man is king...Hope he continues to grow and gets more minutes from DC...

Interesting work, thanks for the numbers...Now if Rudee can get his offense more efficient
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Old 11-27-2013, 08:40 AM   #17 (permalink)
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Last one, as the rest of the team has less than 200 possessions each to their name (prior to last night), so the samples would get pretty small (Fields, this last one, has 339 possessions).

Landry Fields:

Expected Performance:

Value: Team | Opponent
eFG%: 48.0% | 50.1%
ORB%: 28.6% | 25.9%
FT/100: 22.5 | 16.9
TOV%: 13.0% | 15.7%

Actual Performance:

Value: Team | Opponent
eFG%: 45.9% | 48.3%
ORB%: 34.0% | 21.7%
FT/100: 23.0 | 23.6
TOV%: 13.0% | 12.6%

Difference:

Value: Team | Opponent
eFG%: -4.3% | -3.7%
ORB%: +18.8% | -16.1%
FT/100: +2.3% | +39.8%
TOV%: -0.3% | -19.8%

ORTG: 102.5
DRTG: 106.2
Wins: 31

Solid everywhere, great rebounder, good defender, giving back way too much with a LOT of defensive fouls and not forcing enough turnovers.
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Old 11-27-2013, 08:46 AM   #18 (permalink)
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So, after that last one, I'll take a weighted average (by possessions) and calculate the expected win% for the team (using only the players I calculated - the rest amount to only 11% of the possessions used for the team).

Total win % = .455.

That amounts to a record of 5.9 - 7.1 after 13 games. Pretty close to our 6-7 (prior to last night, since I didn't include last night's stats in the calculations). Also predicts a final record of 37 wins if the performances hold up. So maybe this method holds some value. Pretty time intensive, but could be automated easily enough with access to a database like nbaWOWY.
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Old 11-27-2013, 09:24 AM   #19 (permalink)
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I was going to ask what you used to do the math. It seems like it should be a reasonably straightforward programming problem, but pretty cumbersome to do by hand. It would be interesting to automate it and then do it for the entire league.

I like the conceptual simplicity of the formula and the comparison to the opponent's expected performance. The latter piece is often lost or ignored in analytics (PER, Win Shares).
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Old 11-27-2013, 09:42 AM   #20 (permalink)
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It would a fairly straightforward programming problem, but I don't have direct access to the data. I had to pull it manually from nbaWOWY.com. So I set up a simple excel spreadsheet, making the calculation itself instantaneous, but the data entry was the bottle neck for me. That's why I did it for a subset of the team rather than the entire team, and won't be updating the numbers regularly.
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