Expected Performance and the 4 Factors

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). See this post (Pension Plan Puppets dCorsi) for the details. Lots of good stats work going on in hockey lately. 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 to put together these stats. I started with a list of each teammate a player has played with this year (note that I compiled this information prior to the Nets game). I compiled how many possessions they've played together with the player of interest, 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 team would perform while they were on the court if that player put in a performance typical for the team. In other words, that player's expected performance.

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.

I also see the concerns some will have with small sample size. It is indeed early, but you work with what you have. And since this is possession based, the number of possessions is actually pretty significant at this stage of the season, except for the deep bench players on the team, who will be excluded.

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. 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 (divided by 2, so the offense and defense sum to the weights shown above) 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 1.4%, and his defensive impact comes to 4.3% (remember that in DRTG, an increase is a bad thing). So applying those to a 100 RTG team gives an ORTG of 101.4 and a DRTG of 104.3. These calculate to a pythagorean win% of 40%, or 33 wins in an 82 games season. So by my method, we can say that DeRozan is a 33 win player. This is not great.

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 post the impact numbers, RTGs and wins for each player below. If anyone wants to see the expected performance and actual performance numbers, I can post them as well, but am leaving them off so this post doesn't end up any longer than it has to be.

Rudy Gay:

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: 96.9
DRTG: 101.5
Wins: 28


Kyle Lowry:

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: 100.4
DRTG: 99.2
Wins: 44

Amir Johnson:

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: 101.4
DRTG: 96.3
Wins: 55

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.

Jonas Valanciunas:

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: 94.3
DRTG: 98.6
Wins: 29

Well that's surprising. With the huge turnover impact he has, and the fact that the team's defense seems to suffer when he plays, there doesn't seem any way around the fact that he's had a rough start to the season. One thing to note is that his free throws from fouls drawn and committed are really low - this could be attributed to his lack of playing time at the end of quarters when teams are in the penalty. I tried excluding free throws from the calculation for him to see if that was skewing the win number, but it seems to have little effect.

Terrence Ross:

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: 101.7
DRTG: 97.9
Wins: 52

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.

Tyler Hansbrough:

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: 99.6
DRTG: 99.3
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.

Landry Fields:

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: 101.2
DRTG: 103.1
Wins: 36

Solid everywhere, great rebounder, good defender, giving back a little too much with a LOT of defensive fouls and not forcing enough turnovers.

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).


Final bit of fun: verifying that the numbers I came up with for wins calculate out to a value that reflects the performance thus far this season. I've excluded the players with less than 200 possessions played, and they account for only 11% of total possessions, so this seems like a good approach. If you take a possessions-played-weighted-average of the wins calculated here you get a win % of .476, which translates to a 6.2-6.8 record after 13 games (the sample over which this data was taken). That's pretty darn close to our actual 6-7 record. Probably meaningless and I wouldn't feel any worse about this approach if it was off by a win or two early on, but nice to see. Also, if used predictively (and I've done zero analysis to see whether this is a good idea), suggests we'll end up with 39 wins - which sounds about right for this team.


As always, please feel free to critique, comment or question any part of this. Any suggestions on how to better use this data, or what limitations I might have overlooked, would be much appreciated.


Edited to improve ORTG and DRTG calculation.

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