Predicted FTA vs. Actual FTA

[ambchang]

After compiling the data for the 05 – 06 NBA regular season, I was able to create a model to predict the number of FTAs a player should have based on his shot attempts on 3 pters, outside shots excluding 3 pters, inside shots excluding dunks and tips, dunks, and tips shots.
The model has an R-Sq of 0.849, and Multiple R of 0.922, which means that it gives an extremely high level of accuracy, and is a decent predictor.
The P-value of all the numbers are pretty close to zero, with the tip shot attempts at 0.026 (which is far greater than the next worse predictor, 3PTA P-Value at 0.000358), in other words, all of these values are good predictors of FTA of a particular player.
I then compare this predicted FTA with actual FTA value, and project it to per 48 minutes, this gives a good comparison on a comparable time basis. For the team numbers, I took the actually numbers rather than the projected per 48 minute numbers, and added the predicted FTA difference of all the players belonging to one team.
I removed all the players with less than 10 minutes of playing time, then ranked them.
This way, it gives an indication of the difference between expected FTA vs real FTA for all the teams with significant players factored in (garbage time should be removed), and the results are as follows:

TEAM:

Rank Team FT Difference
1 NYK 1061.35
2 UTH 700.56
3 DAL 666.04
4 WAS 530.21
5 CLE 335.66
6 IND 275.55
7 NJN 167.37
8 HOU 129.86
9 SAC 102.99
10 SEA 77.65
11 ATL 11.19
12 MEM -58.12
13 NOH -96.63
14 LAC -108.43
15 MIA -122.22
16 ORL -128.29
17 LAL -138.11
18 DEN -168.09
19 GSW -198.63
20 TOR -266.2
21 PHI -286.14
22 CHA -294.17
23 BOS -324.28
24 CHI -328.98
25 MIN -357.62
26 DET -358.74
27 POR -371.54
28 SAS -534.59
29 MIL -598.48
30 PHO -1167.01

Not surprisingly, a run and gun team with a philosophy of not fouling comes out at the bottom (fast break points are usually layups or dunks, which skews the model), and a guard oriented team like the Knicks get the benefit of the doubt from the zebras over the season.

INDIVIDUAL PLAYERS:

1 NYK Steve Francis 512.184
2 DET ChaunceyBillups 339.8756
3 BOS Paul Pierce 337.4764
4 WAS Gilbert Arenas 326.105
5 UTH Jarron Collins 304.2742
6 UTH Andrei Kirilenko 282.7088
7 WAS Antonio Daniels 243.0784
8 NYK Eddy Curry 235.5243
9 WAS Michael Ruffin 230.6811
10 LAC Corey Maggette 223.5334
11 SAS Manu Ginobili 221.7554
12 MIA Dwyane Wade 219.6897
13 CLE Anderson Varejao 209.1999
14 NYK Jalen Rose 200.4176
15 PHI Allen Iverson 196.4751
16 DEN Reggie Evans 190.9741
17 CHI Tyson Chandler 189.7837
18 HOU Dikembe Mutombo 187.1032
19 TOR Chris Bosh 186.2103
20 NJN Richard Jefferson 180.27
21 NOH Chris Andersen 175.3615
22 ATL Zaza Pachulia 174.6493
23 NOH Chris Paul 172.8765
24 DAL Dirk Nowitzki 167.4831
25 NYK Jamal Crawford 157.3348
26 LAL Kobe Bryant 154.4837
27 CLE LeBron James 151.9473
28 CHI Othella Harrington151.7997
29 CHA Matt Carroll 145.7785
30 DAL Erick Dampier 141.1516

I will use the same method and run them for the playoffs, and see whether the conspiracy theorists’ arguments hold any water.

BTW, there are limitations to the model. A player like Shaq should get an unusually high number of FTA because other teams intentionally foul him during close games, while a player like Corey Maggette, though scoring most of his points on the perimeter, are quite skilled at drawing contacts on drives.

[ShoogarBear]

Interesting.

I'm getting ready to go to the game, so I'll have to come back to this. A few quick questions:

-Why is it "not surprising" that a "guard-oriented team" would get a highest fraction of the FTs. And I wouldn't call Utah or Dallas guard-oriented teams. Also, I'm not quite sure I understand how you calculated the team results.

-Usually for regression models, the lower the p-value, the more significant the variable is. So the tip shot value of 0.026 should mean that it is a less significant predictor than the 3-pt attempt value.

-I also assume that your p values indicate both positive and negative correlation, i.e., tips and dunks mean more free throws and three-point attempts mean fewer. It would be nice to see the individual correlation coefficients for each variable.

[ambchang]

Sorry for being unclear. The P value of tip shot does show that it is the least significant variable, the other P-values are all quite a bit lower, meaning that they are, at least statistically, significant.
Category Coefficients P-Value
Jump shots 0.27 4.37 E-28
Close shots 0.63 4.5 E-36
Dunk 1.04 4.42E-17
Tip -0.71 0.02594
3PT 0.10 0.000358

Note that all the factors are attempts, not makes.
I am a little puzzled by the negative correlation with Tips, all of the them, I at first hypothesized, should have been positive, because the more shots you take, the more you get fouled, just that the likelihood of getting fouled on a layup is higher than that of a 3pter.
I should also note that if I strictly take FGA as a factor, the R2 value is around 0.75, not bad, but not as close as this model.
As for the NYK comment, I just thought that it makes sense that a guy like Francis and Marbury, who creates their offense through drives, can get a good share of FTAs even though they don't shoot that much from the paint area.
As for why the Jazz and Mavs are that high on the list, I have no idea, can't think of one good reason. I also was surprised that the Spurs finish so low on the list, given their low post heavy offense, but it could be because they lack a penetrator outside of Manu (note Manu gets a good deal of FTs, all the flopping must have worked :lol).