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Foul Trouble?
NBA Performance by Team Foul State

Watching an NBA game, you'll hear commentators remark that a team is "now in the penalty" and the tone often suggests that this has major implications. While it seems obvious that having a team in foul trouble should provide an advantageous position for the offense, we've never seen a study published that looked at how being in the bonus changes your expectations, particularly on a points per possession basis. Thankfully, this is something we can immediately rectify...

1) League Wide Numbers
So for starters we track possessions by the following states:

0 fouls left before bonus (eg in bonus from this point on)
1 foul left
2 fouls left
3 fouls left
4 fouls left

So at the start of a game, both teams are at zero team fouls committed for the quarter, and have four to give before they enter the bonus, thus are in the '4 fouls left' category. The first team foul knocks them to '3 fouls left' and so on. The only real thing to note is that when the quarter enters the final two minutes, only two states remain possible -- 0 fouls left (in bonus) or 1 foul left, since the second foul in the last two minutes puts a team into the bonus.

The first place to start is simply how the expectations change as the foul state changes:

Stat
4 Fouls Left
3 Fouls Left
2 Fouls Left
1 Fouls Left
0 Fouls
(In Bonus)
 Points per 100 Possessions 102.0  105.1  106.1  105.9  112.0 
 Field Goal % .450  .456  .450  .450  .433 
 Effective FG % (eFG) .480  .488  .486  .487  .471 
 Assisted FGM 61%  60%  60%  58%  57% 
 Blocked FGA 5.9%  6.3%  6.1%  6.2%  6.0% 
 Free Throws per Possession .21  .22  .23  .23  .44 
 Offensive Rebound% 29.9%  29.6%  31.4%  31.7%  31.2% 
 Turnover/Possession 16.5%  16.3%  16.3%  16.5%  15.1% 

So being in the bonus shifts the points per 100 possessions mark to 112.0 on a leaguewide average (all 30 teams count the same in the average), which is some improvement over the other states, but probably not as much as most people would expect. To put it another way, getting into the bonus shifts your expectations such that a typical NBA team would gain about .07 points per possession over not being in the bonus.

Curiously, while one would expect the free throws per possession to be much higher in the bonus, it wouldn't seem obvious that the field goal percentage would drop at the same time. In fact you might have guessed the opposite would be true -- with the defense in the bonus they would contest shots less aggressively. Perhaps the reason for this is that offenses do adjust their strategy to try and initiate more contact, go inside, drive to the hoop, etc which does achieve more fouls, but at the expense of a tougher shot when they don't get the whistle.

Now, one problem is there are some inherent biases in these states -- for instance good offensive teams will typically be more adept at drawing fouls, thus they will be more often close to the bonus or in the bonus, whereas poor offensive teams will be in the 'many fouls left to give' stage on offense. Another bias is officiating -- if the officials are not calling many fouls just because they are choosing to let things go a bit more in a given game, then the points per possession would be expected to go down, and these types of game would have more time spent in the 'many fouls to give' categories. Then there are all the intentional fouls at the end of games, that bias the bonus state up a bit as well.

One more point to consider before moving on to team specific numbers is just how often a team is in each state on average over the course of a game:

21% - 4 Fouls left to give
18% - 3 Fouls left to give
15% - 2 Fouls left to give
16% - 1 Fouls left to give
30% - 0 Fouls left/In Bonus

So in fact, teams spend about 30% of the time in the bonus, hence 70% of the time out of the bonus.

2) Team Offense by Foul State
The league averages above are a useful reference point, but it would seem likely that different teams might be more or less able to take advantage of having the opposing defense in the bonus state. Thus a team-by-team look at the key points per 100 possessions number is in order:

#
Team
4 Fouls left
3 Fouls left
2 Fouls left
1 Fouls left
0 Fouls left
In Bonus
1
SEA
106.3  118.9  119.5  108.4  118.4  31% 
2
LAL
104.4  105.7  104.3  109.6  117.2  28% 
3
MIA
104.4  108.0  118.9  111.0  117.2  35% 
4
UTA
96.0  102.7  100.0  104.9  117.1  33% 
5
PHO
111.1  111.0  124.0  117.9  116.2  29% 
6
CLE
101.0  107.6  112.1  98.5  116.1  28% 
7
SAC
105.9  113.7  103.4  105.3  115.8  29% 
8
MIN
104.6  101.3  106.1  112.1  115.5  26% 
9
LAC
101.6  102.1  104.5  106.3  115.4  31% 
10
IND
103.6  102.8  94.3  107.0  114.8  30% 
11
DEN
102.2  101.4  101.0  102.5  113.7  32% 
12
TOR
102.8  104.8  107.0  110.4  113.3  27% 
13
DAL
105.6  107.0  111.0  112.8  113.1  32% 
14
MIL
104.0  108.4  104.9  102.0  113.1  31% 
15
HOU
97.2  107.7  106.3  107.0  113.0  28% 
16
BOS
99.1  109.3  113.3  105.1  112.9  32% 
17
WAS
104.9  108.0  107.3  103.3  112.7  31% 
18
DET
101.2  104.7  104.8  104.8  112.3  29% 
19
NYK
102.5  101.4  107.0  109.0  111.6  26% 
20
SAS
106.8  111.5  109.3  109.7  110.8  31% 
21
GSW
100.1  98.8  104.2  99.0  110.3  26% 
22
PHI
101.3  104.2  99.1  102.7  110.0  31% 
23
POR
99.1  101.3  103.6  102.4  109.7  27% 
24
ORL
106.9  102.6  106.1  105.0  108.8  32% 
25
MEM
103.6  110.0  104.6  104.2  108.5  30% 
26
CHA
96.0  100.3  102.7  101.2  106.4  30% 
27
NOH
89.7  99.7  105.5  104.6  106.2  25% 
28
ATL
98.8  97.4  98.8  98.6  106.1  28% 
29
NJN
99.2  101.8  97.7  104.6  102.1  30% 
30
CHI
99.5  98.7  103.0  107.9  101.2  31% 

The mix of top teams sorted by the efficiency per possession in the bonus is an odd one -- you have some powerhouse teams (Seattle, Miami, Phoenix), but also a number of clubs that aren't going to even make the playoffs (Lakers, Jazz, T-Wolves, Clippers). On the other hand, of the bottom ten teams, eight have losing records at this point in time.

If you sort by the percentage of the game a team is in the bonus on offense, it's:

35% Miami
33% Utah
32% Denver
32% Dallas
32% Boston
...
27% Portland
26% Minnesota
26% New York
26% Golden State
25% New Orleans

Shaq has helped Miami in a number of ways, but getting the team into the bonus quickly on offense may be one of his less emphasized contributions. Utah meanwhile seems to be doing all right on offense...perhaps defense might be the problem? Let's check!

3) Team Defense by Foul State

#
Team
4 Fouls left
3 Fouls left
2 Fouls left
1 Fouls left
0 Fouls left
In Bonus
1
DET
101.9  100.8  101.5  102.4  102.2  25% 
2
PHI
100.6  108.4  107.5  105.6  104.7  31% 
3
SAS
94.5  92.2  99.0  102.6  105.8  25% 
4
DAL
102.4  103.8  107.1  104.5  106.2  32% 
5
HOU
95.1  105.8  106.8  99.4  107.4  31% 
6
CHI
97.4  102.2  99.9  97.1  108.1  32% 
7
DEN
101.2  100.1  103.9  105.0  109.2  31% 
8
MEM
97.0  100.3  102.5  102.0  109.6  33% 
9
CLE
103.2  102.3  100.7  108.0  110.2  30% 
10
MIA
98.4  101.4  103.6  103.8  110.2  28% 
11
GSW
100.4  109.2  111.7  106.8  110.4  28% 
12
BOS
100.2  104.0  110.8  107.0  111.2  35% 
13
NJN
101.3  103.2  101.1  99.0  111.5  34% 
14
PHO
104.0  104.7  111.1  108.5  112.5  23% 
15
TOR
104.6  109.0  108.8  106.8  113.5  30% 
16
CHA
100.4  111.2  114.4  106.4  113.7  32% 
17
MIL
105.6  109.9  105.8  111.1  113.8  28% 
18
ORL
106.0  104.3  103.6  105.5  113.9  30% 
19
POR
106.4  104.5  105.2  107.7  114.1  27% 
20
SEA
107.5  102.9  108.3  108.4  114.6  33% 
21
SAC
97.3  104.7  109.8  113.5  115.0  24% 
22
WAS
99.1  102.9  107.4  113.6  115.1  28% 
23
NYK
107.6  106.0  109.9  103.3  115.3  28% 
24
ATL
105.9  113.3  110.4  108.3  115.4  32% 
25
LAL
107.7  112.5  110.5  103.6  115.7  28% 
26
MIN
103.3  109.0  100.3  105.8  115.9  29% 
27
IND
101.5  100.7  99.4  109.4  116.2  28% 
28
LAC
102.5  105.5  106.4  104.1  116.2  28% 
29
NOH
103.1  109.4  106.5  108.2  116.3  30% 
30
UTA
102.7  109.3  109.9  109.8  116.7  39% 

Those Pistons have had a kind of up and down season so far given the expectations, but they still know how to play defense, and they are the least bothered of all NBA teams by being in the penalty. In truth, they may even enjoy seeing opposing offenses try to drive it into the paint more what with Big Ben manning the goal line. The Spurs are the best by far on defense when not in foul trouble, and still a might good third when they are dealing with a bonus situation, but that alone makes you wonder doesn't it? Perhaps a part of the San Antonio defensive strategy revolves around "non shooting hinderance" (eg holds, bumps, checks) and refs who call those things more strictly can put them somewhat off their game on defense.

And yes, ahem, Utah checks in as the worst in the league on defense when they've entered a bonus situation. Indeed, the defensive ranks seem to carry more weight for a team's won-lost standing, since all of the top ten could be in the playoffs if the Sixers can hold on.

If you sort by the percentage of the game a team is in the bonus on defense, it's:

23% Phoenix
24% Sacramento
25% Detroit
25% San Antonio
27% Portland
...
33% Memphis
33% Seattle
34% New Jersey
35% Boston
39% Utah

The Suns and Kings can sometimes seem too busy pushing it on offense to worry about fouling, but the fact that hard-nosed defenses like the Spurs and Pistons can stay out of foul trouble is impressive, and a testament to their abilities. On the other hand, having an inclination to foul may not be the worst thing either, since four of the bottom five teams may be playoff bound. Pat Riley had the Knicks adopt a "no layups" philosophy to playing defense, and obviously that strategy can be more than a little effective, albeit ugly.

4) Correlating performance in Foul States to Wins
The less mathematically inclined may want to skip the rest of this article, but it seems a worthwhile point to explore -- what correlation is seen between some of these foul state numbers and a team's record?

Foul State
Offense
Correlation
Defense
Correlation
Net
Correlation
95% CI
4 fouls left
.71
-.36
.80
.61 to .90
3 fouls left
.73
-.71
.85
.71 to .93
2 fouls left
.61
-.36
.76
.56 to .88
1 fouls left
.61
-.20
.53
.22 to .75
In Bonus
.44
-.48
.72
.49 to .86
Bonus Poss%
.42
-.33
.61
.31 to .79

So as it turns out, with this very limited sample (n=30), the top correlators with winning percentage are actually the points per possession numbers when a team is not in foul trouble -- typically the early parts of a quarter. The "In Bonus" performance was about the lowest correlation to wins. Still, the correlations are pretty good for say net offense minus defense on the 4 and 3 fouls left states. Or even for that matter, the straight offense on 4/3 fouls left. What this says is that it's important to be able to score efficiently when you don't have the opposing team in foul trouble, or when the refs aren't calling a lot of fouls, or just simply 'get out of the gate' well at the start of a quarter.

If you run a quick regression on the pts per possession for each offensive and defensive foul state, you get a nifty .95 R^2 (and .93 adjusted R^2), with the following four categories topping the order of importance:

Offense, 4 fouls left
Defense, in Bonus
Offense, 3 fouls left
Offense, in Bonus

However, the standard errors are so large that it could easily get re-ordered in a hurry, but if you take the results at face value, we're saying the performance in the bonus is actually quite a good differentiator between good and bad teams, and offense without having already collected fouls is of primary concern. It makes sense in some ways -- if you can score without relying on the refs to give you a call that's clearly a plus, and if you can make the most of the situation in games where the refs are handing out lots of fouls, why you're a team that is able to adapt well to the circumstances!


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