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Should Teams Foul Earlier?

March 26th, 2010 Sebastian Pruiti Leave a comment Go to comments

Note: This isn’t really a breakdown, more of a rant

Fighting for their playoff lives, the Houston Rockets were down 4 points with 1:06 seconds left. Their opponent the L.A. Clippers just pulled down an offensive rebound and bring the ball upcourt:

Now, it is obvious that the Clippers are trying to kill some clock here, and they effectively do. 20 valuable seconds come off the clock before Baron Davis hits his jumper. This brings up something that has always bothered me when it comes down to coaches strategy, why don’t NBA teams foul earlier when they are losing (not counting the Hack-a-Shaq)? The Rockets don’t foul in this situation, but they aren’t the only one, most teams in the NBA won’t foul here, and I think it’s silly. In my opinion, when you are down by more than 1 possession with a minute left you want to extend the game as long as you can, and one way to do that is you foul.

Now, let’s use the above situation from the Rockets game as our starting point. If the Rockets foul as soon as the Clippers get the ball and Baron Davis makes both of them, they are down 6 points with 1:06 left instead of being down 6 with 46 seconds left. That is 20 seconds he could have saved, and in a NBA game 20 seconds is pretty damn valuable. Another benefit of fouling is that there is no guarantee that the shooter will make both (remember that Golden State-Phoenix game a couple of days back).

The Rockets actually come down and quickly score in their next possession, they are now once again down four, but this time with 40 seconds left:

Again, the Rockets don’t foul and again Baron Davis runs down the clock, but this time he hits a three instead of a two and effectively closes out the game.

If the Clippers would have fouled in both of these situations, they would only be down 6 with about 40 seconds left, and while it is still a long shot, it is much more manageable than being down 7 with 17 seconds left. Also, that is if the opposing team makes both of them, and that is never a guarantee, especially late.

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K

How about foul earlier but only if they put the ball in the hands of a poor foul shooter? And perhaps throw a double team at Baron at the 1:06 mark (in this case) and hope he passes to a less clutch foul shooter? And instead of just blatantly fouling, gamble for the steal, hoping for either the ball, a jump ball, or a foul?

Seems like the idea of fouling earlier (and gambling soon) makes sense assuming that the players can make some quick calculations in their head.

BTW, I'm a fan of throwing a second player at the primary ball handler in these cases. I'm a Portland fan and the few times that opposing coaches throw a double team at Roy in these cases, it seems to end badly (maybe not so badly now that we have Miller).
Brian Tung

@khandor: As I said, the assumptions are rather artificial. I think you're focusing too much on the assumptions and not enough on the methodology. You've laid out some good points about the assumptions (which I made in order to do a Q&D analysis), but your own conclusions don't seem to have any real analysis behind them--just intuitive arguments that I certainly think are plausible but aren't (without that analysis) terribly compelling.
JP

Brian Tung is spot on here. He even concedes that he doesnt have the definitive answer himself (at least without further research) but he's backed up my initial thoughts on this that Sebastian's breakdown/rant is extremely inconclusive and more likely to be wrong then right.

Im surprised at Sebastian here truth be told, I thought you were sharper then that Seb!

The whole "case" here appears to be based around the assumption that Davis is going to hit a contested long range two pt jumper and a 25-26ft three-pointer.

What is more puzzling/irritating is when teams who are behind let the team run down the shot clock a substantial amount and THEN foul! Getting the worse of both Worlds then. Teams dont go for the aggressive 8 second count violation enough in my view either.
Nathan

Obviously this strategy will, on average, lose points for the comeback team (or teams would foul one another the entire game). The advantage is that it allows literally about three or four times as many possessions for the comeback team to work with. Because the opponent will be advancing the lead by 1's and 2's, not 2's and 3's, the comeback team can stay in the game longer. Also, the comeback team is a lot more likely to get offensive rebounds and steals than their opponent. With 1:06 left, the comeback team can jack up 8 or even 10 3's if they are lucky, and if these fall early and often it is difficult for the opponent to maintain a lead.

If you don't foul down 4 with 1:06 left, you can expect to get a possession starting with 0:46 left and another possession starting with around 15 seconds left. To win, realistically, you have to score on both of these possessions and hope the opponent doesn't score on both of theirs. If you give both teams about a 50-50 chance of scoring, you find that the comeback team has about a 6% chance of making up the difference.

The goal of the comeback team is not to have the most efficient offense. The goal is to have the most variable offense. It is far better for the comeback team to have a possible +/- of -10 to +10 than to have a possible +/- of -5 to +5 (I use +/- because both teams are going to score more points if the comeback team fouls) because this puts more of the probability curve in the win-or-tie range (+4 or better).

Finally, a couple of links:
http://sports.espn.go.com/ncb/news/story?id=4982961 (third para from bottom)
http://scores.espn.go.com/ncb/playbyplay?gameId=300860096&period=2 (4:30 to end)
khandor

Sorry, that should as: "... in the first place ..."
khandor

Brian Tung,

Thanks for making that correction to the initial situation described by Sebastian, i.e. down by 4 points with 66 seconds in the 4th quarter, opponent with possession of the ball.

What this does, however, is further accentuate why the best available strategy for the defense on that initial possession was not to foul, and then to evaluate on a possession-by-possession basis, thereafter, whether fouling [or not] on any given possession would have been a better option, considering the specific time, score, number of fouls committed, number of time-outs left, etc., they found themselves in, as time continued to tick off the clock.

It's a false assumption in the first to believe that Team A will only get a certain limited number of possessions the rest of the way.
Tadex

Kevin - what about the chances of forcing a turnover? I've no idea what is the right probability here, but shouldn't you assume that in say 10% cases the Clippers don't even get a shot off? Also, in case the Rockets get a steal their FG% in the ensuing posession gets much higher as as scoring in transition is easier.
Brian Tung

@khandor: The original situation is down four with 66 seconds on the clock. The Rockets choose not to foul, and Baron Davis cans the deuce. The Rockets score and the *next* situation is the one you name, where they are down four with 40 seconds left. Sebastian mentions, correctly, that if the Rockets foul, the Clippers might not hit both free throws, but for whatever reason, he inappropriately omits that if they don't foul but play straight-up D, the Clippers might not hit the field goal. No real clue as to why he was inconsistent about that.

At any rate, the right approach is to consider the various options. The choice as to whether to foul or not may well depend on what you plan to do on subsequent possessions, so they do need to be taken into account. You can't necessarily assume that the tactic will be to continue to foul. For instance, for the down eight with a minute left situation, I consider fouling each time, not fouling each time, or not fouling this time, but fouling subsequent times. I chose not to do that for down four, but I could do that, too. The point was less to come to a concrete conclusion (since the underlying assumptions are open to debate), but to illustrate methodology.

Either way, I think it is totally unclear that the right tactic, down four, with over a minute to go, is to foul. That seems pretty unlikely to me, but I haven't done all the numbers.
khandor

Brian Tung,

I believe the original situation was ...

- 40 secs left
- down by 4 points
- opponent with possession
- the defense decides not to foul on THIS specific possession

Although I could certainly be incorrect in my interpretation of the original scenario ... from what's actually written here, it does not appear to be the case that what's being discussed involves the decision not to foul on ANY of the remaining opponent possessions.
Brian Tung

@khandor: The claim was only that the losing team would only have the ball (at most) twice with 40 seconds left *if they chose not to foul*. If they choose to foul then the number of possessions they expect to get would of course be greater, with additional time-outs helping to increase it further.

That being said, the officials often make it difficult to get an intentional foul off in the waning seconds. It is by no means certain that a pair of possessions (one for each team) could be obtained in just a few seconds. At any rate, you give a number of plausible situations where fouling could help, but nothing of the sort of analysis that either I or Kevin give that would substantiate your claim that fouling is the best option mathematically. I of course agree that most coaches are loathe to foul under those circumstances.

@Kevin: That's sort of the kind of analysis that I have in mind, but I wouldn't short-circuit to the table, but would continue on using the sort of analysis that you use in the first possession. The reason is that these numbers--presumably derived empirically--reflect the kind of coaching decisions that we're trying to validate in the first place! Just continue the analysis further on to the actual end of regulation. We can then assume 50-50 wins in OT. Also, the table doesn't seem to reflect possession, unless it's implied somewhere that I didn't see.
khandor

In the situation which you've described, experienced coaches would always choose to play solid defense with a 24 sec shot clock in use.

[Aside: Much of the argumentation presented thus far is not accurate since the assumption is that with 40 ticks left this would properly be categorized as a situation where the losing team would only get possession of the ball twice in the remaining 40 secs, which is a patently false assumption. e.g. If Team A can get a stop on defense and then gain possession of the ball, say, after a loose ball scrum for the rebound, following Team B's use of all 24 secs, this would mean that Team A would have aproximately 13-14 secs left on the game clock. If Team calls time-out and moves the ball to the offensive front-court, it is reasonable that Team A could score either 1FT, 2FT's, a 2FG or a #FG with as few as 3 secs [or less] ticking off the game clock. If Team B then shoots its FT's and Team A follows with another time-out, then, Team A may well get its 2nd possession with as many as 10 secs left on the game clock ... down by as many as 5 points (i.e. if Team made only 1FT and Team B made 2FT's in return) or as few as 1 point (i.e. if Team A made a 3FG and Team B missed 2FT's). If the same scenario then repeats itself again and again, it would mean that Team A would in fact get at least 2 additional possessions in the remaining 10 secs ... and mean that Team A would end up getting a minimum of 4 possessions altogether in the final 40 secs, when Team A decides to not foul intentionally on the initial possession of this specific scenario, i.e. 40 secs left, down by 4, oppoenent with possession of the ball.]

Both, mathematically and from a basketball acumen perspective, it's the best option possible, if the goal is to maximize your team's win probability.
Kevin

Isn't this the sort of thing win probability analysis is for? (I'm using the chart at the bottom of this page: http://sonicscentral.com/apbrmetrics/viewtopic.php?t=586, which is the most available data I could find).

First case: 1:00 left, down 4.

Option 1: play defense. Houston will run 20 seconds off, so there will be :40 left. Just to throw out some numbers, let's say there's a 67% chance the possession ends in a two-point jumper with a .4 success rate, and a 33% chance it ends in a three-ball with a .3 success rate (argue with my numbers if you wish, methodology is the point).

So, Houston has a .33*.3=.1 chance of going up seven, a .67*.4=.268 chance of going up six, and a .632 chance of staying up four, all with :40 remaining.

Using the win probabilities from the table, we can determine Houston's chance of winning:

WP% = .632(.11) + .268(.02) + .1(.00) = .075 (7.5%)

If they foul, Baron's a .82% FT shooter. So there's a .82*.82 = .672 chance he makes both, a .18*.18 = .032 chance he misses both, and a .295 chance he makes one. So Houston will be down 4, 5, or 6 with a minute left:

WP% = .032(.18) + .295(.10) + .672(.05) = .069 (6.9%)

These two probabilities are close enough that other factors (specific personnel, different chances of a turnover/offensive rebound, etc) might be able to make the difference, and I couldn't really criticize either decision.

The second case, down 4 with :40, assuming the same scoring probabilities:

Play defense: WP% = .632(.03) + .268(.00) + .1(.00) = .019 (1.9%)

Foul: WP% = .032(.11) + .295(.05) + .672(.02) = .032 (3.2%)

...which pretty clearly shows that fouling is the better strategy.
Brian Tung

@MathWiz: I think his math is just fine. He's not computing the probability that both free throws will be hit; he's computing expected points. Since the expected points on any single free throw is equal to the FT%, the expected points on both would be twice that. And the expected points on a two-point shot is also equal to twice the FG% (for that type of shot).

@peter: There are times when fouling under other situations (than what you describe) would improve your chances of winning. You would seem to have us disregard that and decrease the chances of winning, just because it doesn't happen to make sense to you. Sometimes things are just counter-intuitive.
peter

guys, don't talk about chances here.
at this situation chances (or probability) are not important.

firstly, you have to count the clock - we are down 4 points, we've got two possesions.
now, you make naive assumption - clippers won't score during their two possesions. I know it's naive, but that's the way you do it. you don't count probability or chances that you will win.

fauling is 100% logical only when there are less possiesions left than points difference.
for example, when there are two possesion game and you lose more than 6pts, than you have to look for more possesions by giving your oppositions free thows.

here, rockets are down by 4, two possesion game, simple game we all saw tens of that game where losing team won that game at the end.
MathWiz

@Don

your math is incorrect. It's actually a 66% chance that Davis will hit both free throws, with a free throw percentage of 82% on the season. You take the square of that average to find the odds of hitting both.

.82 x .82 = .66

And with a 40% field goal percentage, since he is only taking 1 shot to score 2 points, you accept that at face value.

So,

66% chance to score 2 points by getting fouled
or
40% chance to score 2 points by allowing him to shoot.

Obviously this doesn't account for X-factors, like spectator pressure, home court or away, the effectiveness of the defender, shot selection etc.. but generally BD scores at a higher efficiency at the free throw line
mike

I have to strongly disagree here Sebastian. If you don't trust your defense, your fouling and potentially putting yourself down 6 points with the other teams defense set. If you play straight up defense, you might waste 20 seconds but the chance of the other team scoring is A LOT lower than the most likely 2 free points your giving away. From here, you get the rebound and push the tempo. If you don't have an easy transition opportunity, you might have a mismatch from the other teams scramble to get back. At the very least, you push it up and the defense isn't completely set as they would be when you get the rebound of a made or missed free throw.

If you're fouling a poor free throw shooter, I'm all for it. But if you're fouling Baron Davis, I feel like you're just throwing the game away. You're turning the game into their best shooter shooting free throws vs. your team scoring quickly (and from long range) against a set defense. 1 minute is way too much time to start fouling. At the point in the game, players probably aren't even as nervous as they would be at the line when there's 20 seconds left.

I don't know much about stats but I'd never foul in this situation.
Brian Tung

OK, *really* simple analysis. Opponents are up four, with a minute to go. We'll assume for the sake of argument that if you play straight-up D, both teams will get two possessions; if you foul early in the clock, both teams will get four possessions. Opponents shoot free throws at 80 percent, and if allowed to run their offense, will shoot a deuce at a 50 percent clip. Your team will try to shoot treys, which they will do at 40 percent. (I realize this is a huge simplification, but it also allows one to do a Q&D analysis.)

Under these pretty restrictive assumptions, playing D straight up is preferred to fouling, by 8 percent to 4.5 percent (probability of winning). Down six, playing D straight up is still preferred, by 2 percent to 1 percent.

Down eight, however, there's obviously no percentage at all in playing straight up D, since you can't score eight points in two possessions (assuming your opponents aren't complete morons, heh heh). Fouling, though, gives you about a 0.1 percent chance of winning; not great, but it's something.

However, you might argue that you could play straight up D the first possession, then after half a minute has passed, foul the next two possessions, and maybe that would be better than fouling each time. Turns out that's not the case: Such a tactic allows you to win about 0.05 percent of the time. So with that large a margin, you really are better off fouling each time. And yet, I do think that most teams would play straight up D the first time, then foul with only half a minute left on the clock. The above analysis is naive enough not to be conclusive, but it suggests that fouling each time ought to be considered, at least.
Brian Tung

It's possible that fouling when down four with over a minute left is the right play, but this line of argument seems anecdotal and not very convincing. What I'd like to see, speaking as a stochastic processes guy, is a Markov chain analysis with two basic approaches to defense: playing hard-nosed defense for the full shot clock, as compared with fouling early in the clock. Perhaps a third option, when the opponents take the ball out along the baseline, is to try to force an eight-count, then foul once they get across halfcourt. I realize that such an analysis would probably be mind-numbingly dull for most basketball fans (and I sympathize), but to make this decision on rational grounds you need something like that.

Peter's exactly right that this is an endgame situation where all you care about is winning. You don't care if you increase your average margin of loss, so long as you increase your probability of winning.

All this reminds me that the time-out situation is important, and yet it isn't really taken into account here. Understandably, too: It really complicates matters. Nonetheless, it might be interesting to do a no-time-outs analysis and see if you can at least derive a basic rule of thumb.
peter

oh come on.
there are two options, you win or you lose. there's nothing in between. Does it make the difference to rockets if they lose by 1 point or by 7 pts? nope.
here's the point where you have to take the risk and relay on heroic performence.
you probably remember final jordan game as a bull. one possesion game, utah had the ball and were up by one point. did bulls faul them? 14sec on the clock and jordan stole the ball.
gidons

It definitely depends on the situation. Down 4 with 1:06 is actually not so bad: there's time for about two more possessions for each team (assuming you're quick on offense), and if you get a stop or two you're in good shape.

However, a lot of coaches won't start fouling until about 0:30, even down 6-7. That's silly to me. If the other team can dribble out the game unless you score 2+ points per (quick) possession, then you can't let them do it. You have to start gambling. You don't have to just foul the first guy you can, though. You can try to direct the ball to poor foul shooters, for example (e.g. double Davis as soon as he crosses half court), press full-court, go for a steal, whatever. Just don't let them dribble the 24 seconds away.
Albert

The only problem with your argument is that it seems to be based on the assumption that a possession is likely to end with points. Statistics may point to a correlation there, but an NBA coach would essentially be asserting his own worthlessness if he made a decision that basically said, "Nothing I do as a coach here can prevent the other team from scoring points." Yeah, the foul shooter might miss one of two - hey, he might even miss both - but in general, NBA players are far more likely to make free throws than they are to make, say, a contested jumper. Or even a contested layup at the rim. What if that first possession had ended with Davis bricking a long jumper? Or turning the ball over?

The point is that at the beginning of the possession, the Rockets had some measure of control over the outcome, determined by the extent to which they could effectively defend the Clippers. Fouling gives that up: either Davis makes the gimmes, or he doesn't. From a competitive standpoint, you kinda HAVE to proceed as though you think it's possible you can get the stop.
Don

Putting Davis on the line: 0.80*2=1.6
Letting Davis shoot a jumper: 0.43*2=.80

If you put Davis on the line, you have to spend your whole next possession making up the difference, which AT BEST leaves you w/ the same differential if you're making the shot. on AVG you have lost more time and are down more.
Sebastian Pruiti

I don't think that's how it works...