# Intentionally Fouling at the End of the 1st Half

Submitted by rc15 on February 9th, 2018 at 10:39 AM

Before the last possession of the 1st half of the Northwestern game, when they took a timeout, I started wondering: “When the opposing team can hold the ball for the final shot of the 1st half, is it better to intentionally foul if they’re only in the 1-and-1?” So I decide to look at the math…

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Assuming for this analysis that every team scores 1.1 points per possession on average, if you don’t foul, and the other team executes properly in not letting you get a shot afterwards, they’ll get 1.1 points on average.

NET: -1.1pts

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If you do foul: (assuming 75% FT percentage)

Opposing Team: (0.25)*0+(0.75)(0.25)*1+(0.75)(0.75)*2 = 0.1875 + 1.125 = 1.3125 pts

Good Guys: 1.1 pts

NET: -0.2125pts

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In the end, you end up net positive almost 0.9 points! To me, that’s well worth someone getting an additional foul (of your choice), especially if you can substitute in a bench warmer before the play when the other coach calls a timeout to setup. You could also use the opposing team’s timeout to setup your offensive possession, which could increase you average PPP for your next possession.

Have no coaches ever thought of this? Or am I missing something?

This is an interesting idea, but I do think there are a few things you might be missing.  There are some second-order issues, like the value of that foul (don't want to put a good player in foul trouble needlessly, for example), but there's a bigger one that I'd have to see ironed out to be convinced.

You assume 1.1 PPP as the average here, but are last-possession shots normal?  Usually when a team has the ball right before half, they dribble out the shot clock until there are just 5-10 seconds left, and then run a quick set or an iso play.  Intuitively, I'd expect this to be a lower-percentage opportunity than a typical possession in which you run your full offense for 30 seconds.  Straightening that out would be key for this analysis.

Since your intentionally fouling, I assume the team would be smart enough not to have someone who's already in foul trouble or gets into foul trouble do it. For UM, it would be pretty easy for Simpson to take the foul since it would be the PG dribbling wasting time, and he never gets into foul trouble. Also, like I said in the post, if the opposing coach calls a timeout, you could sub in a walk-on to take the foul, and then sub him back out before the FT.

I did think about PPP being different because it's the last shot, but I didn't know how to find that information. The breakeven point is at about 0.65 PPP, which would seem really low.

There's got to be a stat out there for end-of-half PPP.  And if there isn't, you could use a few good proxys. Ideas:

1.) use end-of-possession (last 10 seconds) FG% (or eFG%), and assume average T/O & oREB percentages.  Brian has used end-of-possession FG% a few times here, and I'd assume its on KenPom as well.

2.) aw. . . forgot it already.  Idea #1 is a good proxy tho.  So I'm still smart I say!

I see what you are doing.  You are leveraging the fact that there is advantage for the last possession.  The rhetorical question is if that is indeed the case the other team can foul back presuming both teams are in the 1-and-1.  As someone pointed out there is a point where you cannot say it is worth it because as pointed out there may be concerns of running out the clock so the other team does not get a possesion for free or there may not be adequate time to run a meaningful play.

The implication is even if a team is in the double bonus it would be worthwhile to foul.  I think to draw a conclusion we would have to look at the success rate of last possessions in general

One thing you are accidently assuming is that if they miss the free throw, you are getting the rebound. They could get the offensive rebound, too.

Good point! Found a stat saying 11.5% of FT are rebounded by the offense, so assuming you repeated the same logic and immediately fouled again, that would give the opposing team an additional (1-.75^2)*(.115)*(1.3125) = 0.066 PPP

The OREB was my concern as well. Good intergration into the model. I like the idea. As metioned by someone above, if you're able to pull the data on final possessions, maybe which start with at least 10-15 seconds left on the clock, and get a PPP for that, you're pretty much on the money.

I also think it helps prevent against the momentum of the other team making a long shot, while it gives you a chance to have the "final word" in the first stanza.

So, let's see.  Michigan is only allowing 22.7% OREB in conference play, and they have the advantage of inside position on a free throw, so let's call it a 20% OREB chance.  To simplify the analysis, let's further assume that you'd only foul the one time, that if they get the OREB, you'd just play defense, and that they're unable to tip the ball back in and have to pass it out and hold for the last shot.

So now you've got:  Do nothing, -1.1 points

Foul, Miss front end, DREB, 0 points OPP 1.1 points UM: 0.25*0.8*(1.1-0) = +0.22 points
Foul, Miss front end, OREB, 1.1 points OPP, 0 points UM: 0.25*0.2*(0-1.1) = -0.055 points
Foul, Hit front end, miss back end, DREB, 1 point OPP 1.1 points UM: (0.75*0.8*(1.1-1) = +0.06 points
Foul, Hit front end, miss back end, OREB, 2.1 points OPP 0 points UM: 0.75*0.2*(0-2.1) = -0.315 points
Foul, Hit both: 2 points OPP, 1 point UM: 0.75*0.75*(1-2) = -0.5625 points

Total expectancy of the fouling scenario: -0.6525 points

So, you're still ahead, but now it's by less than half a point.

Why isn't it done?  Because coaches are conservative.  You could make an argument that you should foul when up 1 or 2 and the opposition has the ball at the end of the game with the shot clock off, but nobody ever does that because... nobody ever does that, and if it doesn't work there would be a ton of criticism.

Scenario you're describing at the end of the game, I agree with you. There'd be a lot of criticism if it didn't work out. End of a half, I don't think people would really care. I think people would accept it's statistically the better option once the coach explained his logic.

The real problem is, if the opposing team decided to intentionally foul you right back... Then it'd come down to whoever has the better FT shooters, and would be an extremely boring end to the half.

Why isn't it done? Because coaches are conservative. You could make an argument that you should foul when up 1 or 2 and the opposition has the ball at the end of the game with the shot clock off, but nobody ever does that because... nobody ever does that, and if it doesn't work there would be a ton of criticism.

It isn't done because of sample size.  Not because coaches are conservative.

Sure, over infinite possessions, there may be an advantage to getting an extra possession.  However, in a game, it's an n-value of 1.  There's no guarantee that the next possession you'll score even if over a large n-value the PPP is 1.0+.

From my perspective, as a coach:  I probably trust my defense to get a stop more than 50% of the time.  If that's the case, I should never put a team on the line where you are conceding points.  Throw in a millions other details and my thoughts may change, of course.  However, that's part of my issue with these analyses - Brian is a major victim... They assume large n-values for events that might occur a handful of times in a season.

What about the affect on the team's offense? If you foul, that takes away the opportunity of transition offense. Most teams are better in transition than 5-on-5. It would be interesting to see how much success NBA teams had with hack-a-blank and the impact it had on their offense.

I believe the honest reason this isn't done is most people are afraid to break convention.

This is good analysis.  The conclusion makes logical sense.  But it's outside of most coaches' comfort zones.  (Not to mention it takes extra logical thought that, if not previously considered, likely isn't the first thing on a coach's mind in the heat of the moment.)

Sports paradigms are changed by a select few who are brave enough to break the status quo and are repeatedly successful in their results.

There’s enough intentional fouling at the end of game that makes basketball annoying to watch. Let’s not suggest any more. K, thanks

Just speculating that if this actually became a strategy that worked, the other team might just try to do the same to you. My guess is that the statistics don't quite line up regarding points per possession on offense in cases where the offense has to contend with a definite time limit in addition to the shot clock and scoring. I.e. if they know you are going to make your move in a five second window, they can probably plan accordingly.

All seriousness aside, it's probably purely theoretical in B1G play anyhow, as sometimes it seems like your PG can get dogpiled by three defenders all trying to bring the foul in front of the side ref, and they end up calling traveling once he's literally pushed over.

There is also the case where the other team screws up, shoots too early, you get the rebound, and get a scoring opportunity.  We make an assumption that the other team is going to get the last shot.  Either by good defense or a fubar that might not happen.  Any calculation would also have to look at how many times the initial defensive team scored when the shot clock was off at the end of the 1st half.

End of game situations that are tied, at least back in 2010, showed about a PPP of 0.77 on sets out of timeouts (meaning no transition buckets, etc.). Say that's about 0.8 PPP, as likely the game theory for that possession is similar.

I know you considered the case of an offensive rebound. Did you also update to include a make on free throw #1 and a miss/rebound on #2? There are going to be instances, certainly, when an OREB results in an immediate put-back, rather than an opportunity to foul.

I think what you are getting toward is at least very close to something that is break even, and with a small sample size. It's an interesting idea, but if we're talking <0.1 ppg because of it, then most are going to conclude it isn't worth the risk/reward.