Mailbag: The Fouling Question

Submitted by Brian on April 4th, 2014 at 12:35 PM


to foul or not to foul this stroke

Foul? An excessively long answer to an excessively long email.

Brain & Staff -

I'm a templar with high INT.

Here is my question - Would it have been a better move for Michigan to commit two quick fouls and put Kentucky on the line shooting 1 and 1 at the end of the game? After Michigan tied the game there were about 27 seconds left. After two fouls Michigan would likely have 20 seconds remaining to take the ball and make a game winning shot of their own.

Oh man, you are about to enter the final frontier of basketball strategy. For starters, this is never happening. John Beilein is a genius but he's not the kind of mad genius who would, say, leave his guys out there with two fouls in the first half even though they don't foul very much. This is a bridge too far.

But, yeah, I thought about it too. Let's look at it.

Here is why I think this is a superior strategy - please feel free to poke holes in it.

1) Kentucky was making 53.40% of their shots. Assuming this is a reasonable expectation for Kentucky's chance of success on its last possession and that they hold for the last shot, Michigan has a 53% chance of losing and a 47% of going to overtime. Michigan has no chance of winning (in regulation) under this scenario baring a huge mistake by Kentucky.

This is optimistic for your strategy. Last shots are bad shots, as Kentucky amply demonstrated. Ken Pomeroy frequently tweets out the fact that teams tied and in possession with the shot clock turned off win 67% of the time, which means they're hitting 34%. Last shots also usually don't provide much of an opportunity for a putback, and anyway that stat about winning the game folds all results in.

2) Putting Kentucky on the line for a one on one yields the following probabilities (assuming a 75% free throw shooter - which is higher than Kentucky's 54.5% average for the game):

56.25% chance Kentucky hits both shots = 2 points

18.75% chance Kentucky hits one shot = 1 point

25.00% chance Kentucky misses the first shot = 0 points

I'm assuming Michigan is able to grab any rebounds (perhaps a big assumption). The key here is that Michigan heads back down the floor with a 25% chance to win with a made shot and tie with a miss, an 18.75% chance that any shot will win the game. and 56.25% chance that any made shot will win or tie.

This is a bit pessimistic for your strategy. Hack-a-blank has been an infrequently deployed strategy throughout basketball history, and never has it drawn an intentional foul call. Michigan had two attractive targets: Alex Poythress, a 64% shooter, and Dakari Johnson, a 45% shooter. Johnson was on the floor. Hack-a-Dakari gives you the ball tied over half the time.

Well, about half the time. The rebound assumption is kind of a big one. In the NBA, about 14% of FT misses are grabbed by the offense. Michigan was giving up an epic OREB rate in this game, though that's somewhat mitigated by the fact that in our hypothetical scenario one of Kentucky's bigs is stuck on the free throw line and can't move until the ball hits the rim. But since your FT% assumption is high it's probably a wash.

3) Assuming we use Michigan's 47.8% field goal percentage in the game as a proxy for their changes of making a shot. I'm also assuming that the chance of taking a 2 or 3 mirror the game percentages as well.

Again, late shots are bad shots.


although sometimes they go in

The impact on Michigan would presumably be less since they're just running their offense looking for the best shot they can in about 25 seconds, so maybe the assumption about Michigan is on more solid ground. But then you've got a potential response from Kentucky and things get complicated fast.

I'm eliding the math based on this assumption in the email provided to cut to the chase, which is that fouling for a one-and-one against a 75% FT shooter looks like this:




This breakdown looks better to me than Kentucky holding for the last shot:



So, where am I going wrong OR why don't we see this strategy more often - especially with teams who have better free throw shooters (ie trading fouls at the end of the game would typically be a losing strategy for the other team).


Jamie (6th Generation - still have never posted)

The main thing that's off about this analysis is the assumption that Kentucky hits a shot at the same rate they did during the game; this is clearly not true otherwise teams would be winning closer to 75% of their games when they've got the ball with the shot clock off in a tie game.

The other thing that's off is that 75% assumption. Here's what the universe looks like if you foul someone you should foul:

Player Down 2 Down 1 Tied
Poythress (64%) 41% 23% 36%
Johnson (45%) 20% 25% 55%

Down one is worse than being tied but it's hardly worse than a coinflip. When Arizona got the ball back with 31 seconds to go against Wisconsin down 64-63 Kenpom gave them a 45% shot at the game. It's basically compressing overtime into one shot. Meanwhile, being down two means you're now in a lose-or-OT situation similar to the one Kentucky just had with win-or-OT, except you have the option of hitting a 3. Michigan's quite good at this.

Things get complicated fast, but there is a threshold at which the foul is the right move. I think that threshold was breached once Calipari put Johnson on the floor. Part of this is the fact that Michigan is a brilliant offensive team. If the game's coming down to a last shot I want it to be Michigan's. And part of it is the stark line in the table above. Even including a standard OREB chance of 15%*, about 70% of the time you send Johnson to the line you get the ball and any bucket wins. The rest of the time you have a shot to go to OT or win with a three. I'm taking that chance.

…in the long-delayed aftermath, anyway. This isn't (much of) a criticism of Beilein. It's more of a thought experiment. Most people who have brought this up have done so in the context of "I wonder what if…" and then scribbled out assumption-laden percentages. During the event I was just trying not to die. I'm not sure Michigan should have spent any time figuring out how to shift the odds a bit in their favor if this one particular situation came up.

But, yeah, I think if there's a 45% FT shooter on the floor and you have the opportunity to put him on the line for a 1-and-1 in a tie game you do it.

*[Given the way the game was going you may question this but remember that Johnson's at the line and Kentucky is unlikely to have anyone other than Randle as a post since a Michigan rebound would then put Kentucky in a very awkward place defensively. Also Michigan can put two bigs in and call timeout after. Seems fair enough.]



April 4th, 2014 at 12:45 PM ^

JB expected them to run it down that far.  Young players tend to start their "last second move" with about 9 to go on the clock (Walton did it all year).  Way to early.  I think we were banking on 1) they would make this mistake, and 2) the play would be going to the basket (and that there would likely end up being a foul anyway, albeit with about 5 or 6 on the clock).  I started to panic around the 7 second mark when Harrison had yet to make a move.  It was at that moment that I knew that Calapari had drawn up "Dagger."  I panicked, but I also had a sense of relief because I thought that they were taking about the most difficult shot they could have gotten.  Bottom line, if your opponent decides to run the clock down and take a 24 foot contested 3 with the game tied you roll out the red carpet for them and shake their hand if they make it.

Snow Sucks

April 4th, 2014 at 12:53 PM ^

Perhaps, but I think had UK been losing at that point, they would have shot earlier than they did. With a tie ball game, the worst that will likely happen is overtime and the best that can happen, which unfortunately did, is the guy buries the shot with minimal to no time remaining.


April 4th, 2014 at 1:01 PM ^

circumstance, you believe, although you do so with some trepidation, that the minimal time will be more than 2.1.  Harrison showed some wiser-than-his-year savy to run that thing down that far.  Late in games, player start to think their actions take longer than they actually do.  They start to get really antsy around the 10 second mark.  I don't think JB thought for a second he would take it down that far.  At around the 8 second mark, the move would have been to send somebody out for a token double to at least throw Kentucky off balance.  But I don't think for a second that Beilien thought  that Calapari had the audacity to call "fade-away pro 3 pointer" for their game winning attempt.  It was really a great call by him.  It was great coaching that looked like no coaching at all.


April 4th, 2014 at 4:31 PM ^

This is a great point. We start fouling, and Kentucky would have every reason to get their best free throw shooters out there. Plus, we've all seen before that it can be hard to foul the person you want to foul. In a love game situation with the clock running down, we may end up having to foul one of their better shooters and the percentages change drastically.


April 4th, 2014 at 12:55 PM ^

In my EA Sports basketball game days, I would always foul up one or tied when the other team had the ball with the shot clock off. I won four straight national titles too, so I know what I'm doing.


April 4th, 2014 at 12:55 PM ^

Do the shooting percentages take into account half court sets late in the shot clock?  Overall field goal percentage for a game reflect both transition baskets and very good looks early in the shot clock.  As the team going for the last shot pass up transition baskets and early good looks, I would assume that shots take in the last 5 seconds of a shot clock have a much lower percentage of success than all shots taken through out the game.


April 4th, 2014 at 1:02 PM ^

but i don't understand why beilein didn't call time out as soon as nik caught that last inbounds pass to get the ball near half court with 2 secs left.  still a remote chance of getting off a good luck but better than a half court chuck.


April 4th, 2014 at 1:08 PM ^

If MIchigan wanted to be down 2 with the ball and a chance for the last shot, they could have pulled it back out after one of the offensive rebounds in that epic stretch just before this.  (Admittedly, maybe JB would have wanted to do that, but the players didn't consider it; still, he could have called a time-out.  It's not like they're all that limited in basketball).

Having said that, I'd have been in favor of fouling in many circumstances, but not when Kentucky was getting so many offensive rebounds.  Even with Michigan being given inside position by rule, I would be very worried about Kentucky scoring a point and then getting the ball back on a missed second free throw.

Still, one shot away from a back-to-back Final Four.  It's nice to be upset about this instead of Evan Turner. :-)

Go Blue!


April 4th, 2014 at 2:48 PM ^

The initial shot was taken with more than 35 seconds left, which meant the UM would get likely the ball back - which I thought was good time management.  Unfortunately, by the time all the second chance shots were taken and the shot finally dropped, there was less than 35 seconds left.    My guess is that all of the hurried second chance shots were made in hopes that there would still be more than 35 seconds left on the clock.


April 4th, 2014 at 1:18 PM ^

Do you want your defense... Which has been struggling all year and in this game... Or your high powered Offense ... Which could be considered one of the best in the last decade. Fouling while tied goes against the grain and maybe not following basketball etiquette. With Michigan's team I wanted to see the offense determine our fate and we could have been playing for the tie or win if we gave up some free throws.

My other thought is that we should have given the Harrison twins a different look. We just played straight up man to man. How about a trap on the first pass or handoff. These are freshman. Doing things they expect put them in a place to succeed. This has to be put into place long before the last 10 seconds of this game, but I like the idea that you might reveal a different defense/look for a team running on instinct and a short clock.

biakabutuka ex…

April 4th, 2014 at 1:36 PM ^

If there's one empirical counterpoint to the conclusion here, it's the fact that Kentucky chucked a terrible 3 that by all rights they should have missed. Everything that Beilein could have wanted to happen happened, except for the 35 ft contested shot going in. 



April 4th, 2014 at 2:00 PM ^

When Kentucky was getting layup after layup.  With 10 minutes to go in game, M had plenty of fouls available.  Foul the guy and make them hit free throws.  


April 4th, 2014 at 2:35 PM ^

I have to believe Cal would've taken at least Johnson out after one foul.  Even if he didn't, he's probably not going to touch the ball early in the possession, and if he doesn't it is a lot more difficult to foul him without picking up an intentional foul.


April 4th, 2014 at 9:12 PM ^

conversation with the refs about off ball fouls and specifically what would happen if Johnson was fouled. This also may have been passed on to Beilein. I don't believe Beilein didn't consider that they could fould Johnson. I'm sure he had reasons for not doing it.

Maize and Luke

April 4th, 2014 at 2:36 PM ^

It doesn't matter if they have 3 or 4 guys on the floor that shoot 20% from the stripe, those guys were not getting the ball.  Unless I'm mistaken Harrison is near an 80% FT shooter.  You can't put an 80% shooter on the line for freebies.  You would have seen some serious smoothering defense on the other end there's no guarantee we even get a good look at a win or tie.


April 4th, 2014 at 2:54 PM ^

Yeah I think the big flaw in this thought process is the idea that dakari would have touched the ball, Kentucky wasn't going to johnson in that situation the only people touching the ball were the harrison twins or randle, all good enough ft shooters that you prefer to just play defense.


April 4th, 2014 at 3:10 PM ^

Most of the number crunching in this post assumes that Michigan would have had the opportunity to put Johnson or Poythres on the line, right? I'd have to watch the last minute again but I doubt either handled the ball in the last 60 seconds. Calipari isn't the smartest coach but I'm sure he would have figured out that Michigan was intending to force them to the free throw line after the first of two required fouls to put them in the bonus. In a nutshell he would have screamed for the ball to go to the highest percentage shooters and not Dakari or Alex. Second stupid question - Brian did you ever play basketball at a competive level? If you did you didn't learn much because this stuff is 101 level in terms of strategy.  

kevin holt

April 4th, 2014 at 3:11 PM ^

You don't have to have the ball to get fouled. Brian implied this when he referred to hack-a-blank and when he said it's rare to get an intentional foul (when fouling off the ball). Do you think Shaq (or, more recently, Dwight Howard) always had the ball when they got fouled? I'm pretty sure they knew not to pass it to Shaq.


April 4th, 2014 at 3:50 PM ^

I'm not sure exactly how this works, but if it's that easy, why don't we see bad free-throw shooters go to the line all the time for off-ball fouls in late game situations?  It seems like it never happens.  Wouldn't every team be fouling Morgan off the ball when we're up late?  I don't think that happened once this year.

Blue Mike

April 4th, 2014 at 4:14 PM ^

The rules do actually have a case for when a player that is not part of the play getting fouled in an attempt to stop the clock.  It is determined to be an flagrant 1 (intentional) foul, meaning two shots and the ball.

I'd guess you don't see it in the NCAA because coaches are afraid that it will be called correctly and defeat the purpose.

The NBA tweaked their rule to cover the "Hack-a-Shaq" strategy; they make any off-the-ball foul in the last two minutes as an intentional foul.  Don Nelson changed the game by starting the fouling earlier in the game, then stopping in the last two minutes.


April 4th, 2014 at 8:28 PM ^

I don't understand why this topic keeps coming up. If Kentucky had been running a play (which Michigan said they didn't all game) I suppose you could have an off the ball foul that was clearly an effort to make a play (like holding a cutter or being overly physical with a guy trying to establish position in the paint). That isn't what was going on as I remember though.

Michigan did what they wanted by keeping them out of the paint. I think Caris could have a fouled a little later and maybe made Kentucky rush the last shot a bit more but beyond that I can't second guess.


April 4th, 2014 at 2:53 PM ^

This scenario is simply not happening until someone at a lower level of basketball tries it and succeeds.  Whether it statistically increases the odds of winning or not, no coach is going to "cause" their team to lose the game.  By "cause"- I mean providing an action rather than an inaction.  The action being to foul and in most cases, cause your team to get behind.  The inaction is to play defense and let the other team create the "cause" of getting ahead (or remain tied).  Psychologically this is a big's the same reason football coaches punt on 4th and short...they don't want to directly cause their team a disadvantage. 

I remember reading about this in the book Scorecasting if anyone is interested.


April 4th, 2014 at 3:08 PM ^

If this posts proves anything it is that the King of all Dipsh*ts will second guess every decision a Michigan coach makes. If Michigan had excuted the fouling strategy suggested in this post and UK hit two free throws and Michigan missed the last shot he'd be second guessing in the opposite direction. Life is fun and easy for critics that never have actually been in the real life situation. BTW, could someone remind us why Brian became a blogger instead of using his education to be an actual, ya know, engineer?

Blue Mike

April 4th, 2014 at 3:27 PM ^

I have to believe there would be a LOT of pressure for the officials to call an intentional foul in that situation if we foul Johnson there.  That would be an easy "I'm taking a stand and making the right call" type situation for an official to burn us with.

Another situation I don't understand:  On an inbounds play, someone off the ball can get fouled before the ball is inbounded, and they treat it like a normal foul.  Why don't more teams do this at the end of games?  Absolutely no time comes off the clock, and you get to pick who takes the foul shots.  I'm sure refs would crack down on it eventually, but until they do, it has to be the best end-of-game strategy, right?

Swayze Howell Sheen

April 4th, 2014 at 4:11 PM ^

The reason I did a diary on this topic was to show ALL the percentages, and see how outcomes change as a result:

That said, one thing missing from this whole line of thinking is psychology. The psychology of Kentucky on the last shot was *no pressure* -- miss and you just go to OT. If UM had fouled, the psychology changes to *serious, high-pressure* -- miss the free throws, you might lose, and make them, and you STILL might lose on a three. 

I think we could have turned the tables on a young team and given ourselves a better chance by fouling, and the numbers *and* the psychology agree.



April 4th, 2014 at 5:57 PM ^

This may be a stupid question, but there is discussion about not always being able to foul who you want (implied, the person you want to shoot may not touch the ball).  Why not foul who you want even if they don't have the ball?   Sure, you can't make it look intentional but there are tons of fouls away from the ball.  Yeah, and you'd have to make sure the ref notices quickly w/o much time wasting off the clock.


April 4th, 2014 at 6:03 PM ^

Guys, it was an unbelievable shot he made. Good defense but better O, nothing we can do about it. It's done and over with. Let's move past this fouling non issue. I trust coach B.

Boom Goes the …

April 4th, 2014 at 7:32 PM ^

but man if Johnson could have been on the line, he would have missed the front end, which gives us the chance to win at the end. Even if by some miracle he makes 2, I like our chances of winning or tying with the ball.  Would take serious cahones to foul in that situation though.  Reminds me of Brady going for 2 (I think it was the correct call btw)