# Michigan foul rate & autobenching

Submitted by WestBrew on March 5th, 2019 at 2:14 PM

First diary post!

Lets take a look at our foul rates in light of the autobenching discussion. More than trying to take a position on the debate I wanted to add some #'s similar to what was requested.

Some basics: Foul rate per 40 is the number of fouls that the player would get on average if they played all 40 minutes of the game.

This is the actual distribution of foul counts per game on the season so far. We have 2 foul outs on the season: Teske @ Iowa & Matthews @ Penn State.

The same table but looking at the percentages:

OK so lets mix in some statistics here.  I use what's called a poisson distribution to estimate the expected counts of the number of fouls based purely on the average foul rate.

Note: This makes some assumptions/simplifications that aren't too terrible (beyond the scope for me to explain here). Also, I'm not doing any complicated modeling taking into account any other variables like home/away, change in behavior of opponent/player, opponent foul drawing rate, etc.

So here are the expected counts of fouls for each player based on the number of minutes they play per game and their respective foul rate:

So based purely on probability we would expect each player to foul out at the percentages highlighted in yellow.

Lets compare what we would statistically expect based on their foul rate to the actual distribution of fouls:

A few things jump out to me personally here:

• The general squeezing towards the middle of the distribution (aka red at 0 & 5 and green at 2 & 3).  This shows that the players/coaches are controlling their rates either through substitution or altering their play to be more/less aggressive based on # of fouls (duh).
• Some players control foul rate better than others. E.g. Livers pretty much doesn't alter his foul rate (either doesn't have to or can't). Matthews seems to be excellent at controlling his number of fouls -- he lands right at 2 much more often than we'd expect and his 0 and 4+ are reduced. This also begs the question what happened at Penn State?? I didn't see the game(flight) but 5 fouls for him is some kind of crazy outlier given his control/foul rate. Matthews hadn't previously/since reached even 4 fouls in a game.
• Without some sort of benching/play alteration we would expect to see a significant # of foul outs ~ 5-7% per player & 4 fouls ~10% of the time. We've seen 2 total foul outs. So autobenching is certainly working to limit foul outs.

For the statsy inclined people, here are some tables for comparing expected foul probabilities for different minutes played.

Example of how you could read the charts (see below):

So lets say we were planning on playing Simpson all 40 minutes (hook shots galore!). We'd expect (disregarding any ability to control fouls by adjusting play as mentioned above) an 11% foul out chance.  Now lets say he immediately gets 1 foul within the first minute. Now his foul-out probability jumps to 13%+11%= 24% because he only has 4 left, and a 21+13+11=45% chance to get at least 4 fouls, and so on.

We decide to take a risk and leave him in.  He plays 5 minutes with no fouls so his % is now down to 18%.  At the 30 minute mark he picks up another one. Now he's got 2 fouls and a 17+8+4=29% chance of fouling out if he plays every minute the rest of the game. Ouch. Lets sit him since he probably needs a breather anyways.

Now do we wait for 5 minutes or sit him till halftime?  If he goes back in at 25mins: 13+5+2=20% vs 20mins: 9+3+1=13%.  Up to you.

Picking up a 3rd foul right after half:   22+9+3+1=35% is definitely worth a sit.

4th foul at the 10 minute mark: 33+10+2=45% obviously also worth a sit.

Playing out last 5 minutes with 4 fouls: 25% chance to foul out.

Here is a better visualize of the risk at different time-points vs foul counts:

Obviously all this has to be taken alongside a vast combination of other game factors like when players would naturally be getting rest, player matchups/combinations, in-game momentum and the score, needing Simpson pg skills for the end of the game, etc, which Beilein knows best.

Conventional autobenching seems to do an ok job of getting players away from the dangerzones above the high 20s.

There's probably some excessive benching on every team (very hard to measure) -- I'd guess specifically early in games and with players who have low foul rates and a strong ability to control their foul rate. You're probably fine playing Matthews with 2 fouls in the last 5 minutes before half or after an immediate foul #1 in the first 5 minutes.

Ideally, you'd like to have a sort of smooth decision making curve which keeps players in safer zone closer to the 10-20% mark while minimizing sacrifice of minutes you'd like them to be on the court.

Nice analysis. To me, this supports the auto bench. You want to avoid foul outs, which we've done, and have fouls to give near the end of the game If you are losing and have to foul. I think ideally all players are finishing games with 3 fouls, that way you've been playing d hard and made them earn it from the stripe instead of giving up easy baskets.

The graphs really show that it makes sense to sit the whole first half with 2 fouls. The weakness seems to be benching players with 3 fouls until the 10 min mark in the 2nd half. This says you should only sit them for a few minutes, depending how risk averse you are.

The biggest problem with the auto bench is the inability to be flexible. An analysis like this could allow Beilein to modify his standard rules, for example if after X fouls youre normally allowed back in the game at the Y minute mark, for a player like Matthews he could let him back in 2 min early. (He actually did this with Simpson last game, bringing him in 1:30 early)

My thoughts exactly, even though that may not be the intent here, and the old man in me didnt want to come to that conclusion either...

Beilein said specifically in his postgame after Maryland that with 3 fouls, he's generally holding the player out until the under 12:00 timeout. He said (paraphrased) if Maryland would have went on a run and opened up a lead, he probably would've had to roll the dice and get Zavier back out there sooner, but the reserve guards held the game within reasonable striking distance.

Agreed about needing fouls to spare for the end of the game.  Depending on the game flow, you may also need to save some fouls for OT.  In a close game it makes sense to stretch the auto bench so long as your team doesnt fall behind, because you may be playing extra minutes.

Great analysis. Hard to take into account, but if MD goes at Simpson immediately and hard the possibility he acquires another foul may rise, or his D may slacken. His edge as an on-court threat over the guy on the bench who subs in for him may diminish. He gets a fourth foul and he is playing differently for the rest of the game; Beilein is (then) juggling a whole 'nother set of variables.

Beilein enumerated all of these possibilities under questioning at the postgame presser.

Yet another plus is that a sometimes-tired thirty-minute-a-game guy comes in extremely refreshed, having obtained a great read on what the opponent is doing on O and D, and takes over the game. Which of course happened.

Yes, I'm fine with Beilein's benching strategies.  There are two things that are usually missed when the auto-bench is discussed:

1) If you assume a player doesn't change his aggressiveness, the distribution of fouls would follow a memoryless distribution, probably most closely a Poisson like you used (nice work!). Brian made the comment on the podcast that since Simpson picked up his third foul with 18 minutes to go and he averages 1 foul per 17 minutes, he wouldn't be expected to get his next foul for 17 more minutes which is not correct.

If he didn't change his aggressiveness, he would be "expected" to get his next foul in about 8-9 minutes (i.e. he's about as likely to pick it up in the first half of the 17 minutes as the second half).  So if he picks up his 4th with 10 minutes to go, you're really playing with fire for a guy that is essential to the team.  Then you either need to bench him then to ensure he's available in the last four or so minutes, which is a worse time to have benched him than at the 18 minute mark, or you risk it and have him out there playing probably very much not aggressively.

2) Players do change the way they play, and that's been statistically proven by kenpom and this data supports that.  When players get into "foul trouble" they ease up.  So leaving that player on the floor may not be as effective as you want and is still a risk so just putting him on the bench is perfectly reasonable.

Good assessment and understanding of the results. More recently, Brian has been a little more 'emotional' with his takes and opinions and enjoys supplying conjecture and hawt takes just like the rest of us.

Another factor recently mentioned by Beilein is fatigue = poor decision making, which presumably raises the probability of fouling. Autobench helps mitigate that risk factor as well.

In addition to your very good points, strategy to get another foul on the guy in foul trouble is a timeless basketball tradition. That's not just going at a dude when he's on D, but jumping in front and forcing refs to make block/charge calls.

I think the one foul brief autobench is kind of silly, but as others have pointed out it functions as a stupid early foul deterrent for Michigan players.

Great first Diary post!  Thanks for the french fishy data analysis!

Thanks for doing this analysis.

I think this makes a lot of sense if your main goal is to not have your player foul out, but the reason we don't want a player to foul out is because then he can't play, which is the same outcome as autobench.

In order for autobench to make sense, you have to show that the number of on-court minutes for a player goes UP because you voluntairy take him out of the game.  The goal is not to avoid fouling out but maximizing playing time for your best players.

but the reason we don't want a player to foul out is because then he can't play, which is the same outcome as autobench.

Not exactly.  Autobench sits a guy relatively early in the game.  The objective is to preserve the player for the end of the game, when possessions are at their highest leverage point.

You may say "a basket is a basket" but one with 15 minutes to go barely changes a win probability while one with 1 minute to go massively swings things.  Beilein wants his best players on the floor for those final possessions and I can't argue with that.

I so wish more people understood the concept of leverage.

I read all this nonsense like "a basket is worth the same at the end of the game as at the beginning."

OK, yes, fine, it's worth 2 points.  However.

If the score is tied, and you get a basket to break the tie, and you get the choice of when that scenario occurs, you'd be an idiot if you chose "39 minutes left in the game" instead of "one second left in the game."

It's not about how many points go up on the scoreboard....it's about how much each basket increases or decreases your chances of winning the game.

Nonsense....we don't get the choice of when that occurs in the game, however.  Ah, but we do.  Or at least, the chance to influence it.  Autobenching, as well as things like timeout management, is how coaches decide to exert their high-probability possessions in high-leverage situations.

Very well done.  Is that you John Beilein ?

Beat Sparty!!

Maybe I can look this up myself but a data test is how many games (%) were lost with early or strict auto-bench?  (Not many) Last year’s NC game still bothers me on so many dimensions.

2013 was a magical season. And I still cant bring myself to watch that title game again.  Too heartbreaking.  We had everything lined up to win that game until that damn Hancock caught fire in the 2nd half.

Fuck Louisville and the strippers they rode in on.

I hate when guys get benched after 2 fouls. ...  This has cost Michigan a few wins over the years,how many momentum swings have we seen ?