## Graphs of the Game 11: To foul or not to foul

USA TODAY Sports

I have a feeling that whether or not Ken Bone keeps his job at the end of the season, Thursday's decision not to foul at the end of the ASU game will be an talking point for someone saying Bone should have stayed or should be gone. As we have seen on this site, it is already drawing strong reactions from people both for and against.

I don't have a particularly strong view on way or the other. I didn't watch the game, and don't have strong enough feelings about basketball strategy to really second guess the decision myself. Reading Jeff's earlier post, however, I did realize this is a scenario that either decision can be simulated pretty easily. There is only a short time left int he game at that point, and just about anything that could happen has a pretty well defined, or estimable probability. That being said, I simulated the effects of both possible decisions to see which leads to tie or victory for WSU more often.

#### Simulation 1: No fouling

This simulation was pretty easy. First I simulate a possession for ASU, in which they can make or miss a 2 pt shot, make or miss a 3 point shot, draw a foul and shoot free throws, or turn over the ball. All probabilities for these events are the %s they did these things for the rest of the game, except free throw %, which I took season averages. Then WSU got a possession with the same possibilities (except adjusted probabilities given what they had done in the game up to that point). One simplifying factor here, I didn't factor in slightly lower offensive efficiency for WSU with a short game clock (~ 10 sec).

#### Simulation 2: Fouling

This simulation was a bit more complicated. When WSU is down, on defense they foul. This took 0-3 sec to accomplish (randomly generated), and ASU will shoot their team season average for each shot. When down, on offense WSU runs a hurried possession, taking a random number of seconds (mean of 10s, with a standard deviation of 3 sec), with success at the same offensive efficiency they have had for the rest of the game. When WSU is tied to winning, on defense there is no automatic fouling (still change for incidental fouls, however), and ASU runs a regular possession, taking up to 35s. When the game is tied or WSU is winning, WSU runs a full possession, taking up to 35 sec. The possibilities for each possession are the same as in simulation 1.

Note: Each of these simulations has a few simplifications that slightly biases the outcome in favor of WSU. Namely the WSU does have a drop in offensive efficiency on hurried possessions and ASU doesn't foul when down in a game. These apply to both simulations, so shouldn't bias the results too badly.

I ran both simulations 100,000 times and here are the results:

The graph you are looking at here shows the results of those simulations. Each bar represents how many times simulations arrived at a given point differential at the end of a game (negative numbers mean ASU win, positive WSU wins, 0 is a tie and headed to OT). Blue bars are the results of the first simulation with no fouling, the yellow bars are the results of the second simulation where WSU fouled (Yellow bars are on top and are transparent, so the green are the blue bars underneath the yellow bars).

In simulations where WSU didn't foul, WSU tied or won at the end of the 4th 22.1% of the time. By employing a fouling strategy WSU tied or won 23.0% of the time. Considering the error introduced by simplifications in the simulations, this is essentially an equal success rate. A fouling strategy did allow for more varied outcomes (from winning by two, to losing by 13), but the average outcome was worse (losing by 3.5 on average while fouling, versus losing by 2 on average when not fouling). It is somewhat interesting to note, if we are just looking at wins (dropping ties that would send the game to OT), fouling lead to wins 5.7% of the time, not fouling leads to wins 8.0% of the time.

So there it is. Based on probabilities, it really looks like the decision to foul or not foul didn't really make any difference.

This FanPost does not necessarily reflect the views of the site's writers or editors, who may not have verified its accuracy. It does, however, reflect the views of this particular fan, which is just as important as the views of our writers or editors.

## Trending Discussions

forgot?

As part of the new SB Nation launch, prior users will need to choose a permanent username, along with a new password.

I already have a Vox Media account!

### Verify Vox Media account

As part of the new SB Nation launch, prior MT authors will need to choose a new username and password.

We'll email you a reset link.

Try another email?

### Almost done,

By becoming a registered user, you are also agreeing to our Terms and confirming that you have read our Privacy Policy.

### Join CougCenter

You must be a member of CougCenter to participate.

We have our own Community Guidelines at CougCenter. You should read them.

### Join CougCenter

You must be a member of CougCenter to participate.

We have our own Community Guidelines at CougCenter. You should read them.