"Breakeven" Analysis on Coach's Challenges

[UNCrules2187]

Really interesting post on Advanced Football Analytics that attempts to quantify the impact of a coach's challenge and whether or not the flag should have been thrown:

 

 

Every replay situation is unique. We can't quantify the probability that a particular play will be overturned statistically, but we can determine the breakeven probability of success for a challenge to be worthwhile for any situation. If a coach believes the chance of overturning the call is above the breakeven level, he should challenge. Below the breakeven level, he should hold onto his red flag.

 

To calculate the breakeven probability of reversal, we need a bit of algebra. Let's define the relevant numbers as follows:

 

B = breakeven probability of reversal

R = win probability given call reversed

U = win probability given call upheld

N = win probability given no challenge is made

 

We just need set the WP of no challenge (N) equal to the "lottery" of challenging the call and we get:

 

N = B * R + (1-B ) * U

 

Solving for B, we get:

 

B = (N - U) / (R - U)

 

This makes sense, because the lower the WP penalty is for a failed challenge, the lower the breakeven success probability needs to be. Likewise, the bigger the WP bonus is for reversal, the lower the breakeven success probability needs to be.

 

The post then analyzes a few challenges, including what I'm sure many of us thought was a dumb challenge by Ron Rivera on that short completion by McCown on 1st and 10 at the beginning of the 3rd quarter:

 

6. 1-10-CAR 41, 14:57 in the 3rd, CAR ahead by 10 -- TB's Josh McCown escapes a sack and completes a 4-yard pass. CAR challenges, hoping McCown was down before throwing but the call is upheld. I commented that I believed it was an unwise challenge at the time, but the breakeven was only 7%.

 

Now, I doubt coaches are thinking in these terms, but the post's conclusion seems to show that coaches' intuition/gut has probably been more correct than we tend to think:

 

 

These six examples are instructive. First, contrary to my intuition, it seems that coaches are not blowing their timeouts on frivolous challenges. If a call is fishy at all--say somewhere in the neighborhood of a 1-in-10 or 1-in-20 chance of being overturned, and the difference in outcomes moves the WP needle at all, it's probably a good idea to challenge it. Certainly any time a score or turnover is on the line, it should be challenged. When a conversion is at stake, or even when the probability of a conversion is significantly affected, it's probably a good idea to challenge.

 

Things change late in close games when timeouts begin to skyrocket in value. But until then, there are just too many different and more important factors than timeouts. A team could end up ahead, and not need their timeouts at all. Or they could easily end up where they would lose even if they had six timeouts.

 

http://www.advancedfootballanalytics.com/2014/09/analyzing-replay-challenges.html#more