January 23, 2016

WHERE WAS TOM OSBORNE WHEN THEY NEEDED HIM?:

NFL Coaches Are Getting Away With Crimes Against Middle-School Math (BENJAMIN MORRIS, 1/21/16, 538)

The opportunity for the Packers to cap off that already legendary drive with a counterintuitive but mathematically sound two-point attempt -- whether successful or not -- had the potential to be another such reason-affirming moment for me. [...]

Now, don't get me wrong: That the Packers should have gone for two wasn't obvious. But just because it wasn't obvious doesn't mean the call was difficult. This requires no advanced math and could literally be on a middle school homework assignment.

The question is: Which is greater, the chances of (1) Aaron Rodgers converting that 2-point conversion, or the chances that the Packers (2) make the extra point and (3) win in overtime? To make this comparison, we need to know or estimate three numbers.

Let's start by looking at league averages:

Two-point conversion success rate: Since 2001,3 teams have converted 47.2 percent of their 2-point tries from the 2-yard line (431 of 913).
Extra point success rate: Since the inception of the longer extra point this season, NFL kickers have made 94.3 percent of their attempts from the 15-yard line (1,131 of 1,199).
Expected winning percentage in overtime: Since 2001, the away team has won in overtime 45.5 percent of the time (110 of 242 overtimes that produced a winner).
With these numbers (which used only division), we can find our chances of winning for each option using -- wait for it -- multiplication.

Go for two: With no time left, this is exactly equal to the estimated 2-point success rate: 47.2 percent.
Send to overtime: Chances of making extra point multiplied by chances of winning in overtime. 94.3 percent * 45.5 percent = 42.9 percent.
There, we already have a baseline 4.3 percentage point advantage to going for two for a typical road team in the Packers' position, using nothing but grade-school mathematics.

But those are just baselines, right? Everyone from coaches to media to fans will tell you that averages miss the hundreds of situation-specific factors at play. This is a technically true but often misleading rejoinder -- and one that's almost always used only to defend the status quo.

But in the spirit of accuracy and transparency, I've tried to refine the assumptions that go into that calculation above.

Two-point conversion success rate: Adjusting for team strength and refining the data to the most comparable situations boosts our estimate to 48.8 percent.
Extra point success rate: Adjusting for league trends and kicker Mason Crosby's skill raises our estimate to 95.9 percent.
Expected winning percentage in overtime: Adjusting for the overtime rules changes and playoff dynamics lowers our estimate to 42.6 percent.
If you would like a little more detail about how I arrived at those estimates, here is a longish footnote.4

So here's where we stand under our revised assumptions:

Go for two: Equals estimated 2-point success rate: 48.8 percent.
Send to overtime: Chances of making extra point multiplied by chances of winning in overtime. 95.9 percent * 42.6 percent = 40.9 percent.
Naturally, these educated guess assumptions could be off in various respects, but that 8 percentage point gap is hard to overcome. When people who argue that there's too much uncertainty to buck the status quo actually list the variables they have in mind (unfortunately, they often don't), they tend to overestimate the amount that situation-specific variables affect the balance of probabilities. And the variables cited often don't even cut the way they think they do. For example: In this case, an oft-cited factor is that the Packers' receiving corps was weakened by injuries, including the loss of Randall Cobb earlier in the game. But, as I discussed in the footnotes, anything that makes the Packers weaker relative to the Cardinals is likely to hurt their chances in overtime more than their chances of converting the 2-point try.

Thus, our best (and perhaps slightly conservative) estimate is that the Packers cost themselves about 7.9 percent of a win by kicking rather than going for two, and this whole thing could have been avoided if NFL coaches took the time to sit down and learn some basic percentages.


Watching two of the NFL's longest serving coaches--Bill Belichick and Andy Reid--mishandle the play clock at the end of the Pats/Chiefs game was excrutiating.

Posted by at January 23, 2016 8:57 AM

  

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