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Tuesday, August 21, 2012

Quick note: What is the coin toss worth?

"blah blah blah and they'll get the ball to start the second half" = .9296317 points

I actually stumbled on this number on accident. I was calculating the value of an onside kick - is the risk worth the reward? - when I came across a snag I may never overcome (more on that another day). But in the mean time I had to calculate the the value of receiving a kickoff. 

On average, the kicking team outscores the receiving team by .0449188 over the next two possessions. Teams should (almost) always choose to kick to start each half except the receiving team has a 50% chance of getting an extra possession in that half. Because the average possession is worth 1.949101 points, the value of receiving the kick to begin the half is 1.949101*.5-.0449188=.9296317. So, the next time you're watching a game with friends, and your team will be getting the ball to start the second half you can say, "blah blah blah and they'll get the ball to start the second half, and that's worth .9296317 points on average."

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