## What is the Best Score Prediction for an NFL Football Game?

The 2016 Super Bowl will be played in two days. My Zoltar system (named after the arcade fortune teller machine) says that the Carolina Panthers are 1 point better than the Denver Broncos. Because the Las Vegas point spread has the Panthers 5.5 points better than the Broncos, Zoltar would recommend betting on the underdog Broncos. You’ll win your bet if the Broncos win outright, or if the Panthers win but by 5 points or less (as Zoltar predicts).

Suppose you’re sitting around with a group of 10 friends on Sunday morning, getting ready to watch the Super Bowl. To make things interesting, you decide to all predict the score of the game (rather than the point spread). Everyone contributes \$100 and whoever has the best prediction wins the \$1000 pot.

An interesting question is, “What exactly do we mean by the best predicted score?” A pure math answer is to compute squared error and the best prediction is the one with the smallest error. For example, if one person predicts the Panther will win 31-27 and the actual result is that the Broncos won 30-24 then the squared error is (31-24)^2 + (27-30)^2 = 58.

But this approach makes no sense because the person making the prediction didn’t even get the correct winner of the game. Anyway, there is no definitive way to define what the best score prediction is; you just have to come up with one of many reasonable alternatives and agree to it before the game starts.

For example, one possible approach is:

1.) Any predicted score that has the correct winner of the game is better than any predicted score that doesn’t get the correct winner.

2.) Define error as abs(winner actual score – winner predicted score) + abs(loser actual score – loser predicted score). Here abs is absolute value, meaning just use the difference in predicted and actual scores.

3.) If errors of two predictions are equal, tie break with closest predicted score of the winner.

4.) If still tied, split pot.

Suppose the actual result of the game turns out to be that the Broncos win 35-32 and suppose four of the predictions were:

a.) Broncos 30-28
b.) Broncos 31-30
c.) Broncos 32-29
d.) Panthers 32-31

Person d.) is immediately eliminated because they didn’t get the correct winner. The errors for the other three predictions are:

a.) 5 + 4 = 9
b.) 4 + 2 = 6
c.) 3 + 3 = 6

So persons b.) and c.) are tied with the lowest error. The person b.) prediction for the winner’s score is off by 4 points but the person c.) prediction is off by only 3 points so person c.) has the best prediction and wins the pot.

The moral of the story is: don’t watch the Super Bowl with a bunch of math and computer geeks.

Update, Monday Feb 8, 2016: The Broncos beat the Panthers 24-10 so you’d have won your bet if you followed Zoltar’s advice.