It’s that time of year: your officemate is collecting money for Super Bowl boxes. Those things where you pay somewhere between $5 to $20 to put your name in a blank box which will eventually have two numbers attached to it. At the end of each quarter, the last number of each team’s score is taken and someone wins. The great thing about these things are that they require absolutely no skill, i.e. non-fans are just as good at it as the guy who watches three games simultaneously every Sunday and is in four fantasy leagues. When you fill in the box, there’s no way of knowing which numbers you are going to get.
You get your numbers and hope for the best. Nonetheless, if you know the first thing about football, with a 2-5, you know you’re sort of screwed and are going to be resigned to rooting for safeties, missed extra points and teams going for two in inappropriate situations. So, what if this were a game of skill, and there’s an auction for the numbers. What’s the most valuable box?
There are three factors that matter and can be easily dealt with:
- The historical odds of a team landing on a given score
- The over/under of the current game
- The payout schedule of your bet
For historical scores by quarter, I used the scores provided on some guy’s blog (section Breaking It Down Even More: Quarter by Quarter).
I didn’t want to spend the time pulling the data myself, though would’ve used more than six years had I done so. Addressing the second point, if the average game has an over/under of 45, this six years of data represents an average. With an expected shootout (O/U 55), I tweaked the odds by quarter to make the less likely scores more likely, especially in the later quarters. Here is my new distribution.
This adjustment was sort of crude and next year, I’ll use actual data sorted by expected over under to avoid making these generalizations. Lastly, we need to assume some sort of payout schedule. Let’s say we have $10 boxes and the payouts are $150, $200, $150, $500, rounded to the nearest dollar, here’s what each box is worth:
The unexciting 0 – 0 is the best box! While it’s value from the actual score being 0 – 0 after the first quarter is virtually nil, 10 – 0, 10 – 10, 20 – 10, 20 – 20, and to a lesser degree scores with a 30 in them have decent odds. Enjoy and remember no matter how bad your numbers are, there’s always a chance.
The guest author created The Efficient Drinker. He’d also like to mention that there’s a fourth factor, which adds a level of complexity that makes his brain hurt. Can you guess what it is and why it’s difficult to deal with?
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