Last year I wrote a column
describing how to value draws in the popular office pool, Super Bowl Squares. I’m going to update it for the 2014 game; if you need more details on the game or the methodology, see last year’s column.
The game is played on a 10 x 10 grid. Players buy squares by paying a fixed amount (I’m using $50 for this example, but it can be any amount) and picking a square by writing their name in it. When all the squares are filled, the organizer draws the number 0 through 9 at random to assign to each of the rows, and then again to assign to each of the columns. In this way, each square gets assigned a row digit from 0 to 9 and a column digit from 0 to 9.
Suppose your square gets 4 for the row and 8 for the column. By convention, the rows represent the NFC team (Seattle Seahawks this year) and columns represent the AFC team (Denver Broncos). You win if the final digit of the Seahawk’s score is 4, and the final digit of the Bronco’s score is 8. Note that this is different from the square with 8 for the row and 4 for the column, which wins if the Seahawk’s last digit is 8 and the Bronco’s last digit is 4.
Rules differ on how to award the prize money, but a common pattern is to award one-eighth of the pool based on the first-quarter score, one-quarter based on the halftime score, one-eighth based on the score at the end of the third quarter, and one-half based on the final score of the game.
There is no skill involved in this game; it’s pure gambling because the row and column assignments are random. Still, it’s nice to know what your square is worth, and sometimes people buy, sell, or trade squares.
The most common method for valuing squares is using the results of past NFL games. This is not accurate. Games differ quite a bit. If you only use similar games, your sample size is too small for accurate value estimates, especially of the less valuable squares. If you use a large sample, you will be including games played under different conditions, by different kinds of teams, possibly in different eras.
A better approach is to simulate games. You don’t need the kind of sophisticated simulation a quantitative sports bettor would use. All you have to do is get a reasonable guess at the most probable numbers of touchdowns and field goals each team might score (we’ll talk about missed extra points, two point conversions, safeties and overtime later).
For 2014, the Broncos are a 2-point favorite over the Seahawks, and the over/under (a bet on the total number of points scored by both teams) is 48. So the oddsmakers are telling us they expect the Broncos to score 25 points, on average, and the Seahawks 23. There are reasons these odds differ from the actual probabilities (and this year more than most), but they’re more accurate forecasts than most people can come up with on their own. They’re certainly good enough for this purpose.
The other thing that matters a lot is the propensity of teams to get touchdowns versus field goals. In the regular season and the play-offs, the Broncos scored 81 touchdowns versus only 30 field goals. That’s a very high ratio of touchdowns, reflecting a potent offense that generally got the ball in the end zone. The Seahawks scored 49 touchdowns and 39 field goals, a low ratio of touchdowns, although not as far from the median as the Broncos in the other direction. The Seahawks were usually ahead in their games, and were content to run the ball with moderate success, eating up the clock and kicking field goals.
If we apply these proportions to the Bronco’s expected 25 points, it suggests that on average they should score 3.1 touchdowns and get 1.1 field goals. The Seahawks project out to 2.5 touchdowns and 2.0 field goals. Given these baseline expectations, any reasonable simple simulation will give decent valuations for the Super Bowl squares. You can get fancy and put in weather-related variables, different game trajectories, injury simulations, and play-by-play statistics; or you can pretend that you’re drawing scoring slips out of an urn.
One thing that does matter is some of the less common events mentioned above. Although individually uncommon, they are important for the values of certain squares. Safeties for one. Here I believe there’s little reason to think any team or game is more or less susceptible to safeties than average; there’s just not enough data. So sticking in some average value is fine. I put missed extra points in the same category, unless you’re doing weather or injury simulations. Two-point conversions can be covered by simple rules that NFL coaches follow most of the time. Overtime can be modeled with sufficient accuracy by flipping a coin and awarding three extra points to the winner.
Here’s how my simulations values this year’s Super Bowl Squares. Squares are colored from green (most valuable) through yellow (average) through red (least valuable). Any number above $50 is good, since the squares cost $50.
Last year 0,0 was the most valuable square, which is often true. But in 2014 there are six more valuable squares led by 3,0. Zeros, 3s, and 7s are always good, but this year 0s and 3s for the Seahawks are particularly good, while the three good digits are closer to equally valuable for the Broncos. Four is the next best number, but this year for the Seahawks it is much worse than 0 or 3, while for the Broncos it’s almost as good as the best numbers.
Six and 1 are usually the average numbers. Last year 6 was pretty good but 1 was bad; this year it’s the reverse. In fact, 6,6 is the worst square of all, an honor that usually goes to 2,2 (on the other hand, you might not care much between an expected value of $1.06 and one of $0.69). Squares with 2s, 5s, 8s, or 9s are generally bad.
In case your game uses a different payout structure, I give the four component tables for the table above: how much you expect to get for the first quarter, half-time, third quarter, and final score payouts.
Finally, if your game has a payout for the score at the end of regulation, here is its value (calibrated to a total payout of $625). These numbers are not included in the total value table above.
As always, enjoy the game, enjoy the play, and let the numbers work for you.
No positions in stocks mentioned.
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