Even in this digital age, if you find yourself at a Super Bowl party on Sunday, you might be asked if you want to participate in a box pool; also known as the ideal remaining use of poster board and Sharpies; also known as Super Bowl squares. There is no skill involved — participants aren’t actually “picking” anything other than a random square on a grid — but there is a chance at a decent payoff if you have one of the winning boxes. And, most interesting for our purposes: You can tell right away if the odds will be in your favor when the Kansas City Chiefs and Philadelphia Eagles take the field, based on what numbers you receive.
First, a step back. For the unfamiliar, Super Bowl squares require participants to place their name or initials in one or more of 100 squares on a 10-by-10 grid. Those initialed squares will eventually cover the entire grid, at which point each column and row will be labeled with a random number from 0 to 9, with each axis corresponding to one of the teams. To determine which box is a winner, you take the last digit of each Super Bowl team’s score — sometimes done at the conclusion of each quarter, at each scoring change and/or at the final whistle — and find the corresponding square on the grid. If you have Chiefs 4 and Eagles 7, and the final score is 34-27 Chiefs — or 27-24 Eagles — you win.
But while every participant has the same chance before the numbers are filled in, every numerical combination does not have the same chance of winning. NFL scoring clusters around the numbers three and seven, making boxes containing those numbers (or 0) the most lucrative. Since 2015, when the league pushed back the line of scrimmage for extra-point kick attempts, the best square to have for an NFL game has been 0|0, a score combination found at the end of around eight percent of quarters of all games over the past eight seasons, including the playoffs. In an imaginary $1 pool that awards $25 at the end of each quarter (for a game ending in regulation), that combination has an expected value of $7.59 per $1 wagered. It’s by far the most lucrative square to own, followed by 7|0; 0|7; 0|3; 3|0; and 7|7. In general, the more 0, 3 and 7 squares you have, the better.
(The first number listed in these combinations is for the home team, which in this Super Bowl is technically the Eagles. Obviously there is no real home-field advantage in the Super Bowl, although the Eagles are slight favorites in the game.)
The worst squares to own are those with the numbers 2, 5, 8 and 9. Most of them return less than $0.50 on the dollar, with some — like 5|2, 2|2 and 9|8 — returning less than a dime per $1 wagered. If you get the 4|2 square, then just enjoy the start of the game or the buffet table: It is the worst one to own for a first-quarter payout. Feel free to commiserate with anyone who has 2|9, 9|8 or 5|9 as those, too, are horrible options.
Historical trends are a good starting point, but we can get a little more specific using data from the teams in Sunday’s matchup. For example, in games with an over/under total set around 50 or 51 points, similar to this Super Bowl, the frequency of the 0|0 box hitting in the first quarter declines from 16 to 12 percent while the 3|3 box almost doubles in frequency, from 4 percent overall to 7 percent. (The over/under total is the betting term for the total points to be scored in the game.) There are some small sample size distortions happening in these calculations, yet it’s still instructive.
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What we really want to know, of course, is what boxes should be the best to have for this specific game. That’s a relatively easy task, since we know how each team has performed this season relative to their competition. The Chiefs led the league with 2.7 points per drive while the Eagles were second with 2.6 points per drive, playoffs included. Philadelphia’s defense, however, was much better at limiting opponents (1.7 points per drive allowed, sixth) than was Kansas City (2.0, 19th), which should slightly skew which boxes are most desirable in this game.
This can be broken down further by quarter, giving use even more granular data to model a potential score. Using this data, and simulating the game 10,000 times while recording how many points are expected in each frame, can yield some reasonable expectations for a squares pool. Based on this model, the most likely score after the first quarter is 3-3, which occurs 14 percent of the time, nearly double the typical frequency it occurs in games with an over/under total of 50 or 51.
In fact, a 3-3 tie after the first quarter is expected to be the best square/quarter combination on this Super Bowl Sunday, outperforming all other squares at each interval. One of the teams leading 3-0 after the first quarter is the next best option (11 percent chance for both 0|3 and 3|0), followed closely by a scoreless first quarter (10 percent of simulations). A box with 3|0 or 0|3 is the best to have for halftime and a 0|3 box, meaning the Eagles have a zero at the end of their score and the Chiefs a three, is projected as the best square to own at the end of the third quarter. According to our projections, the box most likely to take home the final prize at the end of the game is 3|6, which could mean a 23-16, 33-26 or even 13-6 victory by the Eagles — or a 36-33 win by the Chiefs.
For more ways to enjoy the Super Bowl, don’t miss our printable prop bets extravaganza, our look at the odds for who will score the first touchdown, and our favorite bets going into the game.