It feels like a perfect night. You and your friends are gathered around, dressed up like hipsters, as the Super Bowl is about to start. Then someone asks if you want to buy a Super Bowl square.
They explain: Super Bowl squares require participants to fill in 100 squares on an unlabeled 10-by-10 grid. There’s no real strategy; if it’s got a blank space, baby, write your name or initials and wait for the big reveal. The 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. Each axis will correspond to one of the teams in the Super Bowl: either the San Francisco 49ers on the vertical axis and the Kansas City Chiefs on the horizontal, or vice versa.
End of carouselTo determine which tiny little masterpiece is a winner, you take the last digit of each 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 the box at the intersection of Chiefs 0 and 49ers 7, and the final score is 30-27 Chiefs — or 27-20 49ers — you’ll get a prize. If you’re in a contest that rewards participants after every score, and the 49ers reach the end zone first for a 7-0 lead, then — ready for it? — you win!
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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 — field goals are worth three points, and touchdowns with extra points are worth 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 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, including the playoffs.
That means that in an imaginary $1-per-square pool that awards $25 at the end of each quarter (for a game ending in regulation), the enchanted 0|0 combination has an expected value of $7.62 per $1 wagered.
It’s 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, because they never go out of style.
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(The first number listed in these combinations is for the home team, which in this Super Bowl is technically the Chiefs. Obviously there is no real home-field advantage in the Super Bowl.)
I don’t know about you, but I’m not feeling 22. That’s because the worst squares to own are those with the numbers 2, 5, 8 and 9. Most of them return less than $0.10 on the dollar, with some — like 5|2, 5|5 and 2|2 — returning less than five cents per $1 wagered. If you get the 4|1 square take a deep breath and just look forward to the commercials: It is the worst one to own for a first-quarter payout. If you roll the dice and wind up with 0|5, 9|9 or 5|3 then roll your eyes because those aren’t great, either.
Historical trends are a good starting point, but we can get a little more specific using data from the teams in Sunday’s matchup. Both teams ranked in the top 10 in offensive efficiency during the regular season after adjusting for opponent, with the 49ers finishing No. 1 overall. In playoff games featuring two offensively efficient teams, the 4|0 square becomes much more valuable in the first quarter, occurring 10 percent of the time compared to four percent across all games.
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At the half of such games, the 4|7 and 4|0 squares are the most valuable, followed by 4|4. The 0|0 square, the most frequent outcome among all games, is the 10th-most likely outcome in playoff games featuring two teams in the top 10 of adjusted efficiency. As for the final score, the 4|1 square is the most lucrative in these matchups of high-powered offenses, occurring eight percent of the time, nearly four times as often when looking at all games.
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