Overview of Strategy

In the previous posts, we have considered different strategies that can be employed in Football (Super Bowl) Squares. If you are selecting multiple squares, we found different configurations result in different average outcomes. We found that how many squares you select affect the outcome. Finally, your outcome can be different if you choose only to play certain games (like those expected to be low scoring games). In all cases, we found that the game is fair in the sense that no strategy can affect your long term average expectation of winning squares (4% per square per game). What the strategy can affect is the relative likelihood for the different possible outcomes in a single game for winning zero, 1, or 2 or more squares. Here two extreme strategy emerge.

The first strategy assumes you want to maximize your chance of winning something for each game you play. You can do this by picking squares along a diagonal or otherwise such that each square selected has a unique row and column. You minimize the effect of the correlations between the squares in each of the quarters and so you minimize the chances of winning two or more squares. You can maximize this strategy on a per square basis by picking a single square.

The second strategy assumes you want to maximize your chance for winning two or more squares. The strategy essentially trades off a small increased probability that you won't win anything for a much larger (relative) probability that you'll win two or more squares. You can adopt this strategy by picking squares in the row or column corresponding to the team that is the underdog.

To highlight the two strategies, one study showed the following: Picking seven squares in a column gives you nearly the same chance to win something as picking six along the diagonal, but a 75% more chance of winning 2 or more squares.

Here is a grand tabulation of all the possible ways of selecting 1, 2, 3, or 4 squares ordered by the strategy probability for winning 2 or more squares. This tabulation is based upon 1 billion simulations using 5209 games (1994-through the the 2013-2014 regular season). All shown are all the possible ways of selecting 5 squares. Squares in adjacent columns do not need to be next to each other, but anywhere along the same column where the column represents the underdog. Similarly for the rows. If you are picking four squares, you can choose the first strategy (four in a diagonal, labeled A) to give you a maximum probability of 13.47% to win something or the second strategy (four in a column, labeled H) to give you the maximum probability of 2.97% to win two or more squares. Or ... you can choose some other configuration to give you the best of both worlds. The choice of strategy is up to you!

Type of Game Strategy

By type of game, we consider additional information usually available to a player before selecting squares. We have already found that to maximize the probability for winning two or more squares, the optimal  strategy  is to pick squares in a single column corresponding to the underdog team. If the column happens to correspond to the favored team, turn the 10 x 10 grid by 90 degrees. The underdog and favorite teams are determined by the pregame point spread or line (points by which the favorite team is expected to win).

In addition, before a game, the over/under (O/U, how many points are expected to be scored totaled for both teams) is also something that is usually known. The player can use this information and may choose to alter selections depending on the type of game that is involved. We study by selecting sub-samples of the 4953 games from 1994-2012. We divide the total number of games into five sub-samples. We consider 957, 1080, 929, 1102, and 985 games with the O/U<=37.0, 37<O/U<=40, 40<O/U<42.5,42.5<=O/U<45.5, and O/U>=45.5. In terms of expected scoring, these five sub-samples represent expected extreme low scoring, low scoring, average scoring, high scoring, and extreme high scoring games. Simulations of each of these five sub-samples have been run - each with 100 million trials.

The first observation from looking at the results of the trials is that the patterns that represent the possible player selection choices are exactly in the same order as previously discussed under "Configuration Strategy" no matter which sub-sample is considered. A second observation is that the five sub-samples could be described by three: O/U<=37, 37<O/U<42.5, and O/U>=42.5 as there is not much difference between low and average scoring. Nor is there much difference between high and extreme high scoring games. The figure below shows, as a function of the different configuration patterns when selecting four squares, the probability of winning two or more squares. Note how the five sub-samples form essentially three bands.


Consider the configurations A and H which represent selecting four squares each on a unique row and column (A) and selecting four squares in the column of the underdog team (H). When it is expected to be an extreme low scoring game, configuration A has a 2.47% likely chance of winning two or more squares and configuration H has a 3.19% chance. When the game is expected to be high scoring, it is less likely that teams will score "0" in a quarter and less likely that scores will be correlated and thus less likely that winners will win two or more squares. For configuration A, only 2.08% of the time would winning two or more squares occur and for configuration H, only 2.80%.

The basic strategy to be more likely to win two or more squares always holds. Pick them in a column corresponding to the underdog team. If you choose to select squares only if it is also expected to be an extreme low scoring games, you will enhance the likelihood of winning two or more squares. If your goal is to have the largest chance for winning at least one square (most often a single square), then picking squares in unique rows and columns always holds. For a low scoring game, you would have 13.09% chance if you pick four squares. For a high scoring game, your likelihood increases to a probability of winning 13.74% (but from the figure above, you'd only have a 2.08% chance of winning two or more squares).