Thursday, December 26, 2013

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).

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