Betting the over/under of football games is perhaps the most intriguing plays in the world of gambling. It entails the bettor simply choosing whether the final combined score of a given game will be above (over) or below (under) a number designated by the casino. In order to do so with any accuracy, a mathematically inclined bettor must determine which statistical measures of a team's past performance should be used to predict future performance.
A common practice in choosing the over or under of a game is to look at the average points scored for each participating team in their respective seasons. This fails in two regards. First, this method does not take into account the defensive strength of the current opponent. Secondly, points scored is a wildly varying statistic on its own. Through the first five weeks of the 2010 NFL season, the average of all teams' standard deviation of points scored is 8.89. Considering that the average number of points scored by a team is 20.78 over that same period, a standard deviation of 8.89 is so high that any attempt to use past points scored as an indicator of future points scored would be futile.
Since past points scored is not a useful statistic, we turn to more consistent measures of team performance: First Downs Gained, Rushing Yards, and Passing Yards. These statistics translate almost directly to points scored in a game and are far more consistent from game to game (e.g. the average standard deviation of first downs gained is 4.10 while the average total gained is 18.71). Additionally, defensive strength can be accounted for more specifically by averaging the offense's and the defense's season averages in these measures. For example, an offense with an extraordinary number of first downs (24) and rushing yards (150), but weak passing yards (180) that is matching up against a defense that gives up few first downs (16) and rushing yards (80), but a lot of passing yards (280) will result in weaker than usual first downs (20) and rushing yards (115) but stronger passing yards (230) than usual for the offensive unit.
To utilize these consistent statistics we first take the total number of points scored in the NFL over all weeks and divide it by the total number of first downs gained, total rushing yards, and total passing yards. These equations yield the number of points attributable to one unit of measure or "points per unit" (PPU). These values are 1.11 points/first down; 0.19 points/rushing yard; and 0.09 points/passing yard. Then we must calculate the expected performance of each team's offense across these three measures. This is done by finding the season averages for the offense and the average allowed values for the defense and then averaging them together. Next, we multiply these expected offensive numbers by their respective PPU. Finally, we must average (weighted) these values together to yield a total number of points expected from a given offense/defense match up. The weighted average is derived from the correlation of each statistical measure to points scored for every game in the NFL season to this point. First downs gained and rushing yards have the same correlation coefficient to points scored, and passing yards is half as correlated. We weight each performance measure accordingly. We must repeat the entire process for the opposing team.