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In collegiate football, ties are now rare, only two percent of the games ending this way in 1967, the highest scoring tie being 37-37. Ties happen less than half as often as one-point differences. The most frequent outcome of a game was 14-7, although the most frequent winning score was 21 and the most frequent losing score was O. The average winning score was 27, the average losing score, 10. A team score of 11 has a 25 percent chance of being a winning score, a score of 16 a 50 percent chance, a score of 23 a 75 percent chance and a score of 40 is practically certain to win, based on a freehand curve. Scores of 3, 9, 10 are more favorable to winning than their size would suggest, while 18 and 22 are less favorable than theirs suggests. Indeed, a score of 9 is more likely to win than is a score of 15, and nearly as likely as a score of 18. When a loser scores 0, the average winning score is 27, but when the loser scores 3, the average winning score is only 19. Average winning scores are roughly hyperbolically related to losing scores. Looking at it the other way around, losers score most on the average when winners get 31 to 40 points, and then losers average about 13 points. As one would expect, differences in scores of 7, 14, 21, 28, 34, and 35 are especially frequent. When average total score in the game is plotted against difference of score, the fitted curve is approximately a hyperbola. Simulated scores of games obtained by drawing two team scores at random give an average difference in scores of 14.7, considerably less than the actual average difference of 16.7. In 1967 at least, the Southwestern conference and the Big Ten were each composed of teams more closely matched then average pairs of teams. Ivy League teams were more disparately matched than average, and the Pacific Eight and the... [ABSTRACT FROM AUTHOR]

The frequency distribution of grouped scores of individual teams in U.S. collegiate football games closely follows the negative binomial distribution. [ABSTRACT FROM AUTHOR]