Sunday, October 21, 2007

The Tennessee Titans at Houston Texans game completed earlier this afternoon had two major streakiness story lines. Houston, trailing 32-7 entering the fourth quarter, went on a 29-3 burst in the final period to take a 36-35 lead with 57 seconds remaining. Tennessee moved the ball down the field in the closing moments, however, to set up kicker Rob Bironas for a game-winning 29-yard field goal as time ran out ( game recap).

The other streaky element was the "hot foot" of Bironas. His winning kick was his eighth successful field goal of the game, which sets a new NFL record (he had no misses). The yardage distances of the field goals in the order in which they occurred are as follows:

52, 25, 21, 30, 28, 43, 29, 29

Looking at Bironas's career statistics from various distances (which appear to be from before the Houston game, given that shortly after the game, his distance-specific stats for this season hadn't been updated, so I would doubt his career ones had been), they are as follows (career stats offer a bigger sample size than just those from 2007):

20-29 yards 21/23 (.91)
30-39 yards 18/19 (.95)
40-49 yards 11/18 (.61)
50+ yards 3/7 (.43)

To estimate the probability of Bironas's making all eight field-goal attempts he took, given that he would be receiving these opportunities, we multiply the component probabilities together:

(.43) (.91) (.91) (.95) (.91) (.61) (.91) (.91)

which yields .155. If we also factored in the likelihood of an NFL team having so many drives stall in fairly close proximity to the goal line, the probability of Bironas's accomplishment would probably get even smaller.

A couple of cautions are in order about this analysis. First, it is the unusual nature of the feat (or in this case, foot) that drew me to conduct the analysis; I did not seek a random cross-section of games. Second, the equation I used assumes independence of observations, that the outcome of any one kick had no impact on the next.

The independence assumption is typically associated with sequences of coin flips and dice rollings, which unlike humans, cannot experience momentum and other associated psychological states. However, having conducted numerous analyses over the years for this website, I consider the independence assumption to hold pretty well for athletic performances, too.

As for Houston's team-comeback element, which unfortunately for Texans' fans did not hold up, I would direct you to my statistical analysis of a relatively recent, similar comeback by Texas Tech (where I'm on the faculty) against Minnesota in last December's Insight Bowl.

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