Mathematical Application of The Two-point Conversion
In 2007, blogger Eric Menhart analyzed the value of going for a two point conversion compared to a field goal style extra point in the National Football League, concluding that teams are usually better served kicking the extra point in most cases. This was consistent with the results in the XFL, which had an average success rate of 40% for their one-point conversions (the XFL, as previously mentioned, required scrimmage plays for one point and did not allow kicks). This counters Tuesday Morning Quarterback columnist Gregg Easterbrook's theory that since the average yards gained on a typical scrimmage play is 5 yards, that the opposite is true and that the two-point conversion would, on average, bring a greater point value return; furthermore, Easterbrook cites the Football Prospectus, which says that the average success rate on a two-point conversion is between 50% and 55%, depending on the time frame used and the situations in which the conversion is attempted. The two-point conversion usually involves goal-line defenses and are thus not typical scrimmage plays, resulting in shorter average gains. Regardless of the actual success rate, professional teams seldom attempt the two-point conversion, unless an "eight-point" touchdown results in a certain point margin, either leading, tied, or behind, preferring the near-certain single point (see below.)
While in theory a 50% success rate should result in the same amount of points scored as one-point conversions, this approach does not reflect the realities of game situations. While two-point conversions might result in the same number of points over a season long period this is not how success is measured. Even with a 50% success rate it is certainly possible for a team to miss multiple two point conversions in one game, and then lose to a team who scored the same number of touchdowns but scored their points-after, and while this might be followed by a game where a team makes all their two point conversions to give an average of 50% and the same number of points overall, losing and winning games is much more important for determining success.
There is a relatively common game situation in which the two-point conversion can be an optimal strategy even if its likelihood is under 50%. A team down fourteen points in the final minutes must score two touchdowns while keeping their opponents scoreless in order to tie or win the game. In this situation, it is possible (but unlikely for a team) to go for two after the first score, because if the team makes it, they can kick an extra point in their next score to secure a win, while if they miss, they still have a chance to make the next two-point conversion to get to fourteen. Though the logic seems counter-intuitive, this maximizes a team's win probability. The odds of converting a two-point try either on the first attempt (securing a win) or the second (securing a tie and sending the game into overtime) are higher than the odds of missing both (securing a loss), as long as the expected probability is higher than about 39 percent. Notably, Texas Longhorns coach Darrell Royal successfully used this strategy to defeat Arkansas in 1969's Game of the Century. Nevertheless, coaches continually under utilize this strategy, preferring the conservative approach so as not to alienate fans.
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