#### Friday, October 14th, 2011...4:17 pm

## Running the option in football

Last Sunday, the Carolina Panthers narrowly lost to the New Orleans Saints 27-30 in week 5 of the 2011 NFL season. From the score, Cam Newton appears to have led the Panthers to 3 touchdowns and 2 field goals. The score gives a sense of how the game unfolded that afternoon in Charlotte. Or does it? Take a moment and think about the numbers. The Panthers could have converted 9 field goals or could have scored 4 touchdowns and missed an extra point. In fact, the possibility of missing an extra point opens up other options such as scoring one field goal and four touchdowns without any extra points. If we consider field goals, touchdowns and touchdowns without extra points, there are 7 ways the Panthers could have reached 27 points.

There are more options! Safeties, worth 2 points, occur when the offense is tackled in their own end zone. So, 27 points could accrue from 2 touchdowns, 3 field goals and 2 safeties! Or, how about 12 safeties and a field goal? Frankly, probably not probable! In all, there are 31 different scoring combinations equalling 27 points.

What about New Orleans’ score of 30? Simply adding 3 additional points leads to 41 scoring combinations!

How fast does this grow? Consider the 1916 Cumberland versus Georgia Tech game. Georgia Tech won 222-0. Yes, you read that right, I meant to type two hundred twenty two! Make a guess. How many scoring combinations, however unrealistic? Remember the safeties. For instance, Georgia Tech could have scored with 111 safeties that day! In fact, there are 8,162 ways for Georgia Tech to have reached that score.

This is an overwhelming number of possibilities. Can we use available information to simplify the problem? Let’s return to the Panthers’ game. They scored 6, 7, 7, and 7 points in each of the four quarters of the game. The only way to score 7 points is a touchdown or a field goal and 2 safeties. Let’s assume more than 1 safety could be scored, which is unlikely given safeties occur about once in 20 games, according to What’s a Safety Really Worth. Even with this assumption, we significantly reduce the number of scoring options from 31 to 9.

In a similar way, let’s turn to the scoreboard of the Cumberland versus Georgia Tech game.

Recall, if we simply look at the score 222-0. The number of scoring combinations is 8,162. There are 247 ways to score 63 points. Similarly, there are 168 and 90 ways to score 54 points and 42 points, respectively. So, if we consider how many points were scored in each quarter of the game, we find there are 247 + 247 + 168 + 90 = 752 different ways for Georgia Tech to score in their game. If we assume no safeties, then there are only 80!

So, the next time you see a final score for a game, think twice about assuming what happened. If you want to know, take the option of watching the game (or if the game is over the highlights)!

Thanks to Emily Sansale, a fellow in the 2011 Charlotte Teachers Institute *Math through Popular Culture* seminar, for inspiring this blog entry with her curriculum unit ideas for her fifth grade classroom.