from Amazon
Wednesday, October 18, 2006
Game Theory in Football
A look at whether teams should pass more on 1st and ten, from Ben Alamar.
The key data for those who don’t want to read the whole thing is…
... On 1st and ten, when 60 to 80 yards away from the end-zone, teams ran 50% of the time.
As a control, on the 3rd and 7 or more plays, teams passed 88% of the time. The author reports the average yards per rush as 6.7 in the 3rd and long situation, and 4.1 for the 1st and ten, which is what you’d expect. That is, teams are ok giving up a rush of 6 or less yards, and, knowing that teams only run 12% of the time, are willing to concede a first down on a rush every now and then. The author doesn’t report specific numbers on the passing plays on 3rd and long, other than to say that they are not much different than the 1st and ten. I would have preferred to see the actual numbers.
On the 1st and ten, teams got 7+ yards from the passing play 41% of the time, which seems what they get on the rushing plays as well on 3rd and 10. That is, if it’s a given that teams will get a 1st down on 3rd and (exactly) 7 about 40% of the time, then if they get it on a pass or on a rush play each at 40%, then we are in balance (mostly). Not totally, since 7+ yard pass will have a higher mean than a 7+ yard rush.
If the results really shows that the teams are not as successful as they should be on 1st and 10 as opposed to 3rd and 7+ on pass plays, that calls into question that maybe they don’t pass enough on the 1st down.
In football, things aren’t as clearcut, because a “state” would also include the previous play. For example, 41% of the time, a team, following a pass play will be 2nd and 10, while following a rushing play, they will be 2nd and 10 21% of the time. Will a team on 2nd and 10 produce the same results, regardless if the previous play was a pass or run? I don’t know.
The entire theory of “establishing the run” is really what drives this whole game theory process. It would be interesting to see even more data on the subject.