David Romer, a Berkeley economist, ran a statistical analysis of the worth of trying to convert a fourth down on any given point on a football field. Coupling this data with the worth of punting or kicking a field goal from the same position, he was able to assess whether or not a team should go for the 1st down or not at any given point on the field. His answers were surprising. He found that NFL coaches are much more conservative than they should be.
Take, for example, a fourth and three on the opponents' three yard line. According to Romer's data (harvested from the 1999-2001 football seasons), 38 of 47 times the team opted to kick a field goal instead of going for a touchdown. However, a team going for the touchdown in that same situation has a 43% chance of scoring a touchdown. Even if the team's kicker is 100% accurate in all situations at the three yard line, they only gain three points from the play. However, if the team goes for the touchdown they'll gain an average of 3.01 points. Already it is apparent that they may be better off going for the TD. Even if they miss, they pin their opponent within the three, which is optimal for gaining 2 more points off a safety. Adding the potential of these points to the 3.01 average and it becomes abundantly clear that going for the TD is a better idea.
Here is an excerpt from his paper:
Recommended Choices. Figure 5 [below] combines the analyses of kicking and going for it by showing the number of yards to go where the average payoffs to kicking and going for it are equal as a function of the team’s position. On the team’s own half of the field, going for it is better on average as long as there are less than about 4 yards to go. After midfield, the gain from kicking falls, and so the critical value rises. It is 6.5 yards at the opponent’s 45 and peaks at 9.8 on the opponent’s 33. As the team gets into field-goal range, the critical value falls rapidly; its lowest point is 4.0 yards on the 21. Thereafter, the value of kicking changes little while the value of going for it rises. As a result, the critical value rises again. The analysis implies that once a team reaches its opponent’s 5, it is always better off on average going for it. The two dotted lines in the figure show the two-standard-error bands for the critical values.16 The critical values are estimated fairly precisely.
Although these findings contradict the conventional wisdom, they are quite intuitive. As described in the introduction, one case where one can see the intuition clearly is fourth and goal on the 2. The expected payoffs in terms of immediate points to the two choices are very similar, but trying for a touchdown on average leaves the other team in considerably worse field position.
Thus trying for a touchdown is better on average. Another case where one can see the intuition fairly easily is fourth and 3 or 4 on the fifty. If the team goes for a first down, it has about a fifty-fifty chance of success; thus both the team and its opponent have about a 50 percent chance of a first and 10. But the team will gain an average of about 6 yards on the fourth-down play; thus it ison average better off than its opponent if it goes for it. If the team punts, its opponent will on average end up with a first and 10 around its 14. Both standard views about football and the analysis in Section II suggest that the team and its opponent are about equally well off in this situation. Thus, the team is on average better off than its opponent if it goes for a first down, but not if it punts. Going for the first down is therefore preferable on average.
The very high critical values in the dead zone also have an intuitive explanation. The chances of success if the team goes for it decline only moderately as the number of yards to go increases. For example, away from the opponent’s end zone, teams obtain a first down or touchdown on third down 64 percent of the time when they have 1 yard to go, 44 percent of the time when they have 5 yards to go, and 34 percent of the time when they have 10 yards to go. As a result, the value of going for it falls only moderately as the number of yards to go rises. Thus the large decrease in the gain from kicking in the dead zone causes a large increase in the critical value.
Actual Choices. Teams’ actual choices are dramatically more conservative than the choices recommended by the dynamic-programming analysis. On the 1604 fourth downs in the sample where the analysis implies that teams are on average better off kicking, they went for it only 9 times. But on the 1068 fourth downs where the analysis implies that teams are on average better off going for it, they kicked 959 times.
The dashed line in Figure 5 summarizes teams’ actual choices. It shows, for each point on the field, the largest number of yards to go with the property that when teams have that many or fewer yards to go, they go for it at least as often as they kick. Over most of the field, even with 1 yard to go teams usually kick. Teams are slightly more aggressive in the dead zone, but are still far less aggressive than the dynamic-programming analysis suggests.
However, in real life, with factors like momentum and individual teams' offense/defense, these findings cannot be totally accurate, right? Well, Romer's data still stands strong in spite of other factors. I won't go into all the details here, but if you want to learn more about this, I encourage you to read Romer's paper. Here is the link for it. In addition to the paper, I have also linked the hard data too.
Now that your brains are warmed up on this Monday morning, let's get to some links!
With all Cal competitiors finished at NCAA Track&Field-Cal Athletics has closed the book on 2008-09! Congrats to all on an historical year.
Senior Katie Morgan was unable to successfully defend her 2008 NCAA pole vault title on Friday at the NCAA Championships in Fayetteville, Ark. Junior Tracey Stewartwasn't able to qualify for the final in the triple jump and seniors Brook Turner and Kandi Bonty had their seasons come to an end in the semifinals of the 400 meters.
Morgan posted a mark of 13-5.25 (4.10m) to place 13th overall in the pole vault. Indiana State's Kylie Hutson won the event with a score of 14-5.25 (4.40m).
Bonty finished in 13th overall in the semifinals of the 400, clocking in at 53.88. In the other semifinal heat, Turner crossed the finish line at 54.89 to place 17th overall.
Stewart recorded a mark of 39-10.00 (12.14m) to finish in 27th in the prelims of the triple jump.