1st Down Game Theory: Equilibrium and Exploitable Strategies

by Mike Sommers

You are faced with a first and 10 on your own 20 yardline, what percentage of the time should you run vs pass? You are on the 40 yardline, what percentage do you run vs pass?

Equilibrium Strategy
This is a problem that is solvable, but it depends upon your objectives. I used average NFL data. The average pass attempt yields about 11.6 yards per catch with a 60.5% completion rate. I rounded this down to 11 yards and 60% completion rate. The average rush attempt yields 4.36 yards (2011 data) I rounded this down to 4 yards. Now if you approach the problem as an “equilibrium” strategy, your goal is actually to reduce the expected effect on the play to no change in score either way. For those familiar with “EP” (expected points), this doesn’t mean that the EP result would be zero, but that over the long run, the EP would not increase or decrease from it’s current levels. That is, no change in expectation of how many points you score, so if your expected points on first and 10 is .34, using an equilibrium strategy, it will remain .34. This is based upon the assumption that in the very long run, the opponents will either adapt or correctly anticipate how to adapt to exploit whatever strategy you come forward with, so the best plan is to just produce “average” results”. I don’t believe this to be true, but the equilibrium strategy is still valid as a “base strategy”.

When to sacrifice yards for situation

by Mike Sommers

In "A Response To Brian Burke’s Washington Post Article", I stated that a team would actually be better served coming up short of the first down on 1st down. They would be better off setting up a 2nd and short than 1st and 10, unless they were able to surpass the threshold of 4 yards beyond the first down marker. All of these stats are based on normal teams who typically punt on 4th down. If they planned to go for it more optimally on 4th down, I suspect they would need even more than 4 yards to justify getting a conversion.
Before I go on about the exceptions, I thought it would be useful to get a bit more specific about the situations in which a 1st down conversion is not better than a 2nd and short.
Here is a graph and table of the expected points given the situation. While any 1st and 10 is more favorable than a 2nd and 3, a 2nd and 1 would still be 5 yards better than a 1st and 10. In other words, a 2nd and 1 on your own 29 yard-line is worth more expected points than a 1st and 10 on the 34.

Are punters getting better?

by Michael Beuoy
Punts
The second most unloved play in the NFL (behind the extra point and, possibly, the Blaine Gabbert pass). When they show a punt on DirecTV's Redzone Channel, Andrew Siciliano actually apologizes, as if it were an errant f-bomb that made it past their tape delay.

The purpose of this post is to show some statistical love for this less glamorous element of the game. Much has been made of the improvement in field goal accuracy over the years. Do we see a similar improvement in punting? What I found is that punters are improving, having added about 4 net yards to their punts over the past ten years.

Data
For this analysis, I used the play by play data Brian Burke posts on his site, looking at seasons 2002 through 2011. From the fields and the play description, I was able to parse out which plays were punts, as well as the following data fields:

• Field Position (where the team punted from)
• Gross Yards (how far the kick went)
• Net Yards
• Result - Did the play end in a touchback, fair catch, downed by the kicking team, muff, return, or block?
• Penalty Yards (if any) assessed on the punt

I only focused on "normal" punts for this analysis, meaning I excluded any punts that were blocked or that somehow resulted in the punting team retaining possession. If a punt had to be rekicked due to penalty, I am only counting the second "official" punt.

Response to Brian Burke's Washington Post article

By Mike Sommers

NB: I have also posted this on a site that I own and occasionally like to post to here.

I recently read Brian Burke’s article describing how coaches should avoid the mentality of trying to set up 3rd and short or 2nd and short and instead try to convert the first down.

It is not that I don’t agree with the article, but I wanted to consider several exceptions to that rule, and in the process came up with some interesting conclusions.

I can illustrate several instances where it’s best to NOT convert on first down. On 3rd however I can only think of 1, and it isn’t provable so much as it is intuitive, but I do have a statistical reference, unfortunately we just don’t have enough information to account for changes AS the play develops.

Brees, Unitas and DiMaggio: 47-Game Streaks Fifty Years Apart, and that 56-Gamer, in Perspective.

by Jim Glass

Drew Brees is collecting well-deserved congratulations on breaking what many have long considered to be the greatest record in pro-football: the streak of 47 consecutive games with a touchdown pass thrown, set by John Unitas during the 1956 through 1960 seasons. In my youth that was often compared to Joe DiMaggio's famous "unbreakable record" 56-game hitting streak in baseball. Last week it was again.

Yet Brees tied-and-broke that record with no fewer than seven TD passes in his last two games, while looking as if he's going to "keep on going and going and going" like that trademarked battery-packed bunny.

So just how "unbreakable" should these records be considered to be?  With all the changes in the game that have occurred during the last 60 years, has Brees' streak really matched Unitas' as being "comparably unlikely," an equal achievement against the odds?  And how do these streaks actually compare to DiMaggio's.   Here's a quick take:

Running the Numbers

How unlikely were the Brees and Unitas 47-game streaks?   To adjust for the different styles of play of different times, a reasonable measure is the probability of the average team of each era (not quarterbacked by Brees or Unitas) scoring at least one touchdown by passing for that many consecutive games. 

Combining Win Probability Model With Live WP Graph

by Tom Baldwin

Andrew Foland provided a solution to this all the way back in January 2011, but it has not been implemented, perhaps because of the complexity of the solution, perhaps simply because nobody has got around to it yet, whichever the case I am here to provide a simple alternative and hope it gets implemented.

The problem is that of combining the prior strength of the teams – the expected difference in performance over a game, let us call this S, with the current state of the game as expressed as a probability, WP. To do this we must consider the total game time, 60 minutes, and the game time remaining, T, in minutes.

Comeback Wins/Losses: The Comeback Kings

by Clark Heins

For every comeback win there is a corresponding comeback loss, and one cannot be considered without the other. A comeback win occurs when the winning team overcomes a deficit at the start of the fourth quarter, at sometime during the fourth quarter or, if necessary, in overtime. Comeback wins have little to do with “comeback opportunities,” as the latter deal specifically with a point spread of eight or fewer points and include games that are tied in the fourth quarter. A comeback win can occur from any deficit and doesn’t deal with ties.

For the purposes of this study, I have made no attempt to credit a QB’s total of comeback wins/losses based upon whether or not he deserves them, as luck always plays a role. My totals are entirely based upon one criteria---who was the QB of record when the comeback win or loss was attained, regardless of how it was attained. As an example, I didn't credit Dan Marino, John Elway, Kerry Collins, and Warren Moon with comeback wins when they were injured during a game-winning drive and replaced by another QB. To do so would ignore the element of luck. Also, my calculations are based upon “QB starts” rather than “games played”, as it would be extremely unfair to use the latter stat for many of the QBs. “QB starts” isn’t perfect either, as several of the QBs mentioned here scored comeback wins or losses in relief.