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A Mathematical Analysis of Pat Fitzgerald's 4th Down Decisions: Week 1

Fourth down decisions are always a popular subject among college football fans. Should the coach have punted or rolled the dice and gone for it? Should he have attempted a long field goal or punted and pinned the other team deep in their own territory? One of the reason these debates raged on is it's difficult to quantify the pros and cons of each decision; no one knew exactly how much 35 yards of field position was worth. But now, thanks to people who are a lot smarter than I am, it's possible to quantify the relative merits of each fourth down possibility and come up with a reasoned answer. Every week, Sippin' On Purple will focus this analysis on Pat Fitzgerald and see if he's making the right calls on fourth down.

The data I'll be using for these posts comes from two sources. The first is a study by a Cal-Berkeley professor named David Romer. Romer took a look at three seasons worth of NFL data and calculated a ton of interesting things, including a chart that shows how many points a team can expect to score on 1st down at every position on the field (the chart is page 39 of his study). It's important to note that the expected point total isn't just for a team's current possession, it also includes the expected point total when the opponent gets the ball back. That means a team can possess the ball yet have a negative expected point total; inside their own 15 yard line the defense gains the advantage. There's a lot of advanced math in the study, so it's dense reading, but you can skim past the equations and still get a lot out of it, it comes highly recommended.

Of course the one drawback here is that the data is from NFL games, so it's not perfect. However, points per possession for an average college team is similar to an average NFL team, so it works for our purposes here,

Also, an MGoBlog author who goes by The Mathlete looked at every FBS game from 2004 to 2009 and calculated the nationwide success rate on 4th and 1, 4th and 2, etc. The resulting table shows the success rate for an average offensive team and a great offensive team; until proven otherwise we'll use the average offense numbers for Northwestern (there's not much of a difference anyway).

From Saturday's game against BC, there were three fourth down situations I thought were worthy of closer analysis....

For clarity's sake, here are the two charts that will be referenced in the analysis

Value of Situation, via David Romer

MGoBlog 4th down success rates


Decision 1

Situation: 4th and 1 at the BC 10 yard line, 15:00 left in 2nd quarter
Score: Northwestern 3, BC 3

Going for it: The chances of converting 4th and 1 are 72%. If the play is successful, NU will have 1st and Goal at around the 8 yard line. Per Romer, that's worth 4.3 points on average for NU. If the play fails, BC will have the ball at their own 10 yard line; that's worth 0.2 points on average for NU. So going for it has an overall expectation of 3.152 points.

Field goal: Since going for it is worth more than 3 points on average, its clear that kicking a field goal, which is only good for 3 points if successful, is not the right play. For the sake of completeness, assuming Jeff Budzien will make 85% of his 27 yard field goals, kicking the field goal is worth 2.01 points*.

* That may seem like a low number, since 85 percent of 3 is 2.55. The reason for the difference is when the field goal is made, BC will get the ball back on their own 27 yard line on average, which is worth -0.6 points for NU. A failed fourth down attempt gives BC much worse field position.

Verdict: Going for it is clearly the right play.

Fitzgerald's verdict: He went for it. Nice job Fitz.

Result: Kain Colter was stuffed and BC took over

Decision 2

Situation: 4th and 4 at the BC 44 yard line, 6:15 left in 3rd quarter
Score: Northwestern 17, BC 10

Going for it: The chances of success are 47%. If NU gets the first down, they will be at about the BC 35 yard line on average. This is worth 2.6 points for NU. If the conversion fails, BC will take over on about their own 43 yard line on average. This is worth -1.7 points for NU. Overall, going for it gains 0.321 points.

Punting: The only question is what BC's average field position will be after a punt. Some of the time the punt will go into the end zone, and most of the other times it will be downed inside the 20. There's also the rare fumbled snap or blocked punt, but those are extremely unlikely. I'd say BC will probably start at about their own 15 yard line on average, which is worth 0 points for each team.

Verdict: Going for it is slightly better, but it's pretty close.

Fitzgerald's verdict: He punted. Can't fault him too much for this one.

Result: The punt was a touchback, BC took over on their own 20.

Decision 3

Situation: 4th and 1 at the BC 33 yard line, 1:41 left
Score: Northwestern 24, BC 17

Endgame situations are harder to analyze because there are added variables that aren't very relevant earlier in the game (timeouts left, score, etc.), but we'll give it a shot anyway.

Going for it: Since BC has no timeouts left, a first down ends the game; Northwestern can take a knee. So 72% of the time, NU converts and the game is over. The other 28% of the time, BC takes over at about their own 34.

Field goal: A made field goal basically ends the game as well, but not quite: BC does get another chance on offense, and can tie or win if they get a quick score then recover an onside kick. Extremely unlikely, but a lot more likely than a fumbled snap after an NU first down. Regardless, the chances of a made 50 yard field goal are a lot less than the 72% chance of getting a first down, so the field goal is out.

Punting: A punt probably only gains about 20 yards on average, and guarantees BC a chance to tie. Of course, BC is less likely to score a tying touchdown from their own 13 yard line than from the 34 after a failed NU 4th down attempt, but how much less likely?

Conservatively, let's estimate a large difference. Say BC gets a touchdown 25% of the time from the 34 and 10% of the time from the 13. Then the chances of them tying it when NU goes for it on 4th down are 0.28*0.25, or 7% of the time, less than the 10% after a punt.

Verdict: Going for it is the right play.

Fitzgerald's verdict: He went for it, nice job again Fitz.

Result: Colter was tackled behind the line of scrimmage and BC took over at their own 36, but failed to tie the game.

So a good week for Pat Fitzgerald on 4th down. Both times going for it on 4th down was clearly the correct decision, he went for it. And even though he may have made one minor mistake, he's probably doing a better job than most of the risk-adverse coaches in FBS.