Down 7-0 midway through the 1^{st} quarter of the College Football Playoff National Championship game, Ohio State was facing a 4^{th} and 2 at the Oregon 35 yard line. Buckeye coach Urban Meyer had a decision to make. Attempt a 52 yard field goal, punt and try to pin Oregon deep inside their own territory, or attempt to gain the 2 yards and get a fresh set of downs. Meyer decided to go for it. Ohio State got the first down, scored a touchdown on the drive, and didn't trail again the remainder of the game.

Clearly Ohio State made the correct decision. Right?

Too often we wait until we see the outcome of the play before we decide whether a coach’s decision was correct. If Meyer had failed on the 4^{th} down conversion, certainly we would have said it was the wrong decision. But coaches can’t tell the future. So how could we determine what the correct decision is before the play is run? The answer is a 4^{th} down calculator using Minitab Statistical Software.

# How the Calculator Works

To make an informed decision on 4^{th} down, you need to know two things. First is your probability of getting a first down. Obviously your probability increases as the yards you need to gain decrease. Second is the expected points a team would score with a first down at a specific field position. If you go for it on 4^{th} down and fail, your opponent will be more likely to score than if you punted due to better field position. But is that risk outweighed by the increase in expected points you’ll gain by successfully converting on 4^{th} down? That’s the question the calculator will answer.

# Why Specifically the Big 10?

There are already multiple 4^{th} down calculators out there using NFL data, so I wanted to stick to college football since I couldn’t find any calculators that use college data. And because of the massive time investment it took to collect the data, I had to limit my scope. So I decided to collect data from games that involved only teams from the Big 10 Conference. While the resulting model could probably be applied to any college football team, I’m only going to apply it to Big 10 Conference games this season. Particularly, because I want to track each team’s decision.

You always hear stat-heads saying that on 4^{th} down coaches should be punting less and going for it more on. (Spoiler alert: My model is surely going to echo the same sentiments.) But you don’t see anybody compiling what happens next. Are coaches that punt on 4^{th} and short from midfield winning the battle of field position and scoring next? Or are their opponents scoring anyway despite having to drive the length of the field. By tracking both the decision and the result, we can compare the theoretical expected points to what actually happened. And in a perfect world we’ll also have a number of coaches who go for it, so we can compare the two decisions directly and see who scores more points.

Tracking this for every college football team seemed daunting. But doing so for the fourteen Big 10 teams seems feasible. So at least for now, the Big 10 it is!

# Back to the National Championship Game

So did Ohio State make the correct decision? Let’s find out! There are still some variables that we don’t (and can’t) know. For example, if they punt, where will the ball be downed? And if they successfully convert the 4^{th} and 2, how many yards will they gain? So we’re going to make some assumptions.

- If Ohio State punted, they would down the ball at the 1 yard line
- If they convert the 4
^{th}down, they would only gain the minimum yards needed

This assumes the best case scenario for a punt, and the worst case scenario for a successful 4^{th} down conversion.

Our model gives Ohio State a 62% chance of gaining the 1^{st} down, and a 47% chance of making a 52 yard field goal. If Oregon starts with the ball on their own 1 yard line, their expected points are -1.24. That means that even though Oregon has the ball, Ohio State is more likely to be the next team that scores. If Oregon starts at their own 35 yard line (after a failed 4^{th} down or field goal attempt), their expected points are 1.33. And if Ohio State gains 2 yards and has a 1^{st} and 10 on the Oregon 33, their expected points are 3.75. Now we can determine what the correct decision is!

Expected Points FG Att = (3*.47) – (1.33*.53) = **0.71**

Expected Points Punt = **1.24**

Expected Points Go for it = (3.75*.62) – (1.33*.38) = **1.82**

So Meyer made correct decision, regardless of the outcome of the play. And this assumes the best case scenario for a punt and the worst case scenario for a successful 4^{th} down conversion. If you change either of our assumptions, the numbers will favor going for it even more. And of course the outcome worked out in Ohio State’s favor, as they ended up scoring a touchdown on the drive.

Those are the type of situations that will be analyzed this fall. In the following weeks I’ll write a series of posts detailing the model that will be used. Then starting in September, I’ll do a weekly post after each Big 10 Conference game (I won't include non-conference games so I avoid games like Ohio State vs. Hawaii and Wisconsin vs. Troy) summarizing each team’s 4^{th} down decisions from the weekend.

So is your coach costing your team points by making sub optimal 4^{th} down decisions? Stay tuned to find out!