On Saturday night, Tom Herman made the “risky” play call and chose to go for the first down facing a 4th and 3 from the Oklahoma State 28 yard line. It was clear at that point that this would be a difficult game for Texas to come away victorious. Texas was up 14-6 at that point, with the chance to make it a two-score game, so the calls from many fans, especially after the attempt resulted in a loss of a yard and a turnover on downs, was that Herman should have “taken the points” and not gambled with the score.

What follows is a statistical and numerical defense of the decision to go for it.

First, let’s get out of the way the common complaints:

This is going to be a close game. You should just take the points when you have the chance to. You have a stud field goal kicker who just nailed a 57 yard field goal last week against Rice. Let him kick the ball. I agree with gambling sometimes, but I don’t like the decision to gamble here.

All of these are, to some degree, the same complaint phrased differently. Still, I will address each one separately.

1. This is going to be a close game. You should just take the points when you have the chance to.

I agree. When playing a close game, you should do whatever you can to maximize the expected number of points you will score.

Let’s talk about expectation values for a second:

An expectation value is the long run average of outcomes in a trial repeated with the same conditions. For example: the expectation value from rolling a six sided die is 3.5 because you are equally likely to get a 1, 2, 3, 4, 5, or 6 as an outcome and, if you average these values, you get a 3.5.

In this case, we care about the expectation value for how many points one can expect Texas to score facing 4th and 3 from the opponent’s 28 yard line. That is, if Texas repeated the same situation over and over and over again ad nauseam, how many points will Texas, on average, score?

Let’s also state a fact: the absolute maximum the expectation value can be from kicking a field goal is 3. You can never score more than 3 points, therefore assuming a perfect kicker, you could expect 3 points (the maximum) for attempting a field goal in that situation.

Now let’s look at going for it on 4th down:

There are many possible timelines that this can take. For one, you can fail the 4th down conversion and it’s all over right there. Alternatively, if the 4th down conversion is successful, you could continue to drive down the field and score a touchdown. But there are still other options. You could face another 4th down on your way to the end zone and attempt a field goal from there. You could also attempt, once again, to go for it. Maybe something bad happens on the drive and you lose yards. Maybe you turn the ball over. Well, luckily, the data accounts for all these possibilities, so let’s look at it.

How do we use data in this situation?

By looking at the drive-level data, we can take into consideration starting field position and points yielded from the drive. We can then take all data points that share a starting yard mark and average them to get a quasi-expectation value for a drive starting on that yard-line. We can then take those data points a fit a polynomial to get a more smoothed out representation of the expected points we would score at each starting field position. Let me say right now that there are not many drives in a season, so this data is not ideal for making exact conclusions. What it is good for, however, is getting ballpark values. I have no doubt in my mind that Herman and co. have an extensive amount of data that they obtain from Longhorn practice and analysis of their opponents, so their result will be even more informed than mine (but spoiler: mine is still going to come out favoring them).

So I took Longhorn drive data, averaged out common values, fit a polynomial, and got this:

According to the fit: the expectation value for points on a drive starting from the opponent’s 28 (or 72 on this plot) is 4.74.

But wait! Facing 4th and 3 from the 28 is not the same as facing 1st and 10 from the 28. That’s right, there’s a non-zero chance of failing the first down attempt (which we saw on Saturday), and, in fact, if they are successful, the “drive” doesn’t start at the 28, it starts from wherever their successful attempt lands them. To get the expectation value from this situation, in reality, we have to multiply the probability of converting a first down on 4th and 3 by the expectation value for points at whatever yard line they end up on, which is, at worst, on the 25 (so we will use the 25).

So now let’s look at Longhorn 4th down success: Texas was 12/15 on 4th down in 2018 and, going into last night, 3/5 in 2019 (both failures coming on goal-line stands against LSU). From 4th and 3, Texas was 1/1 in 2018, and 2/2 in 2019 before the attempt. We can’t take a value of 100% for this, though, because there is of course the opportunity for failure. Let’s just take our overall 4th down success over the last 2 years, 15/20, into this consideration, given that they are all short-to-medium-yard situations. (Again, I have no doubt that Herman and co. have a TON more data on this and a much more accurate number, but we will use this value here). That’s a success rate of 75%. Furthermore, the expected number of points for a drive starting on the opponent’s 25 (a number that only gets higher the closer you get to the end zone), is 4.91 points. Multiplying the probability of converting the first down by the point expectation value gives 3.68. That means that Texas could expect 3.68 points from going for it and, at most, 3 for kicking the field goal.

Let’s maybe phrase this another way. Texas had the ball 13 times against Oklahoma State. If every one of their drives involved facing a 4th and 3 from the Oklahoma State 28 and Texas chose to kick it every time with perfect accuracy, they would have scored 13*3 = 39 points. If Texas chose to go for it every time, based on 2018 and 2019 results, we would expect them to convert the 4th down about 9.75/13 times (failing 3.25 times), but even with these failures, Texas would end the game with 47.84 points on average giving them an expected 8.84 points more than in the case where they kick it every time (perfectly).

Therefore, in a close game, you should do the thing that is expected to give you more points. It is hard to see that when the attempt results in a failure, but the stats and numbers don’t lie here.

Alternatively, if attempt was successful, and Texas got a touchdown (giving them an extra 4 points over a would-have-been field goal) and the game had ended with a margin fewer than 4 points in Texas’ favor the decision to go for it would have been the difference maker in the game.

2. You have a stud field goal kicker who just nailed a 57 yard field goal last week against Rice. Let him kick the ball.

Yes, Dicker is a stud with an incredibly accurate leg. I am a huge fan of his and I am so happy that we finally have a reliable kicker. The unfortunate thing here, though, is that this is still a 45 yard field goal. Kicking it from 45 yards isn’t trivial for anybody, even the kickers with the highest success rate in the league. So far, in this analysis, we have assumed a perfect kicker who we can guarantee will hit the ball through the uprights every time. Dicker, even with how good he is, is not that.

Here is a plot showing Texas’ field goal kicking in 2018

And here it is in 2019

I really shouldn’t need to go into more detail here, because it’s self-explanatory, but Dicker was 7/11 from this range in 2018 and 3/4 in 2019. If we take his 57 yarder last week to help his average, he is 4/5 this year and 11/16 from 40-49 (and 57) over his career. If we take all of his attempts fewer than 46 yards, even the ones from 20-29 yards (which significantly improve his average), he is 14/19, or 73.7%. That means (really at best) the real expectation value for kicking a 45 yard field goal is 2.21 points.

Factoring this in, in their 13 equivalent drives, Texas would be expected to score 28.74 points, as opposed to the 48.74 points they would get from going for it.

Again, especially with kicking, I am sure the Texas staff has hundreds of data points for Dicker including lateral ball placement, wind speed/direction, and hundreds more kicks worth of data to get a more accurate average. Still, even we assumed a perfect kicker, it was better to go for it. This is just a reminder that even though Dicker is great, he is not perfect. Nobody is. (Really think about it: if Dicker went 13/13 on 45 yard field goals, that would be mind-blowing.)

I also want to note that going for it gives you an opportunity to kick a shorter field goal (with much higher odds) later in the drive. The endzone is not the only objective.

And finally…

3. I agree with gambling sometimes, but I don’t like the decision to gamble here.

While technically, this fits the definition of a gamble (per Wikipedia “Gambling is the wagering of … something of value [points] on an event with an uncertain outcome, with the primary intent of winning [points]. Gambling thus requires three elements to be present: consideration, risk, and a prize.”), to phrase it as a gamble is a little bit disingenuous. A gamble gives the impression that the odds are stacked against you: that in the long run, with repeated attempts at the same action, you will ultimately lose out, but in this short-run instance, you want to roll the dice and try your luck. That is not what this was, though.

The decision to go for it on 4th and 3, numerically speaking, was akin to investing money in an IRA. In the long run, you will win, but you always risk losing some in the short run due to dips in the market (or failed plays).

It’s easy to call a 4th down attempt a gamble because the outcome is so direct. The risk of failure is more obvious. However, numerically speaking, you are not going to lose in the long run.

Conclusion

I understand that sometimes football isn’t rational. I am often an incredibly irrational fan: seeing a DB get beat by one of the top receivers in the country and complaining about their poor performance, getting frustrated that we might lose a game when the odds are more than 90% that we will win…

However, in this case, Herman made the rational decision to go for it on 4th down. It’s unfortunate that we did not convert, but that is always the risk you take. Kicking a field goal is often framed as “taking the points” because it’s a single event which is often successful. In this case, though, Herman “took the points” by choosing the path that would lead to more points on the scoreboard over the long run. I hope this analysis was convincing of that fact, but if it wasn’t, I can understand remaining irrational. Just understand yourself that what you think is the rational decision is, in fact, irrational.

My Own Issues With the Decision

Okay, now that I have just defended the decision to go for it, I will say this. I don’t like how we went for it. Our intention was to run hurry-up offense, catch Oklahoma State off guard or not ready, and run the ball up the middle for 3 quick yards. This is a good idea if it looked like we were actually catching Oklahoma State off guard, but they were lined up to defend the play well before we snapped the ball. That should have been signal to take a step back, change the play, and run something other than a run up the middle when Oklahoma State stacked the box with about 8 people. I like the decision to go for it, I don’t like the manner in which we went for it.