I’ll admit it: I’m not “wired” correctly. I remember being around 8-9 years old, fresh off of playing Madden ’94, yelling at the TV when the Miami Dolphins called a timeout to save themselves the five yard penalty with 11 minutes to go in the second half. “You idiots! That 5 yards is worth a lot less than saving 40 seconds in the waning moments of the game!” I said, probably not nearly as eloquent as I have just phrased it.

I was right then, I’m right now: you should save the timeout and not worry about the yardage. I just need to prove it. And that brings us to this post.

Using 2013 full college football play data collected by Reddit’s CFB Analysis group, I have attempted to parse and determine conversion rate of various down and distances. However, this data is not very clean, so I will present it in two different fashions. If I can ever find a cleaner data source, I will definitely update this, so if you have anything, please contact me.

Part A, the cost of a 5 yard penalty:

First, I calculated the conversion rate on that down. What that means is if you start off on 1st and 10, what is the likelihood that you will convert on that play. This eliminates some of the data abnormalities (that tend to pop up on 4th downs). Here is the table, with YTG being “Yards to go” (for the first down):

Down 0-4 YTG 5-9 YTG 10-14 YTG 15-19 YTG 20-24 YTG 25+ YTG Total 1 50.2% 29.3% 24.0% 15.5% 10.3% 11.6% 24.6% 2 60.7% 34.9% 24.8% 15.9% 12.3% 13.4% 36.5% 3 61.7% 40.2% 31.6% 21.2% 15.7% 10.7% 44.6% Grand Total 60% 36% 25% 18% 13% 12% 33%

In general, what you’ll find is that as you move from one yardage segment to the one to the right, you decrease your conversion % on the next play by about 1/3 of what it was prior to the penalty.

The second data source is whether you convert within that set of downs. This once again becomes a little more confusing due to data issues, but we will assume that this is early enough in the game that one is not going for it on fourth down, in an attempt to minimize the cloudiness in the data. Here’s that table:

Down 0-4 YTG 5-9 YTG 10-14 YTG 15-19 YTG 20-24 YTG 25+ YTG Total 1 91.5% 83.0% 78.8% 67.2% 63.6% 55.4% 78.9% 2 85.4% 70.8% 60.6% 47.6% 40.7% 37.8% 69.5% 3 61.7% 40.2% 31.6% 21.2% 15.7% 10.7% 44.6% Grand Total 75% 61% 72% 44% 39% 33% 69%

As you can see, once you factor in converting on the full set of downs, the conversion rate skyrockets (I was surprised), while moving from one bracket to the right costs you, on average, the following:

1st down: Around 10% (%, not points)

2nd down: Around 20%

3rd down: Around 33%

I do find it interesting how the relationship remains pretty static in going from, say, 0-4 YTG to5-9 YTG compared to 10-14 turning into 15-19. The standard deviation off of the averages is not too high of a number.

So what does this tell us so far? First, it indicates to me that taking a timeout has to offset the negative effect of a 5 yard penalty. As we saw above, that impact is a lot higher on third down, but even then the likelihood of conversion from 3rd and 5 or greater is below 50%.

Unless you are The U:

Let’s move on, shall we?

Part B, the value of the timeout:

This one is a little harder to put your finger on. With the help of Advanced Football Analytics’ Win Probability Calculator, I plugged in a couple of common scenarios.

Scenario 1: You take the ball on your own 25 down 7 points in the fourth quarter, both teams being equal in talent.

Scenario 2: You take the ball on your own 25 down 3 points in the fourth quarter, both teams being equal in talent.

Obviously the line of scrimmage will affect the values of these win probabilities, but the relationship between the times remains similar. Here is the data:

Time left WP down 7 WP down 3 2:40 16% 22% 2:20 14% 20% 2:00 12% 19% 1:40 9% 18% 1:20 7% 15% 1:00 5% 12% 0:40 4% 8% 0:20 2% 5%

As you can see, moving across any 40 second difference within the win probabilities ends up costing you around a 4% chance of winning the game (though the number increases quite a bit inside 1 minute). In this sense, I think it’s fair to say that a timeout that saves you 40 seconds is worth 4% of win probability.

Part C, putting it all together:

So if we think that a timeout in a game you’re trailing is worth about a 4% win probability addition, and that a 5 yard penalty decreases your likelihood of converting for a first down by a function of 10% * the down number (roughly), the only piece left is determining when the tradeoff is worth it.

The main factor is obviously field position. When you’re at the 10 yard line, a 5 yard penalty has a more dramatic impact to the end of the game than a 5 yard penalty when you’re sitting on your own 30. As such, I once again got intricately familiar with the win probability calculator and input all of the combinations for both the third and fourth quarters (as the first half has such minimal impact on win probability with both timeouts and 5 yard penalties, the impact isn’t severe, though I personally believe you should play each half the same).

So here it is, the final, definitive* chart on when you should call a time out versus when you should take a delay of game:

* until someone proves me wrong

The biggest takeaways for me are that in general, you should always call a timeout when in FG range on 2nd or 3rd down, but on first down the 5 yard deficit is easily overcome. Also, that inside of 10 yards on 2nd or 3rd down you should call a timeout in the 4th quarter for practically the entire length of the field. Certainly not what I expected.

Did I do well? Did I miss something? Can I improve? Let me know in the comments.