By Daniel Adler

Here at the Sports Analysis Collective, we often do some pretty complex analysis. However, this post is about something at which this guy excels. One thing that has always interested me is a coach’s decision of when to go for two. Historically, two-point conversions are successful 44% of the time and the one-point attempt rate is successful 99% of the time. Thus, the expected value of a kick is .99 points (99% x 1 point) and the expected value of going for two is .88 points (44% x 2 points). Obviously, there are still situations in which going for two is the right move. Since all that adding by 1, 2, 3, 6, 7, and 8 can be confusing in the heat of the moment, coaches often use a chart, which tells them what to do. Here is a common one. We’ll analyze Tony Sparano’s (seemingly) ridiculous decision after the jump.

With the team up by 11 and just under 9 minutes to play, Sparano went for 2. What is the advantage of being up 13 vs. 12? Blocked extra points aside, there’s not a huge difference if the other team scores 2 TDs. Let’s look at other possibilities…Yes, 12 points loses if you allow a touchdown and two field goals, but with 9 minutes remaining, that seems far-fetched. It seems to me the greater concern should be the TD+2pt and FG combination. However, with 9 minutes to play, three drives is possible. Also, perhaps the odds of TD, FG, FG are greater than TD+2pt, FG. Still, it seems like a bad move. Why not make it a 2 TD game rather than a possible TD+FG game?

Still, Sparano’s decision is supported by this chart (but not this chart). However, analyzing a more nuanced chart created using win probability, we see that Sparano made the wrong decision (unless he felt his team had a >80% chance of converting the two-pointer). However, the chart does reveal a little more. When up by 11, it is never a good idea to go for two (assuming 44% conversion rate), but it is a *less bad* idea with more time remaining. Sparano’s explanation that he did not know how many more “at-bats” the Jets were going to get is actually sensible (however, he does not say he thought that number would be high…if he thought it would be low, his decision was really bad). If he thought the Jets were going to get a lot of “at-bats,” then going for two was not the worst idea in the world. Still, the Jets had only 2 timeouts remaining, which made it less likely they would get lots more chances to score.

In the end, the Dolphins won and Sparano was spared horrible embarrassment. Still, it is interesting to analyze his explanation. To me, it sounds like the “at-bat” comment was just a cover-up, but when we look at the numbers, if you give Sparano the benefit of the doubt, he may just be onto something. In the end, no matter how you cut it, it was the wrong move. Not surprising from a guy who used to be the head coach in New Haven…no, not that New Haven, but this one.

In the context of this specific game I think Sparano was concerned that his offense had been shut down to the tune of 10 first downs (half of which came on the preceding drive) and could easily go 3-and-0 two on their next serieses. That, coupled with a probable concern of his defense’s susceptibility to big plays (hence a quick score or two by the Jets), make this maybe not a good decision but at least not a terrible one and certainly understandable as a judgment made in the heat of the game.

Overall, though, you’re right, NFL coaches are way behind in understanding win probability and things like when to go for two or when to go for it on fourth down.

P.S. Hey, I attended UNH for a little while back in 1991.

One thing I’ve often wondered about is the situation after scoring a touchdown down 16 with maybe 3 minutes left. Coaches always go for 2 in this situation, but I’m not convinced that’s the best move.

The strength of your defense may play a factor here, but lets just look at the possibilities. You either have to:

Make two 2-point conversions and one on-side kick PLUS win in overtime

or

Make two on-side kicks (and a field goal)

I don’t have the number for on-side kick success, I’m sure it’s low, but you’re basically comparing the chance of making an on-side kick to the chance of making two 2-pointers plus winning in overtime. They seem like they should be at least comparable.

Good post. I’ve been trying to spread the word about the wisdom of going for two when down by 14 (pre-touchdown). The “nuanced” chart agrees with this, but the other two don’t.

Assuming a late-game situation where the losing team’s only realistic chance to get back in it is to score two touchdowns, and a conversion rate of 40%, the logic is pretty simple. If you go for two after the first TD and make it you cut the deficit to 6, and the next TD wins the game. If you don’t make it, you still have a chance to force overtime with a conversion after the next TD, a chain of events with a likelihood of 24% (.6 * .4). Assuming overtime is 50/50, the going-for-two strategy yields a win probability of 52% (you know, if you set aside the part about having to score two touchdowns).

The conventional extra point strategy simply gets you into overtime, where your win probability is 50%. Of couse, that’s only a 2% difference, but 40% is probably at the low end of possible conversion rates. A conversion rate of 50% brings the win probability up to 62.5%.

By the way, it seems to me that the main reason the math tends to differ from our own intuition is that we place way too much value on tying the score (or making it more difficult for the other team to tie). So Sparano didn’t take the point to go up by 12–it would’ve taken an unlikely chain of events for the Jets to score 11 and, even then, they would merely tie the game. In fact, my own (possibly faulty) intuition tells me that, if the Jets score and get the ball again, the Dolphins might be better off with a 3-point lead than a 4- or 5-point lead, since the Jets would be conservative and settle for a field goal and overtime instead of trying to win with a touchdown.

The 44%and 99% numbers are widely quoted and also a tad misleading.

Think about the following situation:

The snapper makes a bad snap and the holder can’t get the hold down in time. Realizing this, he picks up the ball and makes a desperation run for the end zone. This gets recorded in the history books as a failed two point attempt when in reality, it was a failed one point attempt.

If you adjust for botched extra points, the conversion percentage of extra points is lower and the conversion % of two points is higher.

Here is a situation I’ve wondered quite a lot. You are down 14 and you score a touchdown. I say you go for 2. Why?

I am assuming that you score two touchdowns, since otherwise this is not important anyways. Here we go.

First Attempt: 44% successful

Now, if you score again, there is a 99% chance you win, .01 chance you go to over time

First Attempt: 56% unsuccessful

Now, you need to convert on the second attempt, which you will 44% of the time, to go to overtime, and you’ll fail 56% of the time to lose.

So, what do we have:

.44*.99= .44 (rounded) chance of victory in regulation

.44*.01 + .56*.44 = .25 chance of overtime

.56*.56 = .31 chance of loss in regulation

Assuming a 50% chance of victory in overtime. By going for two on the first touchdown, you win ~.56% of the time.

Of course, what coach is going to do this.

Great stuff guys. I’m not a football guy, but this is impressive