## Should the Jets Have Gone For 2?

I got a few requests to analyze Rex Ryan’s decision following the Jets' touchdown to go up 7 points with 2 minutes left to play Sunday night. Would it be smart to try for the 2-point conversion? If the Jets convert, they go up by 9, and the game is effectively over. If they fail to convert, they’re still up by 7. On the other hand, kicking the XP puts the Jets up by 8, requiring the Dolphins to go for 2 points themselves if they manage to score.

Looking at things from the Dolphins’ perspective, they would have about a 0.11 Win Probability (WP) being down by 7 with just less than 2 minutes left. (I’ve done some extra analysis by including all similar situations where teams need a TD to win or tie with 2 min left. This expands the sample greatly if we assume it’s the final drive of the game, and each team has a 50/50 WP in overtime. Teams get a needed TD 22% of the time, putting the WP at 0.11, which is the same as what my general WP model estimates.)

Let’s call the probability of converting a 2-point conversion x. The WP of a team down by 8 in the same situation as a team down by 7 would be 0.11x, because they need the TD, plus the conversion, and only then do they get a 50/50 shot in OT.

If the Jets go for the 2-point conversion, the Dolphins' WP would be:

0x + 0.11(1-x)

And if the Jets go for the XP (which is >99%) the Dolphins' WP would be:

0.11x

The break-even probability of converting the 2-point play, where the Jets would be indifferent to either the 2-point attempt or XP, would therefore be:

0.11(1-x) = 0.11x
0.11 – 0.11x = 0.11x
0.22x = 0.11
x = 0.5

And this makes intuitive sense too. In fact, the actual probability of scoring the TD factors out. If the probability of conversion is > 0.5, then the Jets should go for it. If it’s < 0.5, then the Jet’s should kick the XP. If you have a choice between doing something to win, and forcing your opponent to do the same thing to win, all that matters is whether it’s better than a 50/50 proposition, no matter what extra things need to happen along the way.

Say the probability of conversion (x) is 0.6. The Dolphins would have a 0.11(1-0.6) = 0.044 WP if the Jets go for 2, and a 0.11(0.6) = 0.066 WP if the Jets kick the XP.

If the probability of conversion (x) is 0.4, the Dolphins would have a 0.11(1-0.04) = 0.066 WP if the Jets go for 2, and a 0.11(0.4) = 0.044 WP if the Jets kick the extra point.

Knowing that, in general, 2-point conversions are successful slightly less than 50% of the time (i.e. x < 0.5), Rex Ryan probably made the right call by kicking the XP.

### 16 Responses to “Should the Jets Have Gone For 2?”

1. Anonymous says:

Brian, do an analysis on McDaniels decision to go for it on 4th and 3 in the 4th quarter down 7 points.

2. James Sinclair says:

[The James who occasionally comments here—not the James who frequently comments here.]

If you make a few assumptions (extra points are automatic, Miami won't go for two if they can tie it with an extra point, etc.), and ignore any scenario where Miami doesn't score a late touchdown, there are four ways for the game to play out:

Jets go for two:
-NY converts; who cares what Miami does—NY wins.
-NY fails to convert; Miami kicks the extra point—overtime.

Jets kick the extra point:
-Miami fails to convert their two-point conversion—NY wins.
-Miami goes for two and converts—overtime.

In the go-for-it scenarios, the most important factor is NY's likelihood of conversion; in the kick scenarios, the most important factor is NY's likelihood of stopping Miami's conversion attempt. So, unless I'm missing something (a distinct possibility), if the Jets think they have a better chance of making a two-point conversion of their own than they do of stopping a conversion attempt by the Dolphins, they should go for it. If not, they should kick.

3. Brian Burke says:

That would be true.

4. xtimmygx says:

Thanks for looking at this Brian. Definitely should have noticed this on my own. I still wonder about the WP for the Jets when the Dolphins had first down at the 10.5 yard line with just over a minute left. Seems like 0.99 is too high to me in that situation. Even if the Dolphins only had a 25% chance of scoring a TD and a 45% chance of making the 2pt conversion they should still have had more than a 5% chance of winning.

5. James Sinclair says:

Ha, alright—I read more carefully and see now that you made basically the same point. I had thought about this exact question when I saw it come up in a college game last year, so I was excited to show off what I'd figured out.

While I'm at it, it's also interesting to think about whether a team should go for two when down 14 (pre-touchdown) late in the game—late enough that the only real chance of a comeback is two consecutive TDs. If you go for it and convert, the second TD wins the game; if you don't convert, the second TD still gives you a chance to try for overtime (and thus the same 50/50 overtime chance you would've had by kicking two extra points).

The break-even conversion probability is 38.2%, which means most teams should go for it, but I'm not sure I've ever seen it happen.

6. Brian Burke says:

timmy-I think you are right. I'll have to dig into that. The graph has to work automatically, and the algorithm isn't as good as when I can use my own noggin. I think there is a bad number in there somewhere.

7. Brian Burke says:

Ok. Just realized what it is. I just tweaked the model to have yard-by-yard accuracy for TD probability inside the red zone using a Markov process. The new function assumes 7 pts for the TD. I forgot to add an exception for being 8pts down.

8. Anonymous says:

What's interesting is that you might expect the decision to be similar for a TD that puts you up 6, but it's not. The reason makes sense when you think about it: the 2nd team to score can base their decision off of whether or not the 1st team converted. Similar to the college OT system, where if you are on defense first, you know what you have to match when you get on offense.

9. Dan R says:

FYI, Brian Billick did it (go for two after the first TD) in the NFL with the Ravens in the early 2000's, not sure exactly when. It's the only example I've ever seen in the NFL. I cheer for it all the time (whenever I know an onside kick is coming) as succeed the first time vs fail twice doesn't require 50%.

10. Dan R says:

Took a moment to look, Oct 14, 2001 looks like the game. With 38 seconds left on the clock, scoring to go down by 8, they went for 2 instead of 1.

11. James Sinclair says:

@Dan R,
That's cool—I'd love to know how the announcers reacted.

Now that I think about it, Jeff Fisher did it last year (looks like it was the Oct. 4 game against Jacksonville). The Titans were down 21 before the touchdown, but the same logic applies to any multiple-TD deficit. The analysis, I vaguely recall, was along the lines of "I don't know what he's thinking, but they're down by a lot, so I guess they might as well go for it."

12. Eric says:

Here's a way to combine James and Brian's points into one point.

Let's call the probability that the Jets convert their 2PC "J" and the chances of the Dolphins converting their 2PC "D"--which makes the chances of the Dolphins not converting "1-D". Because the chances of making a PAT are around 99.5%, I'm going to ignore it for simplicity (but you could add it in if you wanted).

Rewriting this in symbols, the Jets should go for it if they think
J>1-D
or
J+D>1

The only way this is true is if at least one of "J" or "D" is greater than 0.5. If this were true for either or both teams, then they SHOULD BE GOING FOR TWO ON EVERY TD. The fact that neither team does (and the fact that the 2-pt conversion percentage is below 50% on average) suggests that the play to make in that situation is to kick the PAT.

13. Dan R says:

@James

I don't really recall. They'd been down 31-10, TD, recovered onside, TD at that point. It might have been a momentum call (hey we're hot, better than 50% now). Would love to hear Billick's answer as an analyst.

Checked ESPN's recap and this was indeed the game, the try failed in the box score was intentional. They say "... Billick chose to go for two and Tyrone Williams tipped away the pass to Qadry Ismail..." without any real commentary.

14. Jason says:

why be greedy

15. Chris says:

I've heard many arguments for the 2-pt conversion % over time, and it always goes back to this one statement, made above by Eric:

"The only way this is true is if at least one of "J" or "D" is greater than 0.5. If this were true for either or both teams, then they SHOULD BE GOING FOR TWO ON EVERY TD"

I think there are problems with this, as is seen in many sports, coaches and teams, even if they feel they have a >50% chance of something, don't often go for it for fear of not getting it. Media backlash is a real thing, as well as job security. Nobody will usually get on your case when you are playing it safe, but the goal should be to win, and there are often incentives that lead to taking the safe route, even if it's not the best route.

That being said, I've seen numbers that argue anywhere from 40%-55% on the two point conversion attempts. Many argue that the number used by the NFL on these includes many cases where the idea was to make a PAT and, for whatever reason, ie bad snap, etc, the players end up forcing in a two point conversion, and fail most of these times. I'd like to see some solid numbers on this idea and see what the true % chance of it is.

16. Anonymous says:

@James

If you're behind by 14 with very limited time remaining and then you score a TD, you should go for two after assuming you can convert 38.5+% of the time and everything else being equal. This also assumes that there's only time for you to score a TD and your opponent can't respond. The same logic would apply being down 21.

First note that the conversion is irrelevant unless you score another TD, anyway. If you make the 2-pt conversion on your first attempt, then you'll always win (assuming 100% for PAT kicks). If you miss, then you have another chance to go for the tie. If you make that, then you'll win 50% of the time in OT.

If you kick both times, you'll go to OT (50%).

Therefore, assuming the your team has a success rate of x for 2-pt conversions, 100% for 1-pt kicks, and 50% for OT, then:

P(x) = x + .5(1-x)x > .5
0 > x^2 - 3x + 1

Solving for x, you find that if x is greater than (3 - sqrt(5))/2 = 38.2%, then you'll win more than 50% of the time.

As an example, assume a 40% conversion rate. 40% of the time, you'll win outright because you converted on your first attempt. Of the 60% you miss, you'll make the second 40% forcing overtime. 60% * 40% * 50% = 12%. Thus, you'll win 52% of the time.

I've never heard of a coach going for two in this scenario outside of high school (where kicking PATs isn't nearly as automatic). I mostly want to see the press conference after the game when the coach attempts to explain the math.