Writers of Pro Football Prospectus 2008

23 Nov 2005

Playing with the Percentages When Trailing by Two Touchdowns

"It is relatively common for football teams to find themselves down by two touchdowns late in the game. If they score a first touchdown then coaching folklore says that the team should go for the extra point at that time. In this paper I will show that this strategy, which appears to be universally used in both the NFL and the NCAA, is incorrect, and that going for the two-point conversion after the first touchdown is nearly always significantly better."

The one problem here is that the author is way off on the percentage of extra points missed in the NFL. It isn't six percent, it's one percent. This makes the chances of winning with a "kick extra points" strategy 49.2%, not 45.5%. (You'll understand what I'm talking about after you read this.)

Posted by: Aaron Schatz on 23 Nov 2005

31 comments, Last at 24 Nov 2005, 11:18pm by Felton


by Kevin (not verified) :: Wed, 11/23/2005 - 1:52am

Although messing up the math on this absolutely kills any respect for this guy in most fans' minds, I am glad somebody is going into this area because it lets me talk about one of my pet peeves, not going for two enough. Some others are not going for 4th down enough (especially on the opponent's goal line), not onside kicking enough, and playing for overtime, but this will probably be too long already.

Most people cling hopelessly to the "kick early, go for it late" heuristic in spite of overwhelming evidence, so I'll first go with a situation that I hopefully can convince people with.

Many teams find themselves down in a situation where they need at least one two-point conversion, such as down 15. They almost always defer going for the conversion as long as possible. This is wrong because of the idea of information. You're going to have to go for two some time anyway. If you convert, it doesn't matter when, but what if you fail? If you fail on your last score, you suddenly need an onside kick and a miracle. If you fail on the first touchdown, you get the knowledge that you're going to need two more scores and can adjust your play accordingly.

The general cases, the ones people like Mike Tanier like to talk about, are situations like say late in the 3rd quarter where a team can tie it with a 2. Enough has been said about situations like this, and if you haven't been convinced already, I doubt there's much I can say. But keep in mind: what outcomes are there where going for 1 is the correct play? Make sure there are really enough possessions left. In this situation, the answer is: opponent has time to kick 2 more FGs and you have time to score another TD, then you win in overtime. Compare that to the chances of both teams not scoring again, or the other team kicking a FG, forcing you to go for a TD instead, or maybe the other team scoring a TD, in which case you have the 15 point situation I outlined earlier.

Now for something like what this paper is about (I actually haven't read it), more controversial: when there is no "need" to go for two. Intuitively, in a perfect theoretical world, I think most people could accept that if you could convert even 51% of the time, you should go for it in a neutral situation, like scoring the first TD to go up 6-0. What people don't realize is that even if the conversion rate was not 50%, it is still worth doing this. This is due to going for two being optional. If you're scoring at least two TDs, the only way you get hurt is if you go for two, miss, and then miss the two to fix things. This is because the knowledge of what happens the first time affects the second decision. If you fail, you're not going to go for one. On the other hand, if you succeed the first time, you're not going to go for two again; you can sit on your advantage. Assuming a really low conversion rate like 40%, it still comes out better to try for 8-0.

This is not to say that I advocate rampant going for two in practice like in the last paragraph. This is because most teams have "money" plays in those situations. Go for two all the time, and teams will start to prepare and your conversion rate should drop. (On the other hand, if you feel very confident in a certain play, like HB dive over the top, who's to stop you?) I would bust out this strategy in big games though, like in the playoffs, if you could catch teams by surprise.

The main reason, of course, if sadly that you would look like a buffoon and lose your job. When coaches take risks and fail, they are crucified, but when they make blatantly wrong decisions the other way, I'd like to see them take the same amount of heat. A couple of years ago, I must have been the only angry Georgia Tech fan in the stadium when we scored a TD to go up on FSU 13-0 with about 5 minutes left in the 4th. The final score? FSU wins, 14-13, of course, and nobody makes a peep. Do you really think FSU had time to score a TD and 2 FGs? These types of situations still irk me to this very day. And there's a lot of irking going on, because they happen each and every week.

by shonk (not verified) :: Wed, 11/23/2005 - 1:52am

Addendum to Aaron's caveat: the winning percentage for the "go for two first" strategy also goes up slightly if you use 99% accuracy on extra points, from 54% to 55%.

by Craig B (not verified) :: Wed, 11/23/2005 - 1:57am

Re-running the numbers with 43% as 2-pt conversion rate and 99% as extra point rate, I got 55.0% chance of winning when going for 2 first, 42.8% when going for 1 and then 2, and 49.2% when going for 1 both times.

I had never thought of this strategy, but he could be onto something. Judging by his references, he might be a regular on this website.

by Becephalus (not verified) :: Wed, 11/23/2005 - 2:21am

I think he got the flawed 94% number becuase that INCLUDES 2pt attempts (which have a much lower success rate but are rare).

I still think his overarching point is right though despite the mistake, its just not quite as strong.

Kevin also makes a very good point about realistic drive scenarios...

by bobman (not verified) :: Wed, 11/23/2005 - 2:30am

Numbers aside, some coaches just make dumb play-calling decisions even when they do the right thing in general.

I am referring to matchups such as ther Indy-Cincy game last Sunday. Cincy made the right call to go for it on 4th and one in the 4th quarter, but instead of using their strength against the Colts weakness (a power run up the gut for a yard), they went with a slow-developing sweep, and the speed-based Colts stopped them for no gain, got the ball back, and marched down for a FG.

So for the 2-pt conversion or the 4th and one play, it may be obvious, especially in hindsight, what the right call is, play-callers might try to out-think the opponents, or get cutesy, or use it as a resume-defining play, and they end up failing. Then people criticize the decision to go for it, when the real problem is the play call.

I'm all for more 4th down plays and 2-pt conversions. For teams that are BAD (i.e. Houston) it's the only way they will be able to pull together a few wins. For teams that GOOD (Indy/Cincy) they might as well take advantage of their talented offenses (plus they can always make it up with a slew of additional scores later if they fail).

by Ryan (not verified) :: Wed, 11/23/2005 - 2:31am

Yeah I found this article a few weeks ago and went through it thinking, 'this does seem like a good solution' going for two. Plus the things I liked were the percentages in the NCAA seem to be correct.

However I think that banking on a 50-50 chance on two, two-point conversions is risky for a head coach. But it does make sense because coaches should be thinking of the optimal solution to winning the game. Only thing I question is this guy cited a few sources but not the Sackrowitz article which hints at this method at the end of his article, "Refining the Point(s)-After-Touchdown Decision"

by Travis (not verified) :: Wed, 11/23/2005 - 2:43am

Situtations where I've noticed NFL coaches being unusually aggressive:

2-point conversions and 4th down attempts:
1. Kicker is injured, with no suitable replacement available. Rams-Falcons, October 15th, 2000. Jeff Wilkins hurt his quad on the opening kickoff, kicked one extra point, then left the game, forcing the Rams to go for 2 after every touchdown. The Rams, averaging about 44 points a game, would go on to score 5 more touchdowns, with an NFL-record 4 2-point conversions. Also, since field goals were an impossibility, the Rams went for it on 3 4th downs in Falcon territory, converting a 4th and 2 and a 4th and 15.

2. Coach is thoroughly unfamiliar with the NFL. Cowboys-Eagles, December 10th, 1995. Barry Switzer, goes for it (twice!) on 4th-and-1 at his own 29 in a tie game with 2 minutes to play.

3. Coach has nothing to lose. Vikings-Saints, December 15, 2002. Vikings, 4-9, go for 2 with 5 seconds left and convert to win 32-31.

Surprise onside kicks:
4. Coach is trying to generate momentum. Eagles-Cowboys, 2000, 2003.

5. Coach realizes his defense has no chance to stop the opposing offense. Titans-Colts, 2004; Patriots-Colts, 2005.

6. Coach sees that the front line of the return team runs back way too early. At least 3 times vs. the Jets, early 2002.

by Joon (not verified) :: Wed, 11/23/2005 - 3:55am

finally! my buddies and i thought of this idea a loooong time ago, and it didn't take us long to realize that it's obviously better. i'm a little surprised this article hasn't been written before--if i had known that it wasn't common knowledge among math-savvy fans, i would have written it myself.

he gets one thing totally wrong, though (in addition to the kicking %): the reason why coaches don't actually employ this strategy. the reason is that coaches are risk-averse. the coach is usually not attempting to maximize the chance to win the game, but rather the chance to keep his job and/or get a better job. if you kick twice and lose (either in OT or because of a missed kick), it's not the coach's fault. but if you go for 2 and fail twice (about a 1 in 3 chance), the coach is crucified in the media, even though he was giving his team the best chance to win. TMQ harps about this sort of risk-averse decision-making, and he definitely has a point. (now if he would only stop whining about blitzes and passing plays...)

by Jim C. (not verified) :: Wed, 11/23/2005 - 4:54am

There's a maxim among coaches (I coach at the High School level): you shouldn't do anything to lose the game for your players. This is so ingrained in the way most coaches approach the game, that it colors their decisions far more than anyone realizes. Personally, I'm a big believer in going for it on fourth down, and often go for two points. The kicking game is usually so poor (statistically speaking) at the H.S. level that it makes the percentages tilt radically in favor of the 2-pt conversion.

Most coaches I know breakdown games statistically to determine their game plan... what play does their opponent run most often on First and 10 from outside the red zone, or where do most passes get completed by a QB/WR combo, or what blitz package is most effective against a given formation. This makes their reluctance to take risks like going for the first on 4th-and-X very odd. Our team will go for it in most cases; we punt if our field position is really poor, or if we're leading a team that is superior (talent-wise) to us and we want to stretch the field as much as possible for them.

Just $0.02 from an old football coach... (But not the visor wearing one!)

by foos (not verified) :: Wed, 11/23/2005 - 5:14am

I think that we should not discount the element of surprise involved in going for 2 in a situation not prescribed by "the chart". A defense expecting a 1 point chippie will not have the same personnel or level of readiness as a squad anticipating a pressure-packed 2. Even if a team gets a reputation for going for the 2 at non-conventional times, that diverts the resource of the team that has to prepare for this aberrant behavior. In short, I guess I endorse the article's conclusions.

by houlie (not verified) :: Wed, 11/23/2005 - 9:48am

Re: #9 "The kicking game is usually so poor (statistically speaking) at the H.S. level that it makes the percentages tilt radically in favor of the 2-pt conversion."

There was a bantam-level (age 14-16 I believe) league in my hometown where this was so true that they actually reversed the scoring for the point after touchdown. The kick was worth 2 pts and running a play worth 1 pt. I think it was mainly done to encourage kicking development, i.e. more valuable kicks mean practice your kicking more, etc.

by Felton (not verified) :: Wed, 11/23/2005 - 10:03am

I still see so many teams get themselves in trouble with the following:
Saints trail the Rams 16-17. Saints score TD with about 5 minutes left and miss the 2 pt conversion to lead 22-17. Rams score with about 1 minute left and make the 2 pt conversion to lead 25-22. Saints kick a FG at the end of the game and in OT to win 28-25. Had the Saints not gone for two, they would have led 23-17, then trailed 24-23 and then won the game 26-24 in regulation. Some teams get themselves in trouble doing this in the first half - the score progression being say 6-7, 12-7, 12-14, 18-14, 18-21 - so now a FG only ties instead of wins. Is there is a time factor as well as a team success rate to consider?

by Bill Krasker (not verified) :: Wed, 11/23/2005 - 11:05am

This result has been around for ages. Sackrowitz mentioned it in his article, and I discussed it in May 2004 in an article that was reprinted right here at Football Outsiders. See the link; it's in the section on the Colts vs. Buccanneers.

by calig23 (not verified) :: Wed, 11/23/2005 - 11:11am


By rights, then, any coach with very good job security should be more likely to go for two/go for it on 4th down/etc.

I'm thinking... Bill Belichek, Bill Cowher, Mike Shanahan.... and that's probably it.

by Starshatterer (not verified) :: Wed, 11/23/2005 - 11:25am

Calig23 (#14 )--

Add Andy Reid to the list of coaches with good job security. He needs at least two more years of underachieving before he gets off that list.

On the other hand, coaches with poor job security should also go for two more often, if it increases their odds of winning. Pulling out a win or two by showing an aggressive mindset might save your job, or at least get you noticed for the next one.

by calig23 (not verified) :: Wed, 11/23/2005 - 11:29am

Oh yeah, forgot about Andy Reid. I suppose Tony Dungy is a possibility, too.

Also, perhaps new coaches who are likely to be given some leeway for a few years- i.e. Romeo Crennell, Nick Saban.

by Podge (not verified) :: Wed, 11/23/2005 - 11:58am

Just wondering, what percentage of success do you think a fake FG would have in this situation? On extra points most players generally just stand around doing nothing, so a surprise fake could do well. Kindof a once-in-a-career playcall for a coach though.

by Michael David Smith :: Wed, 11/23/2005 - 12:49pm

If a strategy helps your team win, and I don't think there's much doubt that this strategy does, shouldn't every coach do it regardless of his job security? After all, isn't job security pretty well correlated with winning percentage?

It's interesting that I'm guessing the majority of readers of this site, myself included, agree that it's the better strategy, and yet I'm guessing zero of 32 NFL head coaches think so. I've never heard a TV announcer mention it, either.

by pawnking (not verified) :: Wed, 11/23/2005 - 1:18pm

I anticipate that in the next 2 years you'll see more and more of the 2 point conversion. Consider the fact that most NFL head coaches were not weaned on the 2pt conversion in the pros. It is still a fairly new innovation at this level.

As far as the college level goes, remember how uncompetitive most college games really are. Thus, the most successful coaches are not the ones who manage close games well, but ones who put together jiggernaughts who steamroll over most opponents. i.e. College coaches who go on to coach in the pros are not likely to have a lot of incentive or experience in going for 2 very often.

Factor in the consideration that for every hour your teams spends on 2 point conversion plays is one hour less you have to spend on other situations, and you have a mentality which, although probably incorrect, is very pervasive.

As more and more coaches win by going for 2 to the acclaim of Sportscenter, etc., you'll see all the others fall in line.

by Starshatterer (not verified) :: Wed, 11/23/2005 - 1:23pm

After all, isn’t job security pretty well correlated with winning percentage?
Not entirely. Mike Tice is on his fourth year coaching, more due to his modest salary than his modest winning percentage.

The funny thing is, despite the wide perception of his coaching ineptitude, he's had more success during his tenure (an actual playoff win!) than many more respected coaches over the same stretch.

by Joon (not verified) :: Wed, 11/23/2005 - 2:02pm

Re: #18

After all, isn’t job security pretty well correlated with winning percentage?

sadly, not as well as you might hope. coaches are criticized for losing the game for their team much, much more easily than they come under fire for not putting the team in a position to win. just take a look at post #9--the maxim is "don't do anything to lose the game for your players." normally i think it's bunk when a commentator tries to make a distinction between "playing to win" and "playing not to lose" but in this case it's obviously exactly that difference. coaches are not trying to give their team the best chance to win the game.

by Scott de B. (not verified) :: Wed, 11/23/2005 - 2:05pm

This is wrong because of the idea of information. You’re going to have to go for two some time anyway. If you convert, it doesn’t matter when, but what if you fail?

What about the psychological aspect? Let's say going for two and failing demoralizes your team (-5% performance for the rest of the game) and emboldens the opposing team (+5% performance for the rest of the game). Does that change the equation?

by Kevin (not verified) :: Wed, 11/23/2005 - 2:23pm

Re 12: I hope you're not suggesting that the Saints should have kicked the extra point to go up by 6 with five minutes left? The problem with worrying about the worst case scenarios is that you ignore all the more likely scenarios. Missing the two, Rams TD + two, Saints FG, Saints lose in OT is much less likely than say Rams TD + one for the win. Oh and your 18-21 progression would never happen that way, since you'd probably be kicking the extra point to go up 19-14. And besides, if your team really misses 3 conversions to go down 21-18, I would venture you have more problems on your hands than going for two too much.

Re 22: It's possible, but I still think it's much more important to know how many scores you're going to need. What you're talking about is kind of nebulous. (You could also say there's an emboldening/demoralizing effect if you go for two and make it. And if there was a difference, it wouldn't be as large as 10%.) But I think both teams should be playing hard anyway. I think if you were to take a look at a testable situation like basketball teams missing shots to win in regulation and so forth, I doubt (purely anecdotally) their win% in overtime would be less than 50%. Maybe somebody at 82games.com should get on this.

by Dennis (not verified) :: Wed, 11/23/2005 - 3:12pm

Re 19: Factor in the consideration that for every hour your teams spends on 2 point conversion plays is one hour less you have to spend on other situations, and you have a mentality which, although probably incorrect, is very pervasive.

Two-point conversion plays are the same as any goal line play. I don't think any team practices them separately, they just practice their goal line plays.

by Kibbles (not verified) :: Wed, 11/23/2005 - 5:17pm

Re #14: You just made the point I was about to make. It's one of the big reasons why I love all the job security Mike Shanahan has- it allows him to be more aggressive than pretty much any other coach in the NFL. Just look to last week's game, where he went for it on fourth down several times in the first quarter, and then decided against kicking a chippie field goal to end the half and instead went for a TD. The TD failed, and time ran out, so he cost the team 3 points, but I think he made the right call. 1 yard to go, one play to go, you go for the TD nine times out of ten.

Re #24: Exactly right. In addition, 2 point conversion plays are also great 3rd-and-short/4th-and-short plays. I think spending more time practicing 2 point plays would only increase an offense's efficiency in short yardage situations, and would have the added benefit of preparing your defense a lot more to face short yardage or red zone offenses.

by princeton73 (not verified) :: Wed, 11/23/2005 - 5:36pm

Just wondering, what percentage of success do you think a fake FG would have in this situation? On extra points most players generally just stand around doing nothing, so a surprise fake could do well. Kindof a once-in-a-career playcall for a coach though.

in the very first year of the 2-point conversion in the NFL (1994), that's exactly what Belichik did (twice!!) when he was coaching the Browns. Tupa was the holder and he ran one in and passed for another one.

But they never tried it again.

by MJK (not verified) :: Wed, 11/23/2005 - 6:21pm

Actually, Belichick did something very similar again. Last year (I think, or maybe it was 2003? No, it was the year they had an injury ravaged secondary, which makes it last year), against...the Rams? Chiefs? I think the Rams. Anyway, one of those Missouri teams. The Pats had been held to 4th and goal at like the 2, so essentially 2-point distance, and came out in FG formation, but Troy Brown was the 11th man. He started to trot off the field, stopped in bounds at the sideline, Vinateri took a direct snap and threw a TD pass to him.

I remember listening to the opposing team radio announcer--"wait a second...wait a second...number 80's still on the field...no-one's covering 80...watch out for 80...WATCH OUT FOR 80!!!!...Ahhhrg, touchdown, Patriots". He was apparently the only one paying attention.

by MAW (not verified) :: Thu, 11/24/2005 - 3:31am


Minnesota tried the same play against the Eagles in the playoffs last year, with Moss as the 11th man, but our man Tice called a timeout, not realizing that his team was running a trick play.

by Starshatterer (not verified) :: Thu, 11/24/2005 - 11:17am

MJK (#27 )--

That play to Troy Brown was definitely against the Rams. That was also the first game Troy Brown played cornerback. The game was the week after the Halloween beat-down the Patriots took from Pittsburgh, and many people fully expected the Rams to blow the Pats' doors off. So Belichick emptied the bag of tricks that day.

MAW (#28 )--

The trick play to Moss should have been called off because his substitute ran onto the field, and Moss (recognizing this) ran off to avoid the penalty. Tice tried to call time, but didn't do so quickly enough, and the trick play ran with no lonely end, ending in an incomplete pass, turnover on downs. From NFL GameCenter's play-by-play (linked):
4-3-PHI3 (4:40) (Field Goal formation) G.Frerotte pass incomplete to J.Wiggins.
If my memory of the play is correct, Frerotte looked for Moss, saw him not there, rolled right to keep the play alive, and heaved the ball not all that close to Wiggins, who had been blocking on the right.

by Frank (not verified) :: Thu, 11/24/2005 - 9:24pm

For more on this topic, readers may want to visit www.pigskinrevolution.com

by Felton (not verified) :: Thu, 11/24/2005 - 11:18pm

Re 23 - When behind by 2 prior to a TD, I think the "card" says go for two to get ahead by six and put pressure on the XP, although I would agree with the kick. Example - 12-14, score TD to go ahead 18-14, try the two because there is no difference between 19-14 and 18-14 while 20-14 is different. I think the real question you and I appear to be headed toward is a time factor. I certainly nodded my head when the Saints tried to go ahead 24-17, but in retrospect it could have beenm different. What I am looking for is a better development of "rules" for the go for two as opposed to a rigid points scale. Time is a factor and so is your offensive skill set. This all needs to be studied so coaches are not left hanging in the wind by rules of thumb.