Why it’s almost always a bad idea to go for a two-point conversion in the first half

The 2000 Outback Bowl, one of the most entertaining games in the ballyhooed “Big 10 vs. SEC” category, featured (at the time) the “largest comeback” in bowl history. Purdue, on the strength of game MVP Drew Brees’s four touchdown passes, built a 25 – 0 lead in the first twenty minutes. But Purdue lost 28-25 after Georgia tied the game at 25 to send it to overtime and then kicked the game winning field goal in the the extra period. Brees would finish with over 370 yards passing (on 60 attempts!) while Bulldogs quarterback Quincy Carter went 20-of-33 for 243 yards, had no picks and ran for one touchdown while throwing for another. But it was Purdue’s Tiller who was the affair’s de facto protagonist: His first-half gameplan’s featured a brilliant aerial assault which blitzkrieged Georgia coach Jim Donnan’s blitz-happy strategy (in an early example of the folly of trying to outblitz the spread), but some of his in-game decisions lacked, uh, rigor.

The score should stick out to you: 25? Purdue got that odd total by scoring four touchdowns but then following them with a missed PAT and two failed two-point conversion attempts. The missed PAT was not what one hopes for, but the problem was that Tiller then fell into the classic two-point conversion trap: The coach thinks that because his team missed a PAT he “must” go for two so that his team can have the “correct” score (i.e., some multiple of 7). This is wrong. Unless going for two is simply a better strategy in general (more on that later), it is almost always a bad idea to go for two in the first half simply to achieve some desired score because in the first-half there are far too many unpredictable end-game scores for it to make any specific score worth the cost of choosing a suboptimal strategy to engineer that desired number — it’s only at the end of the game that some specific score (seven versus eight versus or two versus three) really makes a difference. Indeed, this effect was even more acute here because Georgia had no points at all, so it’s not as if Tiller could envision what combination of scores Georgia would actually get to match his team. Put another way, given the point differential, why did it matter that his team was up 21 versus 20, or 27 versus 26? Indeed, it turned out the key difference was not between getting the two-point conversion and getting the PAT, it was between getting the PAT and getting nothing at all — having 19 instead of 20, and 25 instead of 26.

This is a  very different question from whether going for two is better in general: it’s generally not, otherwise it would be a dominant strategy (in the game theory sense) and teams should go for two all the time. (Note that for this analysis I’ve assumed you have a good PAT kicker. Not having one can dramatically change the approach in, say, high school. For Purdue this shouldn’t have been an issue, however, as despite the fact that Purdue missed its PAT its kicker was actually an All-American placekicker, so it truly was Tiller just trying to recoup the score.) My criticism of Tiller is that his odds of converting didn’t change when he missed the first PAT (and they possibly went down given some game theoretic alterations in the defense’s response), so the fact that he changed his strategy was not rational and in actual fact ended up hurting his team’s chances of winning.

Those are the universal reasons why I recommend against going for two except as part of an endgame strategy. But another complaint applies to Tiller’s choice to go for two in this particular game when he had such a big lead. Remember, the probability of winning a football game is not only about expected values but also about the variance of those returns. Risky strategies are better for underdogs not necessarily because they increase their expected offensive or defensive prowess, but because the variance is good in and of itself: risky strategies flatten the bell curve; the risky strategies cause a wider disparity in the outcomes, even if the average outcome is the exact same, thus increasing the “tails”, or the underdog’s chance of winning the game. The Citadel is not going to beat Alabama with a strategy of three-yards and a cloud of dust, punts, and “let’s play for field position.” And the phenomenon works the other way too: if you’re expected to win, uncompensated risk (i.e. that doesn’t carry a higher expected return, like Purdue’s excellent passing attack with Drew Brees) is not your friend. And there is no question that going for two is riskier than going for one.

Even if the expected return were higher when going for two than when going for a PAT (PAT = 1 * 99% or so; 2-point = 2 * between 40-60%, so even assuming on the high-end), the chance of getting zero on the conversion multiple times in a row is higher as well. And if Purdue was sitting on a 19 or 25 point lead already they were clearly in the probabilistic driver’s seat and should have been in the business of reducing uncompensated variance, not increasing it.

So coaches should almost never go for two in the first-half, and in the second half of teams should really only go for it when there will not be only one or two more scores and the specific, necessary scores can be reasonably foreseen. And the choice to go for two twice was especially silly for Tiller, as it opened up an increased risk that his team would miss the two-point conversions and make it easier for a desperate opponent to come back.

And that’s how it played out. Georgia caught up by, among other things, getting a two-point conversion and then scoring a touchdown and only needing to kick an extra point with 1:19 to go in the game to tie the game. Had Purdue kicked one additional PAT Georgia would have had to go for two twice (thus reducing its probability of matching at 25), and had Purdue kicked two PATs Georgia likely would have had to score again, something it likely didn’t have time for. In other words, there’s a very good chance that, despite its other second half struggles, Purdue would have won the game had Tiller just kicked a couple of PATs.

Of course, it’s not like the decisionmaking in this area has gotten much better. I’m generally for aggressive decisions, but it’s usually better to just kick the damn extra point.

  • Shakinthesouthland

    What I usually say is that if you go for 2, you’ll end up losing by 1.

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  • Lenrussell

    As an Oregon fan, I’ve got to point out an option that you’ve not considered. Frequently, we initially line up in various versions of the “swinging gate” formation for an extra point. Depending on the way the defense lines up, they go for two, or shift back into the traditional formation and kick the extra point.

    So they go for two only if the defense’s formation provides a mismatch in our favor that dramatically increases the probability of success.  It isn’t always an either/or decision by the coach.

  • Lenrussell

    As an Oregon fan, I’ve got to point out an option that you’ve not considered. Frequently, we initially line up in various versions of the “swinging gate” formation for an extra point. Depending on the way the defense lines up, they go for two, or shift back into the traditional formation and kick the extra point.

    So they go for two only if the defense’s formation provides a mismatch in our favor that dramatically increases the probability of success.  It isn’t always an either/or decision by the coach.

  • robc

    On the other side is the Florida-Tennessee game in 1999.  Down by 16 (23-7) with 6:19 to go in the third, UT scores a TD and Fulmer decided to kick the xp.

    Final score, 23-21.  They had 1 scoring drive in first 2.5 quarters, did he really think he was going to have 3 scoring opps in the last 1.5?

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  • Nick Kelly

    My brother had recently graduated from Purdue back in ’00 and we went to the game together. That was a PAINFUL game to watch.

  • http://ourfamilyfoodadventures.com/ ChefDad

    Good stuff, Chris.  I hope you don’t mind a little shameless self-promotion–I wrote a bit about this in the Amstat magazine Chance earlier this year.  We looked at end-games in our article but I would like at some point to combine the stuff we did with the stuff Sackrowitz did that they reference in the NYT article you link to create team-specific, game-specific and time-specific PAT charts.  Anyways, here’s the article: 

    Tackling the Chart

    I’m curious though–why is uncompensated variance bad in the context of football?  I get it in the context of risk-averse investors but I’m not sure why I should want my football coach to be risk-averse at any cost in expected value.  Does the question make sense?

  • Spostrel

    I think the idea is that if you are either a) the favorite or b) significantly ahead during the game, then variance (or risk) is bad for you–if variance were zero you’d win for sure. Since your goal is to maximize the probability of winning, favorites and teams that are ahead should shun uncompensated (and even poorly compensated) risk. 

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  • 4.0 Point Stance

    http://smartfootball.blogspot.com/2009/05/david-strategies-and-goliath-strategies.html

    Endgames of course are different. I don’t think anyone begrudges Nebraska going for 2 in the Orange Bowl — if you think your chance of making the 2 is even slightly better than even, it’s the right call.

  • Anonymous

    This is right. I think uncompensated variance is *good* for underdogs; they can keep the same expected values in terms of score, etc while simultaneously increasing their chance for winning by having more “outlier” events. But for goliaths (either going into the game or because of a big lead) it does you no good for the reasons Spostrel said.

  • Stan Brown

    Fla-TN games were never low scoring games.  Fulmer played it right.  A field goal at the end and he wins.  Failed 2 pt attempts after the TDs would have meant that 3 pts at the end of the game wouldn’t even have gotten him a tie.

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  • JT Alden

    Chris,

    I’m not sure what your credentials are, since you fail to mention them on this blog.
    However, I am a high school football coach & have been for many years.

    Your disdain for the 2 point conversion is laughable.

    Here’s the bottom line.  If you practice the 2 point conversion, every day, your success rate will skyrocket.
    You only have to get it over 50 percent and you now are equivalent to making EVERY PAT kick.

    We ALWAYS execute the 2 point conversion after a TD.  I have never kicked a PAT in my 11 years of coaching football.  My teams have about a 75 percent conversion rate.  In addition, we have NEVER lost a single game because of a failed 2 point play.  I have lost some games, based strictly on a superior opponent. However, I have won DOZENS of games by running the 2 point play, as part of our normal game strategy. The kids love it too  !

    Your comments have to do with teams who ” try ” to run the 2 point conversion, without practicing it on a regular basis. This creates a completely different set of statistics.

  • bean

    High school strategy vs college/pro strategy is apples and oranges. Most high schools are stuck with the hand they are dealt in terms of talent. In college, every player was a stud in high school (further compounded in the pros when every player there was a stud in college). While the potential for talent disparity is still there, it is not nearly as pronounced as it is in high school.

    That reality skews the anecdotal evidence given by you more than the concept of teams that “try” versus “practice” 2 pt plays, I think. Most teams and coaches that I know dedicate practice time each week toward specific 2 pt plays.

    In a game against somewhat evenly matched opponents, the downside of having to play catch up if you fail the 2 pt play early is not worth the upside of converting it, even if the probability of success is over 50%. 

    Kudos for the aggressive mentality, but I wouldn’t consider a thought process that runs counter to it to be laughable.

    My bottom line: If you had failed a 2 pt conversion early and are down by 4 late, you could have been down by 3 and would only need a field goal to extend the game versus a touchdown to win it. Touchdowns are harder to score than field goals. Failing the 2 pt conversion earlier in the game forces you to play catchup, when you could play straight up. Taking the counter to that, say you score three TDs and convert all three 2 pt plays. An opponent that plays straight up needs only a field goal to tie. The risk simply outweighs the reward in too many situations, and too many situations are still in play early in a game.

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  • http://pulse.yahoo.com/_UHJHDH6LBIZDC4PZ5UR6HNFQTE joseph

    Bean, 

    Nice comeback.
    However, you still have not made a valid case against the 2 point play.

    Let’s review your reply.  First of all,  our man Chris,  found one game to base his theory on;  the 2000 Outback Bowl.  Hardly enough evidence to prove his point. Heck I could go find one game in history and use it to prove anything.

    Second, you said you know of coaches who  ” dedicate practice time each week toward specific  2 point plays …. ”  Again, you missed the point.  They are practicing plays in case they need 2 points at that moment.  They are STILL kicking the PAT in all other situations.  Therefore, they dont run the 2 point play all the time, like my teams do.  This is a totally different scenario.  We have  8  base play,  2 pt. conversions, with combo plays run off of all of them.  Nobody can scout us or plan against us, with any degree of confidence.  Too much informaton for them to defend against.

    Regarding your bottom line rebuttal.  If we were down by 3 and kicked a field goal, we still didn’t win the game, so your point is mute.  We never play for a tie and see who gets the ball last.  That is equal to a coin flip.  In addition, you said failing the 2 point play forces you to play  catch-up.   Big deal.   Making the 2 point play  forces THEM to play catch up.   And if forces them to run 2 point plays, something they don’t normally do, in order to keep pace with us.  Finally, you said making all 
    3 PATs,  to get to 24 pts. vs their 21,   still allows them to kick a field goal to tie.       Who cares.   We didn’t lose the game in that situation.   Had we taken your advice and kicked all 3 PATs,  their  SAME  field goal just beat us 24-21. 

  • bean

    If you want to engage in the hypothetical that a team always goes for 2 and makes it 75-100% of the time, it’s going to be hard to argue against. My point is that with less of a talent disparity between teams, that success rate isn’t going to be as high, even if the team practices it all the time. And with more parity among teams, you never know when the defenses are going to lock down, points start to come at a premium, and you wish you had that one point instead of trying for 2 and failing early. And there are so many other situations where it is better to go for the easy PAT instead of going for two.

    Take OU vs Missouri in 2010 (although this was a failed attempt in the second half). Down 36-21, OU scored a touchdown and decided to go for two and failed. This disastrously lowered their chances for winning the game. Had they gone for the PAT and made it (much more likely), they’d have been down by a single possession, 36-28. Instead, they were down two scores, which allowed Missouri to just sit on the ball because they knew there wasn’t going to be enough time for OU to score twice without recovering an onside kick. Had OU been down only 8, that would have forced Missouri to actually try to convert first downs instead of kill clock, because OU would have still had enough time to drive and score once. Maybe OU stops them, maybe they don’t. But it was a moot point because they went for 2 earlier than they needed to and failed. But they could have extended that game had they just kicked the PAT.

    Imagine: You were down 14-6 (because you failed the first two pt attempt on your first score, instead of kicking PATs like the other team) and you just punched it in to make it 14-12 late in the game. Obviously, you’re going for two to tie the game. But wouldn’t rather be able to just kick the PAT to tie it, like you could if you had kicked the PAT the first time?

    Your odds of going 1/1 on a PAT are higher than 1/1 on a 2 pt play. Your odds for going 2/2 on PATs are higher than going 1/2 on 2 pt plays, let alone 2/2 on 2 pt plays. You never know when playing that game is going to come back to bite you, and that is why so many coaches don’t play that game until they absolutely have to.

    And this is to say nothing of the fact that going for 2 gives you a greater chance of coming away completely empty handed on point-after-try situations than just kicking the PAT. Imagine that 14-12 score earlier in the game (one of your guys dropped a pass for one failed 2 pt attempt, you got stuffed at the line on the other). You’re down 14-12 and the other team punches in another touchdown and kicks the PAT. As the game winds down, you’re down 9, requiring two scores to get back in it instead of one if you had just kicked the PATs.

    Conversely, if you’re the team that just went up 20-12, why would you go for two when it is easier to make it a 9 point game by kicking the PAT?

    Again, I am a fan of the aggressive mentality. But there are too many situations in play (especially early in the game) where choosing to never kick the PAT can hamper a team’s ability to win the game more than it helps.

  • JosephTAB

    Bean,

    It’s been some time since I looked for a response.
    And yet, you still have not made a valid case.

    Go back up top and look at my original post.
    I am a veteran high school football coach in Missouri.

    Last time I checked, our state association had the PAT kick completion percentage at 69 % of all PAT kicks attempted.

    You said above ……” Your odds of going 1/1 on a PAT are higher than 1/1 on a 2 pt play. Your odds for going 2/2 on PATs are higher than going 1/2 on 2 pt plays, ………….”

    Incorrect again. Last year, my team made 74 % of all 2 point conversion plays for the season, slightly higher than the 69 % average for the PAT kick. Your numbers, with all due respect, are simply bogus. You are attempting to use NFL stats, to prove your point for all levels of football. Those numbers are SKEWED, and therefore inaccurate. Why ? Because your beloved NFL teams don’t run the 2 point conversion all the time. Therefore, their efficiency is MUCH lower, than a team that ALWAYS runs the 2 point play and NEVER kicks.
    My best season ever, was back in 2002. That year, my team completed 83 PERCENT of all 2 point plays.
    I appreciate your response. However, it’s not based in reality.

  • xyz123

    I’m not a huge football fan, so I don’t know what I think about your conclusion in general, but your use of game theory is a bit misplaced. You say that if going for 2 was better in general, it would be a dominant strategy, and use that as evidence that it is not in fact better. First of all, you seem to be assuming perfect rationality among football coaches here, which is not a fair assumption. Second of all, football is far too complex to make such a statement. Some offenses have better chances than others of converting, while some defenses are worse at preventing conversions. Furthermore, there are situation factors, which you yourself admit when you mention that in an endgame situation it can be beneficial. Those still exist earlier in the game. For example, going for 2 in a 14-13 game in the first quarter is different than going for 2 in a 13-7 game in the first quarter. It’s hard for us to figure out exactly how since there’s still so much of the game left, but that doesn’t mean there isn’t a difference.

    There are too many complicating factors in football to determine whether or not you should go for 2 through a simplistic analysis.