Two-point conversions in the NFL

[TimTimSalabim]

I was watching an NFL game the other day, and the announcer said that the league average for two-point conversions last season was 48%. It got me to thinking, that there must therefore be some teams where the average is above 50%. It seems to me that those teams should be going for two-point conversions every single time they score a touchdown, yet I don't see this happening. Are NFL teams that math-challenged? Or is there a flaw in my thinking?

[HDPM]

Shhhh, don't tell Martz or he'll go for two with the game tied and :03 on the clock. /images/graemlins/tongue.gif

Actually, I think many coaching decisions would be made differently if coaches analyzed stuff mathematically. I think Sklansky wrote about this one time. I am not sure about the 2 point deal though. My feeling, without analyzing stats, is that the 2 point conversion should only be used when it's obvious you need 2. Like to tie when there's no time left. Particularly assuming your percentage is at or less than 50%. Points are hard to come by, and a lot of times it seems like teams need a point late when they go for 2 and fail. The 2 point play was more significant in college ball when they had no overtime. It made more sense for a team to go for a win in certain situations. Some of the analysis of going for 2 must depend on overtime stats. But overtime is such a crapshoot it might be hard to analyze.

So I don't know about the 2 pt play, but I think a football team would be well served by analyzing situations better. If I owned a team I would hire Sklansky or somebody like him to analyze situational decisions mathematically. Then I would make the coaches follow it.

[TimTimSalabim]

This is what has kept me from becoming more of a sports fan over the years, is that even teams at the top level seem to shun mathematical analysis in favor of "conventional wisdom" and seat-of-the-pants decision making. They will spend millions to get the best coaches and athletes, but they don't seem to want to spend a dime on any kind of computer simulation or mathematical analysis that would yield the best strategy in a given situation.

[Homer]

Are NFL teams that math-challenged? Or is there a flaw in my thinking?

I'm sure some coaches/teams (i.e. - Mike Martz, who doesn't seem to understand that 7+3=10 ***) are math-challenged, while others are simply afraid to go against the grain for fear of media/fan scrutiny. As HDPM said, Sklansky either wrote an article or posted a question on the forum (I can't remember which), giving a situation along with various percentages, asking us to determine what decision should be made in that situation. It turned out that conventional wisdom was incorrect in that situation.

-- Homer

*** In Week 1, the Rams had 4th and 12 on the Giants 30 with 5:30 remaining in the 4th quarter, trailing by 10 points. Instead of kicking the field goal, they went for the first down!

[clovenhoof]

Injuries. During a PAT, the only way Terrell Owens or Daunte Culpepper are going to get injured is if they trip over the Gatorade table. That, in my view, is enough of a factor to justify taking the safer route unless the extra point is truly meaningful.

'hoof

[daryn]

wasn't there some economist that studied NFL statistics and concluded that a team should ALWAYS go for it on 4th down? for the greater good? does anyone remember this? but you know it would never happen, even if true.

[Wake up CALL]

[ QUOTE ]
wasn't there some economist that studied NFL statistics and concluded that a team should ALWAYS go for it on 4th down? for the greater good? does anyone remember this? but you know it would never happen, even if true.

[/ QUOTE ]

You are correct, here is the formula:

Ei Di(gt) Vi = Pgt + Bgt Ei Di(gt+1) Vi - egt

by Professor David Romer.

ESPN Article (http://espn.go.com/nfl/columns/garber_greg/1453717.html)

[Oski]

[ QUOTE ]
This is what has kept me from becoming more of a sports fan over the years, is that even teams at the top level seem to shun mathematical analysis in favor of "conventional wisdom" and seat-of-the-pants decision making. They will spend millions to get the best coaches and athletes, but they don't seem to want to spend a dime on any kind of computer simulation or mathematical analysis that would yield the best strategy in a given situation.

[/ QUOTE ]

I've often wondered the same thing. I read that this year (or last) the Boston Red Sox actually hired an expert in baseball statistics (Sabermetrics?) I thought that was pretty cool. However, you would think you would see more of this in football because the game seems easy to boil down to percentage plays.

[Stu Pidasso]

[ QUOTE ]
It seems to me that those teams should be going for two-point conversions every single time they score a touchdown

[/ QUOTE ]

Think tournament poker theory. In tournament poker the value of a chip is not constant. In football, the value of a point also changes quite frequently.

Stu

[slider77]

I would say that it depends on the situation. For example, if a team jsut scored 6 points to tie the game with 20 seconds left, they wouldn't go for 2 points - even if there was a 75% chance they would convert it.

I would compare it to bunting in baseball. Bunting a runner to 2nd actually reduces the expected runs scored in that inning. But late in a game, 1 run could be all it takes to win the game. So you increase your chances for scoring 1 run, and decrease the chances for 2 runs, 3 runs, etc.

[Clarkmeister]

In 2001 the league average was 44%. IIRC this is pretty close to the historical average.

[BruceZ]

I know some teams use a table that tells them whether to go for 1 or 2 based on the score, but I don't know if the table correctly takes into account the probability of making it, wind, etc. You wouldn't always go for 2 just because you can make it more than 50% of the time because sometimes getting at least 1 is much more important.

I agree that a good statistician could give a team a big edge over the competition if they don't already use them. Game theory can be used to randomize plays in football, and pitches in baseball, too make them maximally unpredictable.

If any big time sports team owners are reading, I'm available for consulting, and I could do that job as well as anyone in the world.

[Homer]

You are correct, here is the formula:

Ei Di(gt) Vi = Pgt + Bgt Ei Di(gt+1) Vi - egt

Thanks for clearing things up. /images/graemlins/grin.gif

-- Homer

[Dynasty]

[ QUOTE ]
This is what has kept me from becoming more of a sports fan over the years

[/ QUOTE ]

You must be the only man in America which isn't a sports fan because there aren't enough math geeks in athletics.

[Homer]

BTW, that article makes certain coaches (**cough** Fassel **cough**) seem like narrowminded, arrogant pricks.

-- Homer

[HDPM]

I think the strongest application of the formula is probably where the team is around the 50 yard line. It's a 67 yard field goal, so you aren't going for that. A punt might pin the team back, but most often the other team will start with field position between the 15 and 25 I would guess. If I had a strong defense and short yardage, I'd look at going for it a lot more than teams do now. Tampa Bay should go for a lot of 4th and 2's around midfield is my guess. An extra field goal per game really helps them given their defense and offensive struggles. OTOH, a soft "bend but don't break" defense might give up a lot of extra field goals in the same spot. I think Walsh is probably right - there are a lot of variables. Where Fassel is an idiot is that these mathematical analyses can guide coaches and get them thinking about the right strategies. A coach who knows his team and knows football and uses stats and game theory is at a tremendous advantage over a coach who is running scared and plays it safe. Cowher is an example. He is worried about his ability to make the right call given outside factors. Not good. In a way though it is understandable. The math and poker types think in terms of the long term. Football offers a miniscule sample size, as the economist found out. So if an unconventional call costs you one game, it is a huge event. IOW, your results cluster around a few decisions. Not the right environment for a lot of creativity. The math analysis has just started changing baseball, and that's a game which gets to long term results better. I think football will be slower to change, given the mentality and relative parity in economics and talent of the teams. The teams that can risk more are bad teams to begin with. They aren't going to go from a 5-11 team to a 9-7 team because of 4th down strategy I don't think. And their results will be worse because they're a lousy team anyway. And a team close enough to winning a championship to benefit a lot is the least likely team to change. So I think we'll see more Fassels spew cliches in press conferences. (Has Fassel ever answered a question without a coaching cliche?)

[Rushmore]

even if there was a 75% chance they would convert it.

I don't know the % of made PAT's, but I'll bet it's high enough to say that if there were a 92% chance of making the 2-pointer, you still wouldn't go for it.

[Rushmore]

I don't know, but I am POSITIVE they don't go for it on 4th down nearly often enough.

In fact, only about 10 yrs. ago or so did I start noticing coaches going for it on 4th from the opponents 40 or whatever, knowing they were outside of their kicker's range, and concerned that a punt might end up in the end zone, netting them 20 yards when they could have had a reasonable chance to score instead.

I want to say it was Parcells who broke through on this one in particular, but I'm not sure.

Anyway, if you're trailing by 5 with 2:10 on the clock, and you're at midfield, and it's 4th and 4, I say go for it almost every time, regardless of how many timeouts you have remaining. Forget all that crap about your defense holding them to a 3-and-out, etc.

I'd bet that teams who punt in this situation lose a prohibitive amount of THE time, and that going for it and making it is +EV, NFL statistic-wise.

[TimTimSalabim]

Interesting article. I find this Bill Cowher quote very revealing:

[ QUOTE ]
There's so much more involved with the game than just sitting there, looking at the numbers and saying, 'OK, these are my percentages, then I'm going to do it this way,' because that one time it doesn't work could cost your team a football game, and that's the thing a head coach has to live with, not the professor. If we all listened to the professor, we may be all looking for professor jobs.

[/ QUOTE ]

This is proof to me that these coaches are idiots... I mean, he's worried about the occasional game lost by following a correct strategy, while completely ignoring the games that he's losing now by following a conventional one.

[angry young man]

the flaw in your thinking is that football isn't a zero sum game in the same way that poker is. The goal isn't to score as many points as possible in the course of a season, it's to outscore your opponent over a 60 minute game. so, sometimes getting 2 points isn't twice as good as getting 1. For example, say you're losing 3-0 and score a touchdown, would you rather be guaranteed the extra point and the 4 point lead or take (to exaggerate) a 66% chance to get 2 points (for a 5 point lead) with a 33% chance of getting a 3 point lead. I think the answer here is pretty easy since 4 gets you out of range of 1 field goal tieing but 5 doesn't really do that much more than having 4. Other people have probably brought this up so I won't ramble any further.

[TimTimSalabim]

I think you are right, if it's late in the game. I should have specified that there are particular situations where you go for the 1-point conversion instead, but in general, you should go for two if you have a >50% chance of making a two-pointer. I'm thinking of situations in the first three quarters or so of the game, where your objective on offense *is* to maximize your score.

Incidentally, I can think of some situations where it would be correct to go for the two-pointer even if you figured your chance of making it was less than 50%. For example: You just scored a touchdown with a few seconds left in the game, making it 14-13, meaning you're one point behind. You have determined that against this particular team, you have a 45% chance of making a two-point conversion, and a virtually 100% chance of making a one-pointer. You also estimate that if the game goes to overtime, you have a 40% chance of winning (perhaps the other team is much better overall, or maybe you just suck at overtime). So, the play that maximizes your chance of winning the game is to go for the two-point conversion. But I doubt that you could find a single coach in the league who would make the correct play here.