Going for two each time Theory
 

This should maybe be in the sports section but [censored] it.

The stat for the NFL wide % of successful two point conversions is 50%. Correct me if I'm wrong, but I interpret this to mean that an average offence in the national football league will essentially average an extra point if they went for two each time.

If this is true, what really interests me is this: If you are an NFL coach and you know that your offence is well above the league average, i.e. the colts or the sea hawks, isn't it realistic to assume that you can average more than one point, the reward for an extra point, for each try after a touchdown by going for two and thus rack up something like 7.2-7.5 points per touchdown on average?

There must be some snag here, beacuse this seems to obvious and too good to be true. Any thoughts?

Re: Going for two each time Theory
 

I'm not a huge sports expert, but I think that because an extra point is basically automatic for any team with a reasonably competent kicker, the EV loss of getting no points at all is much larger than the EV gain of getting two.

Re: Going for two each time Theory
 

if you get 2 points half the time, and 0 the other half, isn't that the same thing as getting 1 all the time?

also, that 50% stat may be skewed towards teams who already attempt more than 2 points conversions than the average team b/c they are better talented.

but I dunno. the sample size is prolly to small to know for sure. nobody wants to score a TD, miss a 2 pt conversion, then have the other team take the lead w/ a TD and kick

Re: Going for two each time Theory
 

I think this can be put in the same category as a segment I saw on ESPN a month ago.

Some mathematician calculated the "odds" of going for it on fourth down and said that most teams should go for it way more often than they usually do. When they presented this evidence to some head coaches, their reactions were similar:

"Sounds like a good theory, but has this math guy ever had his name on the front page of the sports section because he decided to go for a fourth down early, missed it, gave up a field goal, and lost by two points?"

ScottieK

Re: Going for two each time Theory
 

as soon as you drop the stat to 49% it makes sense why they wouldn't try that. you're further from a lock that you'll make two half the time, than you are from a lock that you'll make one 100% of the time.

Re: Going for two each time Theory
 

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Some mathematician

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Was his name David Sklansky?

Also, hot damn the mods are quick today.

Re: Going for two each time Theory
 

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as soon as you drop the stat to 49% it makes sense why they wouldn't try that. you're further from a lock that you'll make two half the time, than you are from a lock that you'll make one 100% of the time.

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You don't think the colts could average 1.1 or 1.2 points per two point try?

Re: Going for two each time Theory
 

It doesn't seem like it would matter very much...what I mean is for those teams who have a highly capable offense that can score 2pt conversions more than the league average is the extra point or two they'd pick up really going to matter? It seems like most of these teams win by a larger margin than that most of the time anyways.

Hope that makes sense.

J

Re: Going for two each time Theory
 

Two reasons:
1. 6 points only ties 2 FGs, which is a common scoring increment. As you've established, the 2pt is roughly equal to the PAT, but loses big against 2 FGs.
2. Assume that each team scores 1 TD. If the first team goes for 2, it will lose a lot more than 50% of the time. 50% of the time it misses and loses. 50% of the time it makes. Then, the other team knows to go for 2, and ties the game half the time. Obviously, the real life situations aren't so formalistic, but the longer there is remaining in the game, the more this effect costs the converting team.

Re: Going for two each time Theory
 

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It doesn't seem like it would matter very much...what I mean is for those teams who have a highly capable offense that can score 2pt conversions more than the league average is the extra point or two they'd pick up really going to matter? It seems like most of these teams win by a larger margin than that most of the time anyways.


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Success is all about thinking at the margin. I'm sure that if you could convince any NFL owner that going for two each time would get them two more points in a easy, all kickers would be getting their walking papers.

Re: Going for two each time Theory
 

[ QUOTE ]
Two reasons:
1. 6 points only ties 2 FGs, which is a common scoring increment. As you've established, the 2pt is roughly equal to the PAT, but loses big against 2 FGs.
2. Assume that each team scores 1 TD. If the first team goes for 2, it will lose a lot more than 50% of the time. 50% of the time it misses and loses. 50% of the time it makes. Then, the other team knows to go for 2, and ties the game half the time. Obviously, the real life situations aren't so formalistic, but the longer there is remaining in the game, the more this effect costs the converting team.


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It sounds like you have something worth-while to say but I'm not really following. Could you rearticulate?

Re: Going for two each time Theory
 

awful, awful idea to go for two every time

These are not independent trials. The effect of going for two cannot be viewed in isolation. It directly changes the way the rest of the game is played.

missing does not cost just 1 point. There are hidden points lost later based on game situations. A team might have to later go for two to make up for a missed one earlier. It might become advantageous for an opponent to later go for two, and, if they make it, the missed opportunity cost 2 points then.

As the previous poster pointed out...making it might cause the opponent to go for two later where they can make it up.

EDIT: This is an example of what happens

Re: Going for two each time Theory
 

In superbowl XXXVIII, both teams scored 4 touchdwons and one field goal, but the patriots won by 3 in regulation. Why? Because Carolina attempted a two point conversion to early. The failed attempt ultimatly cost them three points, which was the Pats margin of victory.

Re: Going for two each time Theory
 

Another point: two point plays are tough to design. A team usually only has a handful of what they view as successful two point plays. Using them all the time would help defenses prepare for and be successful in stoping them in the future. The conversion rate would be sure to drop IMO.

It would also giveaway plays that teams use in goalline scoring situations.

Re: Going for two each time Theory
 

Teams probably should go for two much more, just like they should go for it on 4th down more often. I think if you had a good offense, especially a good rushing attack that made running the ball a really creditable threat in these situations, and you invested a lot more time in drawing up and practicing conversion plays, you could easily get to a 60% conversion rate.

None of the arguments about the problems with falling a point behind make sense to me, since you are even more likely to pull a point ahead and put pressure on the other team to try a two-point conversion themselves.

Re: Going for two each time Theory
 

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In superbowl XXXVIII, both teams scored 4 touchdwons and one field goal, but the patriots won by 3 in regulation. Why? Because Carolina attempted a two point conversion to early. The failed attempt ultimatly cost them three points, which was the Pats margin of victory.

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No, the failed attempt cost them slightly less than 1 point.

Re: Going for two each time Theory
 

in Friday Night Lights, Dallas Carter went for 2 every time, all season.

seemed to work out fine for them

also, they barked like dogs before the state championship. not sure what affect that had.

Re: Going for two each time Theory
 

No - it would just be increasing variance needlessly. Plus, the teams you'd score 2 on more often are probably teams you should be beating, and the teams you'd miss against are teams you need every point against.

Teams are not going to start going for 2 regularly.

Re: Going for two each time Theory
 

If the success rate is 50% on two point conversions, obviously your expected value is one point. So assuming 100% extra point attempt success rate and 50% 2 point success rate, the two options have equivalent EV(+1), but much different variance.

Of course 100% is obviously not accurate, and from my brief research i think the 2 point conversion success rate is probably more in the 40-45% range.

The key is recognizing the situations where you want higher or lower variance. Obviously if the game is tied with 1 second left, you'd want to reduce variance and kick it, and if you were down 2 with 1 second left, you'd want to increase your variance. Throughout the game obviously the decision would be less clear cut but would depend on the situation. All things equal though you'd want to choose the play with the higher EV, which in my opinion is kicking the extra point for most if not all teams.

Re: Going for two each time Theory
 

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In superbowl XXXVIII, both teams scored 4 touchdwons and one field goal, but the patriots won by 3 in regulation. Why? Because Carolina attempted a two point conversion to early. The failed attempt ultimatly cost them three points, which was the Pats margin of victory.

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No, the failed attempt cost them slightly less than 1 point.

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IIRC, The score was 21-10 pats, car scored and failed a 2-point conversion 21-16 pats (net one point lost for car). Carolina scored again and again failed on a 2 pointer 22-21 car (net 2 points lost for car). The Pats scored, and made a sucesfull 2 pointer 29-22 pats (net 3 points lost for car).then carolina scored a touchdown, and the pats scored a field goal Final score 32-29 pats.

Both teams scored 4 touchdowns and a field gaol.

If carolina had not attempted the their first two pointer, none of the other 2 pointers would have been attempted. Assuming that the rest of the game went the same, had carolina not gone for two, the score would have been 31-31, and the game would have gone to overtime.

Perhapse you would rather look at it from an EV (I will call it EW for expected wins) perspective.

As I stated above, if Carolina had not gone for 2, the game would have been tied EW=0.5

Going for two:
1/8 of the time, the game will turn out as it did: 0.125*0

1/8 of the time, the pats would fail on their 2 pointer
this would have caused carolina to go for two after their final touchdown.
1/2 the time they would have made it, and the score at the end of regulation would be 30-30: 0.125*0.5*0.5
1/2 the time they would have failed, and the pats would win 30-28: 0.125*0.5*0

1/4 of the time, carolina would have been sucesfull on their second 2 pointer. This would have resulted in a 31-31 tie: 0.25*.05

1/2 the time, carolina would have been sucesfull on their first 2 point attempt. This would have caused the Pats to have to make a touchdown instead of a field goal as time expired. Lets assume the probability of them doing that is X: 0.5*X

EW=0.125*0+0.125*0.5*0.5+0.125*0.5*0+0.25*.05+0.5* X=0.15652+0.5*X

Since not going for 2 has an EW of 0.5, I then solve for X with EW=0.5

X=.17174

If you believe that the Pats chances of making a last second touchdown were less that 17.174%, then carolina was correct to go for 2. Otherwise they were not.

Re: Going for two each time Theory
 

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If the success rate is 50% on two point conversions, obviously your expected value is one point. So assuming 100% extra point attempt success rate and 50% 2 point success rate, the two options have equivalent EV(+1), but much different variance.

Of course 100% is obviously not accurate, and from my brief research i think the 2 point conversion success rate is probably more in the 40-45% range.

The key is recognizing the situations where you want higher or lower variance. Obviously if the game is tied with 1 second left, you'd want to reduce variance and kick it, and if you were down 2 with 1 second left, you'd want to increase your variance. Throughout the game obviously the decision would be less clear cut but would depend on the situation. All things equal though you'd want to choose the play with the higher EV, which in my opinion is kicking the extra point for most if not all teams.

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The reason that this is not correct is because by going for 2, you are not just risking the 1 point that you could have kicked. You are also risking other points that come into play when the other team adjusts their strategy to the result of your 2 point attempt.

Suppose a team has a 55% chance of making a 2 point conversion. If they run back the opening kickoff for a touchdown, should they go for 2? I think not.

45% of the time, they miss, and the other team can take the lead with a touchdown.

55% of the time, they are sucesful. Of this 50% of the time, the other team can tie with a touchdown (when they go for two because you did).

So 45% of the time, you would trail by a point if the other team scores.

27.5% of the time, you would be tied if the other team scores.

Only 27.5% of the time, you would lead by two points if the other team scores.

Add to this the fact that if you miss, the other team can tie with 2 field goals, and the argument against going for 2 becomes even stronger.

Unless you are playing a game in which scoring is done with basketball frequency, maximizing your expected points is not the same as maximizing your chance to win.

Re: Going for two each time Theory
 

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in Friday Night Lights, Dallas Carter went for 2 every time, all season.

seemed to work out fine for them

also, they barked like dogs before the state championship. not sure what affect that had.

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I'm sure that this is mostly a joke, but I'll just point out that in HS football, everything is different. Mostly because the extra point is often not a sure thing.

The team that I followed this year should never have kicked because they actually had a better chance at 2 than 1.

Re: Going for two each time Theory
 

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Unless you are playing a game in which scoring is done with basketball frequency, maximizing your expected points is not the same as maximizing your chance to win.

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I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.

That said, I do think there is merit to your point about scoring frequency. Obviously if you scored a touchdown to tie and simultaneously the entire starting offense for the other team tore their ACLs, you'd definitely want to kick, as the chance of them scoring again has suddenly dropped to near 0. But I think that with moderately frequent scoring, maximizing EP is correct under normal circumstances not near the end of the game. But again, I think this will almost always mean kicking the extra point.

Re: Going for two each time Theory
 

There are times it may make sense to go for two even when it seems unnecessary. For example, I wrote this a while ago about being down by 14 late, scoring a TD, and going for 2 anyway:

"Assume you score two TDs, you make the 2-pt conversion 40% of the time, the PAT 100%, and the opponent doesn't score at all. Then the following are possible:

(1) You make your first two-point attempt. In this case you win because you kick the PAT on your second TD and win by 1.
(2) You miss your first and make your second. In this case you tie.
(3) You miss your first and second. You lose.

(2) is identical to kicking two PATs. (1) happens 40% of the time. (3) happens 36% of the time. So you come out ahead!

The problems is that coaches get blasted for unconventional gambles that don't work, but get only a bit of credit for gambles that do. You will be fired if you miss two 2-pt attempts in a playoff game and lose by 2.

...

The breakeven percentage for this is (3-sqrt(5))/2 which is around 38.1%. "

So even under conservative numbers, this works out well. In real life, it makes even more sense to follow this strategy, because 2-point conversions have more than a 40% chance and PATs have less than a 100% chance.

Re: Going for two each time Theory
 

[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.


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I didn't read this, but this idea is pure lunacy

Re: Going for two each time Theory
 

Now the 4th down deal teams should definitely do more often, especially against high scoring teams like Indy or USC who have such a high success rate anyways.

Re: Going for two each time Theory
 

Um, no. You can bet your ass Bill Belichick does this.

Re: Going for two each time Theory
 

[ QUOTE ]
[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.


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I didn't read this, but this idea is pure lunacy

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Okay, what the hell would you base it on? Your gut feeling?

Re: Going for two each time Theory
 

You guys are also forgetting that a PAT is not automatic. Your kicker will miss, occasionally, especially if his name is Jay Feeley. So say you make 50% of 2-pt conversions, but only make 95% of PATs, you already have an EV loss of PATs.

My problem with always going for 2 is defenses will spend a week preparing a goal-line stand against your specific offense and your success rate will drop below 50% to about 42%.

Re: Going for two each time Theory
 

I really don't think NFL kickers miss 1 of 20 PATs.

Re: Going for two each time Theory
 

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I really don't think NFL kickers miss 1 of 20 PATs.

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agreed. after looking at the career stats of a few kickers and then getting tired of it, the lowest among the ones i saw was a little over 98%. Even Feely was 175-177

Re: Going for two each time Theory
 

Insufficient sample size and results based thinking. They didn't lose because they attempted the 2pt - they lost because they failed to convert it.

Re: Going for two each time Theory
 

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I really don't think NFL kickers miss 1 of 20 PATs.

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I was just posing a hypothetical when I said 95%. But even if it's 98%, that affects the EV of the decision. It's not automatic.

Re: Going for two each time Theory
 

It's pretty much 99%

Re: Going for two each time Theory
 

[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.

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Did David pass this off as his own idea? Because a statistics professor at Berkeley wrote a paper a few years back that got a fair amount of press which basically argued the same thing and found that teams should go for it around midfield in 4th and short situations almost every time.

Re: Going for two each time Theory
 

This idea has been around since at least the hidden game of football.

Re: Going for two each time Theory
 

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Did David pass this off as his own idea? Because a statistics professor at Berkeley wrote a paper a few years back that got a fair amount of press which basically argued the same thing and found that teams should go for it around midfield in 4th and short situations almost every time.

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Well I don't think he explicitly said that he was the first to think of it, but he didn't exactly include a works cited page either.

Re: Going for two each time Theory
 

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Two reasons:
1. 6 points only ties 2 FGs, which is a common scoring increment. As you've established, the 2pt is roughly equal to the PAT, but loses big against 2 FGs.
2. Assume that each team scores 1 TD. If the first team goes for 2, it will lose a lot more than 50% of the time. 50% of the time it misses and loses. 50% of the time it makes. Then, the other team knows to go for 2, and ties the game half the time. Obviously, the real life situations aren't so formalistic, but the longer there is remaining in the game, the more this effect costs the converting team.


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It sounds like you have something worth-while to say but I'm not really following. Could you rearticulate?

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1. Points don't have linear utility. Increasing your point total by 8 is better than increasing it by 7, because you'll beat a TD+PAT rather than tying it. But increasing your point total by 7 comparatively even better than increasing it by 6, because you'll tie a TD+PAT and beat 2 FGs. Even though both differences are 1 point, the downside risk of a 2pt conv. is higher than its upside.

2. Going for 2 early in a game gives the other team informational advantages. Whenever they have to make a similar decision, they can act knowing whether or not you made your conversion. If you did not, they can play conservatively to win. If you did make it, they can gamble and sometimes tie you. The benefit is substantially decreased because the other team can adjust if you succeed.

Re: Going for two each time Theory
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
I'm assuming most people here read David Sklansky's article a few months back about going for it on 4th down. The basis of his whole article was that you can calculate your EP(expected points) from any field position, your opponents EP from that same spot in case you fail, and your expected 4th down conversion success rate, and then compute your best play from that. He of course offered the caveat that it doesn't apply in certain situations where you'd want to minimize your variance, but in general it is correct. Now i'm not saying this method of analyzing football decisions is correct just because he says it is, but I do think that carries a lot of weight.


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I didn't read this, but this idea is pure lunacy

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Okay, what the hell would you base it on? Your gut feeling?

[/ QUOTE ]There was some math guy on ESPN trying to convince coaches about the 4 down conversion expected points. The 3 coaches said it was ridiculous that a mathman would dare say anything about football. Percels said that he wanted the mathguy next to him on the sideline so whenever it fails he could punch him in the face. It's too bad, becuase going for it on 4th when your expected pts is positive would really add to the excitement of the game. Luckly for us the NFL can change the rules to artificialy instill more offense into the league anytime they want.

Re: Going for two each time Theory
 

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1. Points don't have linear utility. Increasing your point total by 8 is better than increasing it by 7, because you'll beat a TD+PAT rather than tying it. But increasing your point total by 7 comparatively even better than increasing it by 6, because you'll tie a TD+PAT and beat 2 FGs. Even though both differences are 1 point, the downside risk of a 2pt conv. is higher than its upside.

2. Going for 2 early in a game gives the other team informational advantages. Whenever they have to make a similar decision, they can act knowing whether or not you made your conversion. If you did not, they can play conservatively to win. If you did make it, they can gamble and sometimes tie you. The benefit is substantially decreased because the other team can adjust if you succeed.

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right on...I almost posted something like this, but my economics is quite rusty. I think I did a brain flush the second I dropped out of my PhD work.

I think much of these ideas do not account for the fact that the plays are not held in isolation. A football game is a dynamic system with each play inter-related to the next. Pushing to maximize the output of any one play, or "event," can have very detrimental consequences towards maximizing the output of the entire game, or "system."

While I think that football coaches are too conservative, I do not see the fault in going for two not frequent enough. I see coaches go for two far too frequently. I also think they should go for it on fourth more often, but not nearly as often as suggested in the paper by the Professor out at Berkeley.

What I have seen in football is the total breakdown of risk-taking on the offensive side of the ball. The mid to long range passing game is becoming extinct. I think everyone realized how important turnovers are, but over-reacted. An interception 35 yards downfield is different than a fumble at the line. Oh well...I have a whole notebook full of observations of things I'd change if I were a coach. Maybe after I make millions at poker, I'll work my way up from the low levels of coaching.