6 ms·

Math Meets Football: Is the New Extra Point a Game-Changer?

38 points by rcoppolo 11y ago

rcthompson 11y ago
Even if the expected point value for a 2-point conversion is higher, you don't need to involve resk-averseness to explain why a coach may still prefer 1-point kicks. The quantity to be maximized is not expected point value of the play, but probability of winning, which can be expressed as P(success) * P(win after success) + P(failure) * P(win after failure) where P(failure) = 1 - P(success). (More generally, it's the sum over all outcomes of P(outcome) * P(win | outcome).)
- aggie 11y ago
  You also should account for the fact that coaches are often considering more than just points, and beyond that are often just irrational. Coaches should go for it on 4th-and-short more often than they do, but getting stopped on 4th down is demoralizing and makes the coach look foolish, which shifts their decision-making. Getting stopped on a 2-pt. conversion might also reflect poorly on the coach, so they are averse to calling that play even if it is statistically the right move. I find this psychological side of coaching very interesting, and sports are a great venue for examining the psychology of decision-making. A great example of outcome-bias is the sports world's reaction to the Seahawks decision to throw the ball at the goal line in last year's Super Bowl. I would argue it was the proper decision as it maximized their chances of winning the game (it allowed them time for one passing play and two running plays, as opposed to just two running plays). Unfortunately for them, a very low percentage outcome occurred (interception), and that outcome has strongly biased how the play call has been judged.
  - meatysnapper 11y ago
    The criticism of the play is that Marshawn Lynch nearly always is able to gain yardage with heavy contact. If you have a running back that is able to do this, and do this consistently, why would not go for the run?
    - deleted 11y ago
      [deleted]
    - aggie 11y ago
      Lynch is a great power runner, but even he is not automatic to score on two attempts. If I remember right, he was actually 0/4 on the year inside the 2 yard line. If the Seahawks throw an incomplete pass on 2nd down, they have time left for two running plays. If they run on 2nd down and don't score, they only have time for one more running play. So by passing on 2nd down they get an extra play. Since it would leave them with the same 2 chances to run with Lynch, the 2nd down play can be judged in isolation: the upside is a chance at a touchdown (win the game), the downside is the risk of a turnover (lose the game). I am making these numbers up, but that is probably a 30-50% shot at a touchdown and a low single digit percentage of a turnover. Worth it. To expand on the fateful play itself, the odds of an interception on a short inside slant with a screen are very low. Browner jammed his receiver effectively which allowed Butler to sell out on jumping the route and then somehow hold on to the ball. Amazing awareness/preparation and flawless execution by the Patriots. Russell Wilson also lead Ricardo Lockette (his receiver) just a bit too much with the throw and Lockette doesn't break up Butler's interception as hard as he could have. If any one of these things doesn't happen, it's probably a touchdown or at worst an incomplete pass. It brings up another interesting question: many say Belichick was foolish for not calling a timeout to save a bit of time for a desperation drive. But you could also argue he was trying to put the pressure on Seattle and bait them into a bad play call. I think he got lucky. So really, he was the one who made the bad decision, not Carroll/Bevell/Wilson. Once again, outcome bias.
  - Someone 11y ago
    "coaches are [...] often just irrational. Coaches should go for it on 4th-and-short more often than they do, but getting stopped on 4th down is demoralizing" If it is demoralizing enough, and the game (or the season, if being demoralized has a long enough half-life) still has plenty of time to go, that may mean the coaches are acting rational by not playing the short-term better option. Extreme example: suppose a missed two-point conversion makes your team become absolutely worthless for the rest of the game. If so, you probably shouldn't go for a 2-point conversion at 6-0 in front with 30 minutes to play, even if its success rate is 95%.
- HelloMcFly 11y ago
  I would argue, from the coach's perspective, the quantity to be maximized is not the probability of winning but the probability of retaining their job. 2-pt conversion calls are are judged harshly when they fail, however unfairly, and it's likely in a coach's best interest to just stay conservative and avoid scrutiny, even if that means playing sub-optimally.
harmegido 11y ago
I think the more pressing thing to consider is P(injured player | play call). If you consider the fact that your quarterback is on the field for the 2 pointer, but not the 1 pointer (typically), the slight difference in point expectation is likely not worth the risk to your franchise player.
- vonmoltke 11y ago
  On the other hand, he is on the field for 55-60 snaps anyway. The additional 4 or so from the two-point conversions isn't going to change his risk profile much.
  - honestcoyote 11y ago
    With 16 games, an extra 4 snaps per game means 64 extra snaps per season, which is a bit more than playing one extra game. That seems like a noticeable risk increase, season after season, as well as increased wear-and-tear which would possibly lead to earlier retirements.
- giarc 11y ago
  Good point, not to mention the fact that the defense can now return 2 point conversions for a TD. INT heavy QBs could be in trouble.
  - swyman 11y ago
    Returns by the defense aren't a TD. They're limited to the same 2 points.
    - giarc 11y ago
      Regardless, if you now try to convert more of your touchdowns, and you have Eli throwing the ball, that's going to result in more 2 point conversions for the other team.
- harlanlewis 11y ago
  Point expectation is a good way to think of it, but consider the expected points of a 2pt (or 1pt) play vs the other 50 snaps a qb takes everywhere else on the field, where the expected points are less than 1. An integer point difference on a single play is huge.
no_flags 11y ago
I've always thought coaches were far too conservative by never going for 2 and punting on almost every third down. There's actually a high school coach that starting using a more aggressive strategy. They never punt and always onside kick https://www.youtube.com/watch?v=AGDaOJAYHfo https://www.youtube.com/watch?v=AGDaOJAYHfo
- ericcumbee 11y ago
  Punting on 3rd down would be overly conservative since you get 4 downs. I've always thought the NFL was a little to conservative. But then at the college level I am a fan of Georgia Southern. The Triple Option coaches(Paul Johnson at Ga Tech, Jeff Monken at Army...both formerly of Georgia Southern) their philisophy is if with that type of offense, if you can't move the ball 2-3 yards a play either with a Fullback dive, a QB keeper/midline option, or pitching it to an A-Back. Then we have bigger problems than just turning the ball over.
  - deleted 11y ago
    [deleted]
- tghw 11y ago
  The NYT has put a bot together that looks at the numbers and determines whether you should go for it or not. They have a good article on it here: http://www.nytimes.com/2014/09/05/upshot/4th-down-when-to-go-for-it-and-why.html http://www.nytimes.com/2014/09/05/upshot/4th-down-when-to-go...
- gtaylor 11y ago
  This definitely works at the highschool level, but becomes much more risky and nuanced in major collegiate BCS-level games, or especially in the NFL. On-sides kicks are incredibly difficult to recover when your opponent has been coached to be ready for them. We have a "hands team" for this specific reason. Making things even more difficult, there is game film available to pretty much all college/NFL coaching staffs within hours of a game's completion. If you do stuff like this, your opponents are going to be ready. I know we (Clemson) are always ready for Georgia Tech and Paul Johnson to pull stuff like this, because that's what he does. They're able to make bank on this against lesser opponents, but it doesn't always fly against an equally matched (or better) foe.
gd1 11y ago
I'm not a North American, but a few thoughts: - I see that the defense can now score two points by intercepting a two-point play and returning it. Doesn't this lower the utility of the two-point play as used in the article? Or have I misunderstood? - The article assumes the probabilities won't change. It isn't hard to imagine that teams will get better at executing two-point plays if they attempt more. Also, am I right in thinking that they are typically attempted by a team in a desperate position at the moment? If the existing stats show attempts by inferior teams or teams under pressure, they may be skewed. - Also, since it is now more likely to miss the one-point field goal, you are more likely to fall a point behind the opposition. They score TD and convert, 7-0, you score TD and miss, 7-6, they score TD and convert, 14-6, you score TD, now what are you going to do? You may as well go for the 2-pointer to make up the lost ground, depending on how late in the match it is.
- giarc 11y ago
  As for your second point, a 2 point conversion is basically just like any goal line play which they practice many times and encounter in games often. So I would say they have maximized their ability for this play and it wouldn't change if they attempted it more.
  - 91bananas 11y ago
    I agree here, from my observations teams struggle far more from super short yardage (<3 yards) worse than they struggle from ~10 yards. The lack of space before the goal line limits the routes you can run. The defense clogging the middle becomes easier because there is no deep threat to allocate safeties and linebackers to. I think the more 2 point plays that are run, defenses are going to get better at stopping them. I also wonder what percentage of successful 2 point plays were fake kicks, where special teams defense was out there. Rather than actual defensive starters. I wager that if offenses have to face real defenses in this situation they will perform worse.
    - swyman 11y ago
      > I also wonder what percentage of successful 2 point plays were fake kicks, where special teams defense was out there. Rather than actual defensive starters. I wager that if offenses have to face real defenses in this situation they will perform worse. Fair point, but I don't think I've ever seen any team at any level of play attempt a true fake FG on an extra point. There is, however, a related concept called a "Swinging Gate"[0] that's relatively prevalent at the high school level, rare at the college level, and almost completely unused in the NFL. Interestingly, this rule change completely eliminates the possibility since teams won't be able to reset into a traditional field goal formation at the 2 yard-line. [0] https://en.wikipedia.org/wiki/Swinging_gate_%28American_football%29 https://en.wikipedia.org/wiki/Swinging_gate_%28American_foot...
ojbyrne 11y ago
Counter-argument: Since the 2 point conversion is a more viable alternative than previously, 2 things will happen: 1. teams will practice 2-point conversions more. 2. teams will develop more plays for 2-point conversions. These will probably reduce the variance of the 2-point conversion.
- maxerickson 11y ago
  They already practice and develop plays for short yardage. The short down field at the goal line is different than first down conversions, but it isn't all that different than a red zone offense scheme.
  - kendallpark 11y ago
    Agreed. These plays already exist. If anything, this change will make the red zone play more interesting.
tunesmith 11y ago
I've never liked Expected-Value type calculations because they don't take variance into account. You could have a theoretical messed-up lottery where the payoff is greater than the odds, where EV would tell you to blow all your money on the lottery even if the odds are totally against you winning. Similarly, this wouldn't really imply that coaches should go for 2 all the time (like... you've just scored a TD to tie the game at 6 at the end of regulation, and a tie would mean you'd miss the playoffs). There's a cool equation called the Kelly Criterion to solve this but it only works for single bets. I don't know how to use it to compare between two bets, or for a case like the extra point where you are essentially betting nothing for a 92% chance to get one point.
- jkhiu12 11y ago
  You may have missed it in this article, but he does address variance (in the section explaining external incentives coaches include in their decision-making). I believe you are rephrasing the oft-repeated adage, "The [stock] market can stay wrong longer than you can stay liquid."
andrewrice 11y ago
One downside to the change is that it eliminates one of the NFL's most exciting occurrences: the surprise two-point attempt. Now wherever the offense lines up will be a clear indicator to the defense of what play is about to be run.
- jpalmer 11y ago
  I'd like to think the surprise two-point attempt from the 15 will be even more exciting now.
m_myers 11y ago
A more interesting tidbit from the new rules, from my perspective, is the introduction of the one-point safety. It is now theoretically possible to see a game with a score of 6-1. Team A scores a touchdown (6 points) and attempts to kick an extra point. It is blocked. Under the old rules, the play is over; under the new rules, either team can pick it up and run. Team B does so, picking it up and running downfield. Before reaching the goal, the Team B player fumbles the ball and a chasing Team A player picks it up. The Team A player is surrounded by Team B players and attempts to evade them, but only succeeds in accidentally backtracking into his own end zone, where he is tackled. The result of the play is a safety, which is usually worth two points - but since this is a two-point conversion attempt (after the kick is blocked), the safety is only worth one. So the score is 6-1 in favor of Team A. The odds of such a crazy play are infinitesimal. One-point safeties have happened a few times in college, where it's been legal for decades, but have always been scored by the offense. I am eagerly awaiting the first one-point defensive safety.
cloudkj 11y ago
Interesting side note: the author also happens to be an offensive lineman in the NFL. http://en.wikipedia.org/wiki/John_Urschel http://en.wikipedia.org/wiki/John_Urschel
matmann2001 11y ago
Look at all these engineers in here, talkin bout sportsball.

38 points by rcoppolo 11y ago

Even if the expected point value for a 2-point conversion is higher, you don't need to involve resk-averseness to explain why a coach may still prefer 1-point kicks. The quantity to be maximized is not expected point value of the play, but probability of winning, which can be expressed as P(success) * P(win after success) + P(failure) * P(win after failure) where P(failure) = 1 - P(success). (More generally, it's the sum over all outcomes of P(outcome) * P(win | outcome).)

aggie 11y ago
You also should account for the fact that coaches are often considering more than just points, and beyond that are often just irrational. Coaches should go for it on 4th-and-short more often than they do, but getting stopped on 4th down is demoralizing and makes the coach look foolish, which shifts their decision-making. Getting stopped on a 2-pt. conversion might also reflect poorly on the coach, so they are averse to calling that play even if it is statistically the right move. I find this psychological side of coaching very interesting, and sports are a great venue for examining the psychology of decision-making. A great example of outcome-bias is the sports world's reaction to the Seahawks decision to throw the ball at the goal line in last year's Super Bowl. I would argue it was the proper decision as it maximized their chances of winning the game (it allowed them time for one passing play and two running plays, as opposed to just two running plays). Unfortunately for them, a very low percentage outcome occurred (interception), and that outcome has strongly biased how the play call has been judged.
- meatysnapper 11y ago
  The criticism of the play is that Marshawn Lynch nearly always is able to gain yardage with heavy contact. If you have a running back that is able to do this, and do this consistently, why would not go for the run?
  - deleted 11y ago
    [deleted]
  - aggie 11y ago
    Lynch is a great power runner, but even he is not automatic to score on two attempts. If I remember right, he was actually 0/4 on the year inside the 2 yard line. If the Seahawks throw an incomplete pass on 2nd down, they have time left for two running plays. If they run on 2nd down and don't score, they only have time for one more running play. So by passing on 2nd down they get an extra play. Since it would leave them with the same 2 chances to run with Lynch, the 2nd down play can be judged in isolation: the upside is a chance at a touchdown (win the game), the downside is the risk of a turnover (lose the game). I am making these numbers up, but that is probably a 30-50% shot at a touchdown and a low single digit percentage of a turnover. Worth it. To expand on the fateful play itself, the odds of an interception on a short inside slant with a screen are very low. Browner jammed his receiver effectively which allowed Butler to sell out on jumping the route and then somehow hold on to the ball. Amazing awareness/preparation and flawless execution by the Patriots. Russell Wilson also lead Ricardo Lockette (his receiver) just a bit too much with the throw and Lockette doesn't break up Butler's interception as hard as he could have. If any one of these things doesn't happen, it's probably a touchdown or at worst an incomplete pass. It brings up another interesting question: many say Belichick was foolish for not calling a timeout to save a bit of time for a desperation drive. But you could also argue he was trying to put the pressure on Seattle and bait them into a bad play call. I think he got lucky. So really, he was the one who made the bad decision, not Carroll/Bevell/Wilson. Once again, outcome bias.
- Someone 11y ago
  "coaches are [...] often just irrational. Coaches should go for it on 4th-and-short more often than they do, but getting stopped on 4th down is demoralizing" If it is demoralizing enough, and the game (or the season, if being demoralized has a long enough half-life) still has plenty of time to go, that may mean the coaches are acting rational by not playing the short-term better option. Extreme example: suppose a missed two-point conversion makes your team become absolutely worthless for the rest of the game. If so, you probably shouldn't go for a 2-point conversion at 6-0 in front with 30 minutes to play, even if its success rate is 95%.
HelloMcFly 11y ago
I would argue, from the coach's perspective, the quantity to be maximized is not the probability of winning but the probability of retaining their job. 2-pt conversion calls are are judged harshly when they fail, however unfairly, and it's likely in a coach's best interest to just stay conservative and avoid scrutiny, even if that means playing sub-optimally.

harmegido 11y ago

I think the more pressing thing to consider is P(injured player | play call). If you consider the fact that your quarterback is on the field for the 2 pointer, but not the 1 pointer (typically), the slight difference in point expectation is likely not worth the risk to your franchise player.

vonmoltke 11y ago
On the other hand, he is on the field for 55-60 snaps anyway. The additional 4 or so from the two-point conversions isn't going to change his risk profile much.
- honestcoyote 11y ago
  With 16 games, an extra 4 snaps per game means 64 extra snaps per season, which is a bit more than playing one extra game. That seems like a noticeable risk increase, season after season, as well as increased wear-and-tear which would possibly lead to earlier retirements.
giarc 11y ago
Good point, not to mention the fact that the defense can now return 2 point conversions for a TD. INT heavy QBs could be in trouble.
- swyman 11y ago
  Returns by the defense aren't a TD. They're limited to the same 2 points.
  - giarc 11y ago
    Regardless, if you now try to convert more of your touchdowns, and you have Eli throwing the ball, that's going to result in more 2 point conversions for the other team.
harlanlewis 11y ago
Point expectation is a good way to think of it, but consider the expected points of a 2pt (or 1pt) play vs the other 50 snaps a qb takes everywhere else on the field, where the expected points are less than 1. An integer point difference on a single play is huge.

no_flags 11y ago

I've always thought coaches were far too conservative by never going for 2 and punting on almost every third down. There's actually a high school coach that starting using a more aggressive strategy. They never punt and always onside kick https://www.youtube.com/watch?v=AGDaOJAYHfo https://www.youtube.com/watch?v=AGDaOJAYHfo

ericcumbee 11y ago
Punting on 3rd down would be overly conservative since you get 4 downs. I've always thought the NFL was a little to conservative. But then at the college level I am a fan of Georgia Southern. The Triple Option coaches(Paul Johnson at Ga Tech, Jeff Monken at Army...both formerly of Georgia Southern) their philisophy is if with that type of offense, if you can't move the ball 2-3 yards a play either with a Fullback dive, a QB keeper/midline option, or pitching it to an A-Back. Then we have bigger problems than just turning the ball over.
- deleted 11y ago
  [deleted]
tghw 11y ago
The NYT has put a bot together that looks at the numbers and determines whether you should go for it or not. They have a good article on it here: http://www.nytimes.com/2014/09/05/upshot/4th-down-when-to-go-for-it-and-why.html http://www.nytimes.com/2014/09/05/upshot/4th-down-when-to-go...
gtaylor 11y ago
This definitely works at the highschool level, but becomes much more risky and nuanced in major collegiate BCS-level games, or especially in the NFL. On-sides kicks are incredibly difficult to recover when your opponent has been coached to be ready for them. We have a "hands team" for this specific reason. Making things even more difficult, there is game film available to pretty much all college/NFL coaching staffs within hours of a game's completion. If you do stuff like this, your opponents are going to be ready. I know we (Clemson) are always ready for Georgia Tech and Paul Johnson to pull stuff like this, because that's what he does. They're able to make bank on this against lesser opponents, but it doesn't always fly against an equally matched (or better) foe.

gd1 11y ago

I'm not a North American, but a few thoughts: - I see that the defense can now score two points by intercepting a two-point play and returning it. Doesn't this lower the utility of the two-point play as used in the article? Or have I misunderstood? - The article assumes the probabilities won't change. It isn't hard to imagine that teams will get better at executing two-point plays if they attempt more. Also, am I right in thinking that they are typically attempted by a team in a desperate position at the moment? If the existing stats show attempts by inferior teams or teams under pressure, they may be skewed. - Also, since it is now more likely to miss the one-point field goal, you are more likely to fall a point behind the opposition. They score TD and convert, 7-0, you score TD and miss, 7-6, they score TD and convert, 14-6, you score TD, now what are you going to do? You may as well go for the 2-pointer to make up the lost ground, depending on how late in the match it is.

giarc 11y ago
As for your second point, a 2 point conversion is basically just like any goal line play which they practice many times and encounter in games often. So I would say they have maximized their ability for this play and it wouldn't change if they attempted it more.
- 91bananas 11y ago
  I agree here, from my observations teams struggle far more from super short yardage (<3 yards) worse than they struggle from ~10 yards. The lack of space before the goal line limits the routes you can run. The defense clogging the middle becomes easier because there is no deep threat to allocate safeties and linebackers to. I think the more 2 point plays that are run, defenses are going to get better at stopping them. I also wonder what percentage of successful 2 point plays were fake kicks, where special teams defense was out there. Rather than actual defensive starters. I wager that if offenses have to face real defenses in this situation they will perform worse.
  - swyman 11y ago
    > I also wonder what percentage of successful 2 point plays were fake kicks, where special teams defense was out there. Rather than actual defensive starters. I wager that if offenses have to face real defenses in this situation they will perform worse. Fair point, but I don't think I've ever seen any team at any level of play attempt a true fake FG on an extra point. There is, however, a related concept called a "Swinging Gate"[0] that's relatively prevalent at the high school level, rare at the college level, and almost completely unused in the NFL. Interestingly, this rule change completely eliminates the possibility since teams won't be able to reset into a traditional field goal formation at the 2 yard-line. [0] https://en.wikipedia.org/wiki/Swinging_gate_%28American_football%29 https://en.wikipedia.org/wiki/Swinging_gate_%28American_foot...

ojbyrne 11y ago

Counter-argument: Since the 2 point conversion is a more viable alternative than previously, 2 things will happen: 1. teams will practice 2-point conversions more. 2. teams will develop more plays for 2-point conversions. These will probably reduce the variance of the 2-point conversion.

maxerickson 11y ago
They already practice and develop plays for short yardage. The short down field at the goal line is different than first down conversions, but it isn't all that different than a red zone offense scheme.
- kendallpark 11y ago
  Agreed. These plays already exist. If anything, this change will make the red zone play more interesting.

tunesmith 11y ago

I've never liked Expected-Value type calculations because they don't take variance into account. You could have a theoretical messed-up lottery where the payoff is greater than the odds, where EV would tell you to blow all your money on the lottery even if the odds are totally against you winning. Similarly, this wouldn't really imply that coaches should go for 2 all the time (like... you've just scored a TD to tie the game at 6 at the end of regulation, and a tie would mean you'd miss the playoffs). There's a cool equation called the Kelly Criterion to solve this but it only works for single bets. I don't know how to use it to compare between two bets, or for a case like the extra point where you are essentially betting nothing for a 92% chance to get one point.

jkhiu12 11y ago
You may have missed it in this article, but he does address variance (in the section explaining external incentives coaches include in their decision-making). I believe you are rephrasing the oft-repeated adage, "The [stock] market can stay wrong longer than you can stay liquid."

andrewrice 11y ago

One downside to the change is that it eliminates one of the NFL's most exciting occurrences: the surprise two-point attempt. Now wherever the offense lines up will be a clear indicator to the defense of what play is about to be run.

jpalmer 11y ago
I'd like to think the surprise two-point attempt from the 15 will be even more exciting now.

m_myers 11y ago

A more interesting tidbit from the new rules, from my perspective, is the introduction of the one-point safety. It is now theoretically possible to see a game with a score of 6-1. Team A scores a touchdown (6 points) and attempts to kick an extra point. It is blocked. Under the old rules, the play is over; under the new rules, either team can pick it up and run. Team B does so, picking it up and running downfield. Before reaching the goal, the Team B player fumbles the ball and a chasing Team A player picks it up. The Team A player is surrounded by Team B players and attempts to evade them, but only succeeds in accidentally backtracking into his own end zone, where he is tackled. The result of the play is a safety, which is usually worth two points - but since this is a two-point conversion attempt (after the kick is blocked), the safety is only worth one. So the score is 6-1 in favor of Team A. The odds of such a crazy play are infinitesimal. One-point safeties have happened a few times in college, where it's been legal for decades, but have always been scored by the offense. I am eagerly awaiting the first one-point defensive safety.

cloudkj 11y ago

Interesting side note: the author also happens to be an offensive lineman in the NFL. http://en.wikipedia.org/wiki/John_Urschel http://en.wikipedia.org/wiki/John_Urschel

matmann2001 11y ago

Look at all these engineers in here, talkin bout sportsball.