Have I Discovered Another Mathematical Football Coaching Error?

[Troll_Inc]

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It isn't easier to score touchdowns from the 29 than it is from, say, the 10.

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I'm too lazy to look, but the Eagles redzone offense has been pretty bad this year. They might have more scores from outside the 20.

[rafiki]

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First let me say that the general principle in this and many of these scenarios, is the average person or coach's incorrect gut feeling about going for ties that have to be played off. They just don't gamble enough when they can go for the win.

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I don't know if you saw the Eagles - Patriots game.

The Eagles were down by 3 with a 2 and 4 at about the 29 with a little less than 4 minutes to go.

They went for a touchdown right then and there. At first I hated the call based on them giving up the much easier goal of getting a first down

I don't know if the touchdown pass was the best choice but there is some merit to "gambling" for a win before they hit the red zone where it is much harder to score a touchdown as the defense gets compacted.

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I was about to post exactly this...

[ClarkNasty]

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It isn't easier to score touchdowns from the 29 than it is from, say, the 10.

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I'm too lazy to look, but the Eagles redzone offense has been pretty bad this year. They might have more scores from outside the 20.

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C'mon guys.

[Bulldog]

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I think I have, but it depends on some parameters. So before I reveal it I want to ask some preliminary questions. Please don't answer it before thinking about it a little because I won't let you wiggle out if you try to claim my conclusions are wrong when I base it on your own numbers.

1. Two good equally matched football teams. Two and a half minutes to go in the game. The team losing by 5 is on their own 20 and has two time outs left. About how often will they score a touchdown?

2. Same situation but they are down by one point. About how often will they score a field goal (assuming they have a good field goal kicker.)

3. Same as above. Down by one. About how often will they surprisingly score an unneeded touchdown?

I realize that the answers depend on a lot of unstated things but you can still give me a ballpark average, which should be good enough.

EXTRA CREDIT

Tell me what I am driving at.

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Are you talking NFL or college? Two-minute drill-type scores come more quickly in college, even without the two-minute warning, because of the clock stopping on first downs. I'm pretty sure there'd be a different set of correct responses to your questions if we are talking college instead of NFL.

[Troll_Inc]

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It isn't easier to score touchdowns from the 29 than it is from, say, the 10.

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I'm too lazy to look, but the Eagles redzone offense has been pretty bad this year. They might have more scores from outside the 20.

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C'mon guys.

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It's not that crazy. The Eagles have 8 TDs from outside the redzone and 16 inside with a 0.486 prob of scoring a TD once inside.

To really answer this though you'd also need to know the probability of them being able to go from the 29 to inside the 20 (or 10 as the original poster said) and also what their TD percentage when they went for a TD when outside the redzone.

[MyTurn2Raise]

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LOL @ 'another'

the first one still rests on very questionable assumptions

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like?

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the one where I tear apart an 'expert' who tries to misapply a framed problem to a new context

[gumpzilla]

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LOL @ 'another'

the first one still rests on very questionable assumptions

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like?

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the one where I tear apart an 'expert' who tries to misapply a framed problem to a new context

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That hardly seems like a tearing apart. It seems like you're making a few small counterarguments and then saying "Yep, I'm definitely right."

[CardSharpCook]

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But if you miss the 2 point conversion you can't tie the game with a field goal!

Edit: I will concede that a safety gives us the tie if we convert. Now I see why you think we need a good defense to go for this, but that also requires a good kick-off, so we do in fact need a good kicker.

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Ben, at first I thought your post was playful/sarcastic. But your edit seems to say that you were serious. DS's point is that the emotional response of [ QUOTE ]
But if you miss the 2 point conversion you can't tie the game with a field goal!

[/ QUOTE ] is misleading. Even if you tie the game with an FG, you're still a dog to win the game (assuming some time has been left on the clock). Whereas, if you go for two, 50% of the time you'll be in position to take a 65-75% edge.

I hate it when posters don't do their own math. How many times have I posted, "So you think he should 3bet. Great. I was so curious what XXX thought the OP should do here. XXX says 3bet. Sadly, XXX you've left it up to us to figure out why." If you have a theory post your arguments for it.

OK, we've scored to make the score 23-27 and we have the option of going for 2, converting 50% of the time, or kicking for 1, converting 100% of the time. There is 5min left, and for us to be considering a win, there will be 2-3 more possessions in the game.

We kick the ball off and pray for defense. Our defense holds them to no score 65%. They get a FG 25%, a TD 10%. The TD% is meaningless as it means other team wins whether we're down 2,3,4. The FG% is very meaningful as its value has been greatly effected by our strategy decisions. If we had been down 2 or 3, the FG puts us down 5,6 - a TD wins it for us. If we we're down 4, a FG makes our TD only tie the game with a 7pt TD. So this is the first question. What is the FG% when we give them the ball back?

But we have stellar defense and they go 3 and out. We take 3-4 min to go down the field and score. we were down:
2: a FG gives us a 65% win. A TD gives us a 75% win.
3: a FG gives us a .65(chance other team scores) x .5(win in OT) = 33% win. A TD gives us a 75% win. Which leads to the next question - When down by 3, how often do we score a TD as opposed to a FG?
4: we've been given an extra down instead of a FGA. The extra down results in an eventual TD, (this is our third question: how often does the extra down lead to a TD) lets say 20% of the time. That TD gives us a win 65%, a tie 20%, a loss 15%, so a 75% win 20% of the time. A 15% win when down by 4.

Our defense allows a FG and we get the ball back down:
5: win 25%
6: win 25%
7: win 12.5%

So we do need to remember that our gamble will cost us if we then allow a FG. How much it costs us depends on how often the other team scores a FG, leaving us enough time for a drive.

So we have 3 rather important variables to consider before making the final calculations:
1. What is the FG% when we give them the ball back?
2. When down by 3, how often do we score a TD as opposed to a FG?
3. When forced to go for a TD instead of kicking it on 4th down, how often does the extra down lead to a TD?

Of course that's not even all the extra variables we've added. There is additional value to knowing you only need a FG to win - you can run out the clock before setting up the FG. It feels like there are too many variables here to come up with a sound mathematical answer. Guesstimate final numbers have it as a 54% win if we kick the extra point, and a 45% win if we go for two when down 4. This ignores the value gained from being able to run the clock before setting up for game winning FG. Also ignores the cost of being down 7 when 2pt fails and they get a FG. Questions 2 and 3 have the greatest effect on estimates. Of course, all this is predicated on the DS's notion that the other team WILL get the ball back for that final drive. I think my numbers have been unfair to DS because of this. Being down 2 gives us a great chance of kicking the game-winning FG as time expires.

[smbruin22]

david, which team are you talking about scoring an unnecessary TD?

the team that is down by 1? i.e. they score 2 TD's

or the team that is up by 1? i.e. the ball turns over, they score one TD that takes the margin to 8 and clock down near zero

i'd put first at 1-2%... second at 6-7%, given that the losing team hasn't scored. obviously if losing team scores, then it is necessary

but i'm seeing 10% that losing team scores two TD's from own 20 with little time and 2 timeouts. maybe my 1% was too low.

[Pudge714]

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LOL @ 'another'

the first one still rests on very questionable assumptions

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like?

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the one where I tear apart an 'expert' who tries to misapply a framed problem to a new context

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Two small counterarguments with no proof = ownage imo.