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Houston vs. Tennessee

October 18, 2020
                                     Houston vs. Tennessee

            In the Houston/Tennessee football game Sunday afternoon there was a situation in which Houston was leading by 7 points, 36-29, having just scored a touchdown and being in position to attempt (a) a regular point after touchdown (kick) or (b) a two-point conversion.  Time was running out; Tennessee had. . I don’t know, two minutes to score, or something like that.   The obvious thing to do is to kick the extra point and put the pressure on Tennessee to score 8 points in the last two minutes in order to tie, and, for better or worse, that is what I would have done—the obvious thing.

            The Houston coach, however, did not do the obvious thing.  He decided to go for two.   It didn’t work, so Houston had a 7-point lead with basically one possession left in the game.  Tennessee came back and scored, and won the game in overtime. 

            The TV analyst who was working the game second-guessed the Houston decision in intemperate language, and blamed the decision—repeatedly, and in frankly ugly terms, on "analytics".   It would be difficult to say whether he sounded more like a moron or an asshole; he sounded like a moron and an asshole.   He hit it REALLY hard, laying it in "our" laps, us meaning the analytics community.  It seemed to me unlikely that analytics had very much to do with this, so my gut reaction was that it seemed unlikely that this was an analytics-driven decision.  This led to discussion, and. . .well, here we are. 

            The problem of identifying the optimal strategy in a football game can be stated as

a)     What is the probability that we will win this game if we do (A), and

b)     What is the probability that we will win this game if we do (B). 


If (a) is greater than (b), then you do (a); otherwise, you do (b).   Not in a dogmatic sense, of course; the coach has to do what he believes is "best", but that comes down to the same thing; what is "best" for the coach is that which gives his team the best chance to win.   My point is that the statistical analyst is always dealing with a lot of unknowns which may change the right answer in the real world, and the coach may know things of which we have no knowledge. He may have been convinced that his third blocker on the left side can destroy the man he would have to block.  He may have been convinced that he had drawn up a play that Tennessee had never seen before, which would leave his receiver wide open.   Since we do not KNOW what it was that he knew (or thought he knew), we have to be cautious in our statements about it (unlike the asshole moron on TV), not out of generosity of spirit but as a consequence of logic.  Logically, we have to understand that we do not KNOW what the right answer is. 

But doing the best we can with the mathematical puzzle. . .


It would appear to me that if Houston attempts the two point conversion, then there are five scenarios which are reasonably likely from that point on.   Those five scenarios are:

(1)  Two-point conversion is good; Tennessee does not score subsequently, Houston wins,

(2)  Two-point conversion is good, putting Houston 9 points ahead, Tennessee DOES score on next possession, it doesn’t matter, Houston wins anyway,

(3)  Two-point conversion fails, Tennessee does not score after that, Houston still wins,

(4)  Two-point conversion fails, Tennessee DOES score and kicks the PAT, game goes into overtime, Houston wins it in overtime, Houston wins again, and

(5)  Two-point conversion fails, Tennessee does score and kicks the PAT, game goes into overtime, Tennessee wins it in overtime.


Only in scenario (5) does Tennessee win, and that is what actually happened:  the two-point conversion DID fail, Tennessee DID score and kick the PAT, the game DID go into overtime, and Tennessee DID win it in overtime.   But the issue relevant to us is, what was the LIKELIHOOD that that would happen?

The most critical assumption that we have to make is, "What is the likelihood that Tennessee would score 7 points in those last couple of minutes?"   Let’s assume for the sake of argument that it is 50%.  If that probability is 50%, then Tennessee’s chance of winning the game was, I think, 13.025%--assuming the Houston did attempt the two-point conversion. 

Three things would have to happen in order for Tennessee to win:

1)     The two-point conversion would have to fail,

2)     Tennessee would have to score and hit their extra point, and

3)     Tennessee would have to win the game in overtime. 


According to some source I found online, 52.1% of two-point conversion attempts fail, so we will assume that the chance the two-point conversion would fail is 52.1%. 

We have assumed for the sake of argument that the chance that Tennesee would score seven on their final possession is 50%.

And, since an overtime is basically a tossup, we will assume that the likelihood that Tennessee would win the overtime period is 50%. Noting again that none of those three probabilities is necessarily RIGHT; that’s just as much as we know.  The coaches involved, or some smart person such as yourself, might very probably know more than we do.  But that’s the numbers we have to work with.  

Working with those numbers, the probability that (1) Houston goes for two and (b) Tennessee wins is .521, times .500, times .500.    That’s 13.025%.   Houston’s chance of winning the game, IF they go for two, is .86975. 


I will note in passing that you CAN divide the possibility of Tennessee scoring seven points into many more probabilities:   1.  That Tennessee can score a touchdown, 2. That they decide to go for two points in regulation, rather than risking overtime, 3. That the two-point conversion succeeds, 4. That the two-point conversion fails, 5. That they decide to just kick the PAT, 6. That the PAT kick succeeds, and 7. That the PAT kick fails.   All of those things are possible, thus are probable at some level. 


But that’s not really a BETTER way to analyze the problem; it is merely a more complicated way to analyze the problem.  Since Tennessee did in fact decide to just kick the PAT and did in fact hit it, we can treat that choice as a "known" rather than an "unknown", and spare ourselves more branches breaking off from the tree of probabilities. 


So Houston’s chance of winning if they did go for two was 86.975%.   Now, what was their probability of winning if they had just kicked the PAT like normal people and myself and the asshole in the TV booth all expected them to do?


Here, it seems to me, we have SEVEN probable scenarios, rather than five as we had before—using the same assumed values.   Let me note first of all that if Houston kicks the PAT, Tennessee then HAS to go for a two-point conversion, so that is a "known".  The seven reasonably probable scenarios are:


1)     Houston’s PAT is good and Tennessee does not score, Houston Wins,

2)     Houston’s PAT is good, Tennessee scores and goes for two but misses, Houston Wins. 

3)     Houston’s PAT is good, Tennessee scores and goes for two, makes the two points to put the game in overtime, but Houston wins in overtime,

4)     Houston’s PAT is good, Tennessee scores and goes for two, makes the two points to put the game in overtime, and Tennesee wins the game in overtime. 

5)      Houston’s PAT is NOT good, but Tennessee does not score, Houston wins.

6)      Houston’s PAT is not good, Tennessee scores, games goes into overtime, Houston wins, and

7)      Houston’s misses the PAT kick, Tennessee scores, game goes overtime, Tennessee wins.

There are seven scenarios there, but the only two that we actually need to worry about are the ones in which Tennessee wins, which are numbers 4 and 7—the ones which are in bold face.  (Well, I had to worry about all seven, just to be sure that my math added up to 1.0000.   But to reach the result, we only have to worry about the two in which Tennessee might win.) 


4)     Houston’s PAT is good, Tennessee scores and goes for two, makes the two points to put the game in overtime, and Tennessee wins the game in overtime. 

That depends on five things happening:  Houston hits their PAT, Tennessee scores, Tennessee goes for two, Tennessee makes the two-point conversion, and Tennessee wins in overtime. 

HOUSTON HITS THEIR PAT is assumed to be a 94.4% probability, since 94.4% of all kicks were successful after the distance was increased last year.

TENNESEE SCORES we have assumed to be a 50% probability.

TENNESEE DECIDES TO GO FOR TWO is certain, since they would be 2 points behind with seconds left in the game,

TENNESSEE MAKES THE TWO-POINT CONVERSION is assumed to be a 47.9% probability, consistent with the other scenario, and

TENNESSEE WINS IN OVERTIME is assumed to be a 50% probability, consistent with the other scenarios. 


So the probability of all five of those things happening is .944, times .500, times 1.000, times .479, times .500.   That works out to 11.3044%.   But there is a second way that Tennessee can win, which is #7 on the list above:


7)     Houston’s misses the PAT kick, Tennessee scores, game goes overtime, Tennessee wins.

Three things have to happen there:  Missed PAT attempt, Tennessee scores, Tennessee wins in overtime. 


The probability that the kick will be missed, consistent with earlier analysis, is .056.

The probability that Tennessee will score 7 to tie is assumed to be 50%, and

The probability that Tennessee will win in overtime is assumed to be 50%. 


So the probability of ALL THREE of those things happening appears to be .014--.056, times .500, times .500.  


So if Houston just decides to kick the PAT like a normal person, the probability that Tennessee will win anyway appears to be .127 044.  That means the probability that HOUSTON will win is .872 956.   So the probability that Houston will win appears to me to be:

.872 956 if they just kick the PAT, and

.869 75 if they go for two. 


So far I don’t see the analytical argument for going for two in that situation.   I acknowledge again that this analysis is not absolutely persuasive; no analytical weighing and measuring of the percentages CAN be absolutely persuasive.   But when I suggested earlier on that I was more or less on the side of the asshole (apart from the fact that he was blaming this on analytics), people wrote to tell me that analytically, going for two WAS the better choice.   So far, I don’t see it. 


The critical questionable assumption here is that Tennessee’s chance of scoring 7 in the closing two minutes is 50%.   I mean, ALL of the assumptions are somewhat questionable, but that’s the big one.  There are six key assumptions in this analysis:

1)     That a team’s chance of scoring on a 2-point conversion is .479,

2)     That a team’s chance of kicking a field goal is .944,

3)     That there was only time for ONE remaining drive,

4)     That Tennessee’s chance of scoring 7 on that drive was 50%,

5)     That an overtime result would be 50/50, and

6)     That nothing weird was going to happen like Tennessee fumbling, Houston picking it up, throwing an interception, the man who intercepted it has his pants fall down, he stops to pick them up, the ball is taken away from him but then lateraled to a member of the opposite team, and Houston winds up winning 51-49.   We all know that a lot of weird stuff can happen in two minutes of football. 


But the key questionable assumption there is #4.  We really don’t KNOW whether Tennessee’s chance of scoring 7 there was 50% or 40% or 30% or 80%.   It’s not an easy thing to research.   It’s not an easy thing to put an accurate number on. 


            So let us assume, to make a more fulsome analysis, that it was not 50%, but 40%.

            Then, repeating the entire, analysis but in quicker form, Tennessee’s chance of winning is 10.42% if Houston goes for two, but 10.16% if Houston just does the expected thing, kicks the PAT.    The 10.42% is .521, times .400, times .500.   The 10.16% is .0904 (.944, times .400, times .479, times .500), PLUS .0112 (.056, times .400, times .500.   I probably shouldn’t give you those numbers, because they probably don’t make any sense to you, but I just have a compulsion to make sure you can track my work if you’re a mind to do so.)  So if we assume that Tennessee’s chance of scoring 7 is 40%, then Houston’s chance of winning is:

.8984 if they kick the PAT, and

.8958 if they go for two. 


            Again, analysis does NOT seem to support the notion that going for two is the smart move here.  But let’s assume, instead, that Tennessee’s chance of scoring 7 on their last-minute drive is 60%, rather than 50% or 40%. 

            Same result.   Different numbers, but the same result.   If we assume that Tennessee’s chance of scoring 7 on that drive was 60%, then Houston’s chance of winning the game is:

.8745 if they kick the PAT, and

.8437 if they go for two.  


            What about 70?.  What if we assume that Tennessee’s chance of scoring on the last drive is 70%?

            Still doesn’t work.   If we assume that Tennessee’s chance of scoring is 70% and work the same math, then Houston’s chance of winning the game is


.8221 if Houston kicks the PAT, and

.8177 if Houston goes for two. 



            So. . .I don’t see it.   Not saying my analysis is perfect; not even necessarily saying that my math is right; feel free to run the numbers yourself.   But I don’t see the argument in favor of going for two in that situation.  


COMMENTS (43 Comments, most recent shown first)

Marc Schneider
It seems to me that all these analyses are premised on the assumption that winning in overtime is a 50/50 proposition. But what if it's not?

Going into the game, Tennessee was 4-0, Houston was, I believe, 1-3. Now, records can be deceiving, but it's not unreasonable to believe that Tennessee was the better team. I don't know what the overtime stats show about teams winning if they get the the ball first, etc, but I don't know why you would necessarily assume that each team has an equal chance of winning. In tennis, for sure, the longer the match, the more it favors the better player. And Tennessee had Derrick Henry who no one has been able to stop. Maybe the Houston coach thought that we have to keep from going to overtime because we are going to lose otherwise. In that case, if the chances of Houston winning is not 50% but say 40%, doesn't that change the calculus? I mean, obviously, a lot of things would have had to happen for Tennessee to win if Houston kicked the PAT, but if Houston made the two-points, their chances of winning would have been pretty much 100%.

Maybe the Houston coach knew the team was gassed and had no chance in overtime.

Now, having said all that, I would probably have kicked the PAT and taken my chances. But I can see the argument for trying to put the game away.
5:24 PM Oct 26th
Circling back to my points below on the Eagles-Ravens game, yesterday the Eagles failed on two more 2-point conversions in the fourth quarter.

The Eagles are single-handedly bringing the league average down.
1:48 PM Oct 23rd
One more thing to note:
The PAT success rate for kicks has been about 94 percent since they moved to the longer extra point in 2015.

I couldn't find a similar chart for 2-point conversions, but for the past two years it's been 49 percent.
11:41 AM Oct 22nd
A couple of things to note.
1. Tennessee didn't have plenty of ways to stop the clock. They had one timeout left. They could only stop the clock by going out of bounds or throwing an incomplete pass.

2. You have to take the matchup on the 2-pt conversion into play. The league odds of converting are irrelevant. What were the odds of Houston keeping Derrick Henry from gaining two yards. In the OT, Henry carried three times for two, three and five yards. For the game Henry gained less than 2 yards just three times on 22 carries, 13.6 percent, all of them in the first half.

3. I don't think you can assume a higher likelihood of scoring in a two-minute drill. The higher willingness to risk a turnover also leads to a higher risk of committing a turnover. The defense has an advantage because it doesn't have to worry about a field goal.

All told, I think the big conclusion is football analytics are way, way behind any other sport. I think football coaches face far more scrutiny for game decisions because they only pay once a week. A baseball manager screws up and he has ot answer questions for a night. I don't know what the baseball equivalent of punting down 19 points with five minutes left (bunting with two outs in the seventh down 3?) but it's the standard play in football. It prevents a blowout and the coach doesn't face questions from the media about the decision.

Finally (I hear the cheers) for those of you haven't heard of Kevin Kelley, here's a link. He's an Arkansas high school coach who does his own analytics and therefore never punts and always onside kicks. Not often. Always. Unless he's trying not to run up the score.​er-punts-has-another-radical-idea/

11:34 AM Oct 22nd
Returning to the question of the likelihood Tennessee would score a TD* in final 1:45, this old article by Brian Burke suggests the probability was around 20% (assuming they would take possession at about own 20 yd line). This confirms that HOU's win probability was about 95% before missing the 2PA.

3:56 PM Oct 21st
Sorry, I should have said that if the chance of making a two point conversion is 0%, Houston should of course always kick the extra point because they would almost always win. The point stands.
2:32 PM Oct 21st
Guy123 more or less pointed this out, but I would like to make this explicit: the key variable that determines whether to go for two or not is the chance of success of the two point conversion, because it affects the two calculations in opposite directions.

Bill looked at the sensitivity of the result with respect to the probability of Tennessee getting a touchdown, but that doesn't affect the relative probability very much. If Tennessee is more likely to get a touchdown, Houston is less likely to win, but that is true whether or not they go for two.

However, if you look at the sensitivity of the relative win probabilities with respect to the probability of making it when going for two, they move in opposite directions. If the chance of making a two point conversion is high, then that increases Houston's win probability when they go for two and decreases it when they don't. In the boundary case where the two point conversion probability is 100%, Houston has a 100% chance of winning when they go for two but only 75% when they don't. The chances are essentially reversed when you assume the two point conversion percentage is 0%. So that's the key variable (or variables, since the two point conversion percentage may not be the same for each team) which determines whether "analytics" favors one decision over the other.

This question of what "analytics" says reminds me of a talk show host who was criticizing Minnesota's decision to go for it on fourth and inches at the end of the game against Seattle. His point was that he "completely understood the analytics", but that Russell Wilson was so great that it was essentially certain that he would drive his team to a touchdown and win the game, so Minnesota should have kicked the field goal. But I think any sensible model that assumes Russ is going to score a touchdown in two minutes from his own 5 yard line should probably also assume that he would almost always make the two point conversion, and then probably have a greater than 50% chance in overtime as well. His assumption about Wilson undermined his own claim that he "understood the analytics": the more "automatic" you think Wilson is with the ball in his hands, the more you should be willing to take the chance on a fourth and inches to keep the ball out of his hands. The math is pretty simple.

Frequently, a complaint about "analytics" is just a straw man that many ignorant people use to condemn sports decisions with which they don't agree.
2:27 PM Oct 21st
As regulation time wound down, the crew speculated as to whether Tennessee, if they scored a TD, might choose to go for the win (with a 2-point conversion) instead of just tying it. I'm sure that The Card reads "1", so there should be no debate, right, guys?
12:48 PM Oct 21st
Normally coaches make their decisions to force the other team to play for a tie....
I thought coaches kept a list of scenarios so they can quickly make the right call.

Assuming that coaches "normally" do that, why do you assume that is also the right thing to do? Sometimes the conventional wisdom is wrong. And if you run the numbers for this case (and correct for Bill's error), it seems pretty clear that the right call was going for two (or it was a coin toss). Going for the win, rather than the tie, is particularly likely to be the right call when a team is on the road (as HOU was here).
8:46 AM Oct 21st
I just saw the replay of the game on NFL Net. Bill had it right that the commentator was truly out of control. He was incensed that the coach actually thought it over when he should have whipped the holy "card" out of his back pocket and read the gospel from it, and lectured us on that for the remainder of the game.
2:27 AM Oct 21st
When you toss around highly technical terms, it would help to define them for the analytical layman. So what’s an asshole?
12:41 AM Oct 21st
Normally coaches make their decisions to force the other team to play for a tie.

If a TD puts you one point ahead you go for two so that an opposition FG will only tie the score.

If a TD puts you five points ahead you go for two so a TD and XP only ties the game.

If a TD puts you ahead by seven points ahead you go for one so that it takes a TD and a two point conversion to tie a game.

I thought coaches kept a list of scenarios so they can quickly make the right call.
11:07 PM Oct 20th
With two minutes left on the clock the number would be HIGHER, not lower--much higher.

I agree my estimate of the TD probability (8%) was too low. A desperate team in the final minutes does have an important edge: less the willingness to risk turnovers you cite (turnovers prevent scoring), but more the fact it can use all four downs to achieve first downs. Still, having just 1:45 on the clock is a big constraint. I bet the success rate in that situation is still below average, and is certainly not "much" higher.

ESPN seems to have HOU win probability at about 91% when TEN took possession (down 7): If we assume a 50% OT win probability, that implies an 18% chance of scoring 7, or a 17% chance of scoring a TD. That seems plausible to me.

The 91% also doesn't seem consistent with the reported 98% win probabilities in the ESPN article. I suspect the writer made a mistake -- perhaps those were the probabilities conditional on HOU *making* its 2PA or PAT. In any case, that would still suggest HOU had something like a 95% chance of winning before failing to convert, not that different from 98%.
1:51 PM Oct 20th
I don't know if this played into the outcome but: if you grant the premise that Crennel may have had special knowledge about the chances of succeeding on a 2-point play, there is another factor to set aside it, which is that if you, as the coach, select a strategy in a pivotal moment that is perceived to be "weird" or "risky," there might be a good chance that the players on the team will not mentally be in a position to execute the strategy properly.

The guys on the offensive line, were they saying to themselves, "Whoa, are we really going for this here!? Is this gonna work?! uhhhhh— hut, hut, HUT!"

The coach's job is to put the team in a position to win, and I have to wonder if the coach really did that in this case, just because his own players would have been mentally off-balance whereas the defensive players might have been energized by the sudden prospect of blood in the water.
1:23 PM Oct 20th
Here are Gannon's comments from the game call, for anyone who wants to hear them.
1:12 PM Oct 20th
An interesting point from Kane Kalas. (Harry's father and World Class poker player). The trailing team benefits greatly from knowing how many points they need. In particular, if the 2 pt conversion works, they will be much more aggressive with the clock, knowing they need 2 scores.

Right; that is what I was saying (below). It is a subset of what I call the law of competitive balance. Nature seeks a balance.
11:35 AM Oct 20th
Bonkers? 12% of drives result in a TD. With just 2 minutes on the clock let’s say maybe 8%? 48% on 2P conversions. And 50% win% in OT. So Tennessee was .08 * .48 * .5 = .019. Bingo.

With two minutes left on the clock the number would be HIGHER, not lower--much higher. First of all, "two minutes" does really describe the situation, because there are many ways to stop the clock. But more importantly, the chance of scoring increases when the offense is more willing to gamble. In the middle of the game, you're not going to throw a deep pass that often because the negative consequences can be prohibitive. But when you're in a situation in which you will lose if you DON'T score, the other negative consequences are irrelevant, so you take gambles you would not otherwise take, so your chance of scoring goes WAY up.
11:33 AM Oct 20th
“The chance of winning by going for two is a hunnert f*cking percent if ya don’t miss yer f*cking block.”

—- every high school coach I’ve ever known
8:06 AM Oct 20th
Brian, I just passed along ESPN’s estimates for what they’re worth. I would have kicked.
4:09 AM Oct 20th
Brian, I just provided the ESPN probabilities for what they’re worth. I don’t believe them. I would have taken the PAT.
4:01 AM Oct 20th
An interesting point from Kane Kalas. (Harry's father and World Class poker player). The trailing team benefits greatly from knowing how many points they need. In particular, if the 2 pt conversion works, they will be much more aggressive with the clock, knowing they need 2 scores.
1:24 AM Oct 20th
Oops, should say TD scored in 22% of drives.
11:16 PM Oct 19th
[i] What do you all think of the ESPN claim that Houston had a 98%+ chance to win the game? That seems totally bonkers to me. How do you come up with that? [i/]

Bonkers? 12% of drives result in a TD. With just 2 minutes on the clock let’s say maybe 8%? 48% on 2P conversions. And 50% win% in OT. So Tennessee was .08 * .48 * .5 = .019. Bingo.
10:31 PM Oct 19th
Up 8 points and kicking away with 1:50 to go... I can't say whether it's 98%, but I would bet that historically, a team up 8 in about that time and situation must win 19 games out of 20, which would be 95%.

Going down the field and scoring a touchdown against an NFL defense in that much time, and then converting for two, is damn difficult. And succeeding only gets you a 50% or so chance of winning the game in overtime. Intuitively, I doubt one team in 20 that finds itself down 8 and receiving the kickoff with 2 minutes to play goes on to win, in the NFL.
10:07 PM Oct 19th
Leslein, don’t both of those numbers seem high to you? If you are up by 8 with two minutes left, with the other team having the ball, you have a 98 percent chance of winning? Wow.
9:16 PM Oct 19th
What do you all think of the ESPN claim that Houston had a 98%+ chance to win the game? That seems totally bonkers to me. How do you come up with that?
8:46 PM Oct 19th
I agree with everything you're saying, but I think the most important point is the one you made early on: the coach knows some things about his team that don't factor in to the average probability of making a two point conversion. Also, if the issue is that he doesn't trust his defense to stop the other team from making a touchdown and making a two point conversion after that touchdown, he's probably not going to say that to the reporters after the game.
8:23 PM Oct 19th
Based on prior performance, both of these teams are above-average on offense and below-average on defense, and Tennessee is the stronger team on both dimensions (playing at home). Given all of that, it seems like these would be plausible assumptions:
HOU 2P success rate: 52%
TEN 2P success rate: 56%
HOU win% in OT: 44%

With these assumptions, HOU win probability is then:
87.3% with 2P attempt
83.7% with PAT kick
That's a substantial 3.6% difference in favor of going for two. Feel free to sub in your own assumptions, but there are clearly plausible estimates that would justify Houston making the decision they did.

5:29 PM Oct 19th
I think it is possible to simplify Bill's analysis a little. If Tennessee doesn't score a touchdown, then it doesn't matter whether Houston went for one or two.

So that means that we are allowed to assume that Tennessee will score a touchdown, even though we know they may not. It's a bit like a baserunner with two outs who assumes that an outfielder will always miss a catch.

And this makes things easier for us, because now we don't have to estimate the probability of Tennessee scoring a touchdown.
3:14 PM Oct 19th
Dave: The logic is that when you’re far behind going for 2 on any touchdown becomes more attractive, both because you’re racing the clock to score as many points as you can, and because if you fail you’ll at least have the advantage of being able to plan accordingly if/when you draw to within 8 points.
2:47 PM Oct 19th
My experience is that having to decide if someone is an idiot or an asshole, or both, is a value judgement that comes up WAY to often in life.
2:25 PM Oct 19th
In Sunday’s Eagles-Ravens game, the Eagles scored four TDs and attempted 4 two-pointers, making 2. As far as I know, their kicker was healthy and available the whole game.

The first one came after a third-quarter touchdown to make the score 17-6. They went for two there and failed.

Subsequently they fell behind 24-6, scored a TD and converted a two-point conversion. 24-14 now.

Next, it was 30-14. The Eagles scored another TD and converted a two-point conversion to make it 30-22.

Finally, they scored another TD with about 2 minutes left and had to attempt a two-point conversion to tie it. That failed.

I don’t understand the first attempt when they were behind by 11. I’d think it would be more important to get the margin to 10 then get the margin to 9. If they had kicked then, they would have been able to kick at the end of the game when the score was 30-29.

1:47 PM Oct 19th
Here’s the coach’s explanation. No analytics involved. ESPN later calculated that Houston had a 98.2% chance of winning if they went for the PAT and 98.1% if they went for 2.
1:09 PM Oct 19th
Zeth- that is an excellent point about avoiding the overtime all other things being equal. Hadn’t even considered that.
11:23 AM Oct 19th
There is a small but consequential error in the calculations here: In the 2P attempt scenario, Bill assumes a 50% chance that Tennessee will subsequently score 7 points, meaning *both* a touchdown and EP. In the PAT scenario, Bill makes two different assumptions: if Houston's kick is good, Tennessee is given a 50% chance of scoring a touchdown ( which is not quite the same thing as scoring 7), but if Houston misses the kick then Tennessee again has a 50% chance of scoring 7. If you consistently give Tennessee a 50% chance of scoring a touchdown in all situations, and a 94.4% chance of making the extra point (when they kick), you will find that Houston's win probability is in fact a bit higher when they go for two (.8770) than going for one (.8737), using Bill's assumptions.

The important assumption is really not Tennessee's chance of scoring a touchdown. In fact, all of these calculations are easier if we just assume Tennessee *will* score again, because if they don't then none of this matters at all. And no matter what probability you assign Tennessee scoring again, the relative probability for the two options will be the same.

The assumption that is very important is the teams' likelihood of converting on 2P attempt. If we increase that even slightly over league average, to say 52%, then going for two has a bigger advantage (.886 vs. .864). If you think the teams might succeed on 54% of 2P attempts, the gap grows even larger to about 3% (.891 vs .859).

Bill's assumption that Tennessee will kick if trailing by 7 seems reasonable, given what actually happened. It's interesting to note, though, that under Bill's assumptions Tennessee would be slightly better off going for two in that situation (.479 vs. .472).

I thought that giving home team Tennessee a larger chance of winning in OT might impact the decision, but that doesn't seem to make much difference.
11:09 AM Oct 19th
One more thought: if the probabilities are on a knife's edge already, as a coach I would always tend to minimize the probability of the game going to overtime. Overtime is a 50/50 proposition--just like the decision I'm making now, presumably--with the added downside that making my team play up to 10 extra minutes only helps next week's opponent.
11:03 AM Oct 19th
If there is a flaw in Brian's simplistic logic, I'm not smart enough to find it.

We only have a question to answer if Tennessee scores a touchdown. So assuming that happens, the question is: would we rather attempt a two point conversion ourselves, or defend a conversion attempt?

In principle, it's close, but you would rather defend.

That can change with other data; if you have a strong offense and a weak defense, you might rather attempt the conversion yourself. Same if your opponent has a weak offense and a strong defense. If you've had the ball 12 of the last 14 minutes and the opposing defense is exhausted, that would tend to push you toward attempting the conversion now.

But I don't think any of those factors were in play here, thus Houston was probably better off kicking and leaving it to Tennessee to attempt a conversion. Probably.

It's worth noting that the extra point is no longer automatic, as it had been for 30 years, which also nudges all 1-or-2 decisions a little bit toward 2. But I'm not convinced that's a significant factor here.
10:59 AM Oct 19th
My view is that the right decision was to kick the point-after and go up 8.

It's about maximizing the pressure on the other team, and reducing it for your team. A point-after kick is a 96% probability, and then the other team has to a) score a touchdown, and b) pull off a two-point conversion. Steep hill. Every play, that's in the back of their minds...we gotta do A, and then scramble for B.

Going for the two-point keeps the pressure on you: you have the pressure to make the play, and if you end up losing the coin-flip, you've significantly reduced the pressure on the other they have one difficult task instead of two. Just gotta do A, boys.

If I'm a coach, I want the other team's thinking to be as divided as it can be. Take the point and leave them the pressure.
10:55 AM Oct 19th
I am unsure I can support the comment that NFL coaches always pick the choice that they think gives them the best chance to win. Anytime you see a coach choose to punt when down by more than 16 points in the fourth quarter, they are choosing the option that looks best in the box score the next day, not the option that best gives them the chance to win. I.e. NFL coaches will take the worse option that guarantees a loss (maybe taking it from 95% likely to 100% likely), than taking the option that may increase your chances of winning slightly, but also increases the chances that you will lose by 20+ points as well.

As a concrete example, a really bad Jets team down 24-0 to a just mediocre Dolphins team yesterday, punted on 4th and 5 from their own 29 with 13:07 to play and on 4th and 32 from their own 43 with 8:44 to play. Neither of those plays could have possibly increased their chances of winning and the Jets knew it, they just didn't want a 24-0 shellacking to turn into a 38-0 shellacking.
10:21 AM Oct 19th
Me being a moron too :-) ....but with the benefit of seeing how close those percentages are.....
I would tend to view this simply:

I gotta believe the Houston coach simply thought for whatever reason that they had a particularly good chance to make that 2-point conversion -- a higher chance than usual. (I know that they didn't.)

In view of the percentages being so close, all you need is a somewhat-higher-than-usual chance of making the 2-point conversion for it to be a good choice to try it.
(or, equally, a somewhat-worse-than-usual chance of making the 1-point conversion)
4:15 AM Oct 19th
It's late so I don't have time to defend this, but ultimately I think the basic equation that determines this is much less complicated. Does Houston have a better chance of making the 2 point conversion than Tennessee does of failing. In that case, the traditional 47.9 percent success rate argues for your point. But if both teams succeed at over 50 percent, than Houston should go for it.

The chances of missing a kick may change this. Also if you feel one team or another has a better chance of winning in overtime. But other than that, I think the above equation determines the best choice.
1:15 AM Oct 19th
The 52.1 percent failure rate is what I assume is what is on those cards that coaches have and Gannon (the announcer) pulled out of his pockets. But of course that is an average of everybody's success rate over some period of time. It is like saying a hitter has a 26 percent chance to get a hit because the all time baseball batting average is .260. Here, you have a year where offense has been at all time highs, and you have a team that just scored 36 points. They fell behind early and scored on practically every possession to catch up. They are going against a team who has scored 29 points and who has rushed for over 200 yards, and in fact when it did get to overtime on 3rd down from the 5 just snapped it to Henry to barrel in to win the game. I would have given both teams a 55-60 percent chance of succeeding on 2 point conversions if attempted.. If you plug in those numbers, I think you will get a different result.

The chance that Tennessee would score a touchdown should not ever matter at all, because Houston's decision is predicated on the assumption that Tennessee would score a touchdown. That is the only circumstance under which 1 or 2 points makes any difference in the outcome of the game. So running all those numbers as you did should bring about the same ultimate result - as it did. The percentage chance that matters is the chance of making the conversion.

Where we absolutely agree is that Gannon acted and sounded like a complete idiot. I might go further and say he set football commentary back for everyone.
1:02 AM Oct 19th
When the percentages are as close as they are here - the initial set of assumptions had it 87.3 percent for the PAT and 87.0 percent if they go for two - it seems to me that the decision has to come down to the other, less quantifiable factors. If the Houston coach knows that his defense is gassed and is likely to give up another touchdown, or if he has a new unorthodox two-point play with a high likelihood of success, that's far more important than the slight difference between the two percentages.

12:59 AM Oct 19th
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