Smart Notes 10/6/09

Going for two. I’ve gotten a bunch of emails asking whether Rich Rodriguez should have gone for two instead of kicking the PAT to send the game to overtime against Michigan State. I didn’t get to watch the game closely, but we know what happened: Michigan kicked the PAT and Tate Forcier promptly threw an interception, and Michigan State scored to win the game. The logic of most people who say Rodriguez should have gone for two appears to be something along the lines that Forcier looked dog tired and they needed to win then, and that Michigan had all the momentum and should have used it on that play. I don’t know if I have a definitive answer, but here’s how I look at those judgment calls.

You’re basically comparing two probabilities: One, the chance of succeeding on the two-point play, and second, the chance of winning in overtime. Both numbers have some precedent but also can get clouded by who you’re playing at that moment, how well you’re playing, etc. If Wichita State miraculously gets into that same position against Florida, I’d probably tell them to go for two because, under the NCAA’s unique overtime format, each team has a roughly 50/50 shot at winning before taking into account talent differential, at which time Florida would dominate. We know that two-point tries are successful something between 40-50% of the time, and that is probably greater than the chance of going toe-to-toe with Florida — hence take your 45% chance of winning right there. For Florida, it is the opposite: you want the game to go on so your natural advantage can take over; so kick the PAT and let’s do this. It’s all an offshoot of David and Goliath strategies.

How does that play out in Michigan’s game? Well if Rodriguez thinks he has the better team — including momentum — then it seems to me you play for overtime. That’s because even if you’re better your chance of getting the two-point try caps out at about 50%, whereas the starting point for your chance of winning in OT is 50%, plus whatever natural advantage you have. Had they been playing Southern Cal, the decision is probably the opposite.

The other thing you notice from this is that slight differences in the probabilities can vastly change the right outcome. We know the estimates for overtime and two-point tries, but this was late in the game and therefore those probabilities were dependent to an extent on what had happened earlier. Not necessarily when or how Michigan scored, but fatigue, injuries, and how good the teams were coming in does matter to help revise probabilities going forward. (Again, I’m trying to distinguish revised estimates of forward-looking probabilities with backward-looking events that should have no effect on the decision to go for it or not.) Thus I think Rodriguez’s judgment call (in just this situation at least) was sound at least in the sense that there is no compelling argument that it was flat wrong. If he thought he had the better team — and the records of the teams going into it seemed to indicate that — then overtime seems the wiser move. The bottom line is two-point tries are not high-percentage plays.

(Here’s a thought experiment someone once asked me. This question assumes we know the probabilities with certainty, which if course unrealistic but here goes: You have the ball on the 23 yard line and are down three. Your team and the other team are completely evenly matched. There’s only one second on the clock; time for only one play. Your field goal kicker is mediocre, and is 50/50 from that distance (40 yards) — i.e. 50% of tying the game by kicking it. Or you could go for it and run a pass play, which you estimate had a 33% chance of succeeding. What do you do and why?)

– Big 10 Q&A. I did a Q&A over at The Rivalry, Esq. with the excellent Graham Filler. Topics including Juice Williams, Northwestern, etc. Tomorrow is a post involving me hemorrhaging about Purdue’s ineptitude.

– Mizzou’s run game. The very sharp Dave Matter of the Columbia Daily Tribune takes a look at Gary Pinkel’s Missouri’s running game.

– An easier case. If the Rodriguez situation above is a push, Raheem Morris is not so lucky. Brian Burke shoots up the new Tampa coach’s thought-process:

Raheem Morris is a really optimistic guy: Trailing by 6 points with 4:30 left in the game, the Buccaneers faced a 4th and goal from Washington’s 4-yard line. The Bucs kicked the FG to make the score 16-13 and went on to lose. Columnist Gary Shelton of the St. Petersburg Times wants to know why head coach Raheem Morris didn’t go for the touchdown. That makes at least two of us.

[A]ll things being equal the better decision would have been to go for it. . . .  Morris’ decision basically cut his chances of winning by a third.  Sure, the particular “flow” and match-ups of the game are factors, but those considerations are usually overblown. Besides, if the game is close enough for it to matter, then the two teams are probably fairly equal, at least for that day.

[But] the more interesting thing is the glimpse inside the mind of an NFL coach. Here’s what Morris said when asked about the decision:

“We wanted to stop them, get the ball back, have an opportunity to go down there and put this thing into overtime. Or to win it. I felt really good about that. It worked out in our favor.”

Notice that actually winning the game was almost an afterthought. Overtime was the goal. Here’s the chain of events Morris was counting on:

  1. Make the FG
  2. Make a stop (on the first or second series, so that there is time left)
  3. Drive into FG range
  4. Make a second FG
  5. Score first in overtime, which requires:
  6. (Half the time) Make another stop
  7. Drive into FG range again, and
  8. Make a third FG, or score a TD

And here’s the ‘go for it’ path to winning:

  1. Get 4 yards on a play
  2. Make a stop

Which alternative is more plausible? What does this say about the mentality of some NFL coaches? An 0-3 team is 4 yards and a stop away from their first win, and they decide to play the long odds for shot at overtime.

– Safire Sundays. Language Log on William Safire.

– Unlawfully harboring a D-1 talent? Jenks HS Coach Allan Trimble suspends himself after a report emerged showing that he had arranged for a player to live within his district.

– BGS counters up. The Blue-Gray Sky has a nice look at Notre Dame running their “counter play” from a one-back set.

  • Andy Grey

    You go for the 23 yard TD. The odds of winning an evenly matched game in OT is 50%, and that is dependent on the 50% chance your kickers makes the 40 yard FG. So you’re odds of winning by kicking a FG is 25%. The odds of winning estimated by going for it are 33%. I like winning so I’d go for it.

  • C

    Just wanted to tell you I love your stuff, especially the combination of decision analysis and football know-how. Do you have any formal OR/management science background?

  • joeyb

    Chris, over at MGoBlog, someone breaks down the statistics in the diaries. Essentially, what they should have done is gone for 2 on the first TD. If they make it, they kick the XP on the second TD to win. If not, they go for 2 again to tie. The numbers don’t lie.

  • Joeyb: That might well be true. As I said I didn’t really get to watch the game so I was just going off the scenario as painted and looking just at that last two-point decision.

  • Mathlete

    I want to know how bad the defenses are in this game? A 33% chance of scoring from the 23 yard line? I hope they kick and make the FG so it goes into OT, that would be one heck of a shootout that would almost certainly come down to a 2 pt conversion.

  • joeyb

    Chris, I wasn’t trying to correct you. I was merely trying to add input for those who were asking about whether he should have gone for 2. The circumstances were a little more unique than what you described and I wanted other readers to understand that there was a 3rd option.

  • jack

    I’m surprised to read no mention of the rain during the final minutes of the Michigan game. I believe it was raining on the final drive in regulation. I’m sure rain only lowers the chances of a successful two-point conversion — especially when you’re relying on your passing game and an exhausted freshman quarterback. Oddly enough, the overtime interception was thrown after the rain had let up.

    However, having said this, in this case, I belong to the “strike while the iron’s hot” school of thought for the following reason: an exhausted freshman quarterback might be better off going for one more play, without interruption, while the adrenaline’s still pumping, than performing for — at least — one more series after a considerable break in the action.) The defense would also still be reeling from giving up the last drive. The brief break before overtime only gave the MSU’s defense time to regroup and compose themselves.

  • OldSouth

    If the probability of converting the 2 gets to about 38% or below, going for 2 is actually the worse option. It can even be a little higher than that if the probability of winning in overtime drops a little below 50/50.

    There’s little reason to think 44% should be the right standard either. 44% is taken from all NFL games. Who knows if that would apply to college, much less Michigan specifically?

    The equation is correct. The assumptions are very tenuous, and having no data to inform us, holding to such an analysis as definitive is very, very dangerous.

  • OldSouth

    ^^Saying the formula is correct is a bit of a misnomer. IF we had accurate data to plug in for the variables that the blog just assumes, it would be correct.

    (And even that’s a overgeneralized, as the formula treats making the extra point as 100% likely. See Bengals, Cincinnati).

  • James

    “Your field goal kicker is mediocre, and is 50/50 from that distance (40 yards) — i.e. 50% of tying the game by kicking it. Or you could go for it and run a pass play, which you estimate had a 33% chance of succeeding. What do you do and why?)”

    With those percentages…. you throw the pass play. You are banking on two separate chances of 50% (one for the field goal and one for 50% of overtime) that gives you 25% chance of winning. No thanks, I will take my one shot of 33% chance of winning and would do so every time with those numbers.

  • My answer: The typical play is to kick the field goal: 50/50 (your kicker), and another 50/50 (winning the game in overtime against a perfectly equal team), so a 25% chance of winning. (No ties in college football.)) The atypical play is to go for the win, which has a 33% chance of winning the game, so I say to go for it.

  • Fourth

    It’s an interesting hypothetical, but I have trouble imagining it in practice as I keep thinking that the odds of even a great passing team scoring from that distance (or drawing a penalty) in 1 play are somewhere in the 15-20% range. But yeah obviously 33% > 25% so you’d go for it if that were the case.

  • Not You

    I say field goal, but for… different reasons:

    Field Goal->Made.

    OT Win: Brilliant Move by Coach Whoever!
    OT Loss: He was so close to pulling out the win… it went to OT!

    Field Goal->Miss.

    Coach Whoever would have won, if he had a decent kicker!

    TD attempt->Made.

    Ballsy move by Coach Whoever! It payed off here, but will he get so lucky, next time?

    TD attempt->Failed.


    Sometimes, the correct call isn’t the right call. Sometimes, even if it costs a few percent, you go for the option that keeps the pundits off your team, so they can focus on the next game. (Yes, the above is totally crap, and Football games would be way more entertaining if they actually did the correct thing, instead of the one that keeps people as contented as possible.)

  • Linus

    Actually, don’t both scenarios have a 33% chance? There are only 3 potential outcomes if you kick the field goal: you make it, then win in OT, you make it, then lose in OT, you miss it. Winning is one in three; 33%, not 25%.

  • Fourth

    There is a 50% chance that the third option you presented will happen (missing the kick), leaving only 50% left to divide amongst your first two options (winning/losing in OT). So the chances of losing if you kick = 50% (miss kick) plus 1/2 of 50% (losing in OT).

    Or just think of it as surviving two coin flips. The first is the fg attempt, the second is the OT. Flipping heads twice in a row is a 1/4 probability (1/2 * 1/2).

  • Nole55

    “Your field goal kicker is mediocre, and is 50/50 from that distance (40 yards) — i.e. 50% of tying the game by kicking it. Or you could go for it and run a pass play, which you estimate had a 33% chance of succeeding. What do you do and why”

    Anyone who trusts a 50% kicker from 40 yards out with the game on the line is much more in line to be fired than someone going for a 23yrd pass play that apparently has a 1 in 3 shot of winning you the game. Obviously, if you wanted to create a whole scenario, things could change (their safeties are both all americans, D-end is a beast, etc.), but in this basic situation, you have to go for it.

    As for Raheem Morris, even if he misses the 4 yard play, I’m sure there is still a decent enough chance he gets the ball back to take another crack at winning the thing, considering Washington would be so backed up and Portis/Campbell weren’t exactly dominant to that point. The NFL is getting more and more unwatchable by the season, as fewer and fewer coaches show any cajones whatsoever. Off the top of my head is the Steelers-Pats game however many years ago in Ben’s rookie year, when they were down 7 or 10 or whatever it was, and Cowher kicked a fg from the 1 yard line.

  • Topher

    “under the NCAA’s unique overtime format,”

    Love your stuff Chris, but I’m not sure what you are getting at here – the NCAA “Kansas tiebreaker” is the same system used by the NFHS and USA Football (the overlay of Pop Warner which covers a plurality of youth programs in America.)

    It is the NFL that has a “unique” overtime system, an adult equivalent of the “we have to go in from recess so the next team to score wins.”

    Joeyb – “Essentially, what they should have done is gone for 2 on the first TD. ”

    I have read the mgoblog analysis and I have two quibbles with it. First, I understand lots of teams have a very small number of two-point plays, and coaches might be wary of burning two in the same game when they can only use one. The more they are in an unusual position during a game (two-pointers, onside kicks, inside their own 10, for example) the less likely the overall performance in that position will be quality.

    Secondly, I think a team that has scored two unanswered TDs to cover a 14-point deficit is in a better position momentum-wise and fatigue-wise to score on the defense with the 2-point play. In other words, your odds of making a single 2-pt conversion after the second TD is probably slightly greater than making a single 2-pointer after the first touchdown.

    Had I had the headset, my personal feeling might have been this (warning: geektalk): “We’ve been outplayed in the game as a whole, and are fortunate to be in position to tie. We are better off isolating the game outcome in one play (the two-point conversion) where we have the opponent on our heels, than to try to reverse the overall game performance in an equal possession overtime exchange, where the sample size of plays will regress us to the mean.”

  • Topher

    Er, should have read “their heels.”

  • stan


    Using your reasoning, I have a 50/50 shot to win the big powerball lottery. I buy a ticket and either win or lose.

    BTW — I remember some years ago that someone (Homer Smith?) was using something like 35% as the success figure in college for going for two. Of course, the sample size is so small and suffers from certain selection problems. But I know the number was less than 40.

  • stan


    If you want to have some fun, contrast the decision a lot of coaches will make between going for two and going for a TD on 4th down from the same distance. Amazing how many will go for two (if the chart tells them) in the first half, but will kick the FG from the same distance. Yet all the payoffs are substantially higher to go for the TD and the odds of success (assuming ball in the middle) are identical.

  • cerebral

    I want to point out that another coach messed up his decision on Saturday. And maybe because we think of him as some kind of genius, we let him off easy. I’m talking about Oklahoma’s Bob Stoops.

    Oklahoma had the ball on Miami’s 22 yard line, down 4 points with only 4:23 remaining. Instead of going for it, Stoops decided to go for the 36 yard field go. It was good. Then he kicked off to Miami. Never say the ball again, game over. Oklahoma loses by 1.

    My thinking is this. Whether you go for it or kick the field goal, your team still needs to stop the other team. It doesn’t matter if you are successful or not. The better call was to go for it. I think.

  • cerebral

    Dang sorry guys i have bad spelling on that post.

    I want to point out that another coach messed up his decision on Saturday. And maybe because we think of him as some kind of genius, we let him off easy. I’m talking about Oklahoma’s Bob Stoops.

    Oklahoma had the ball on Miami’s 22 yard line, down 4 points with only 4:23 remaining (Oklahoma still had 2 time outs). Instead of going for it, Stoops decided to go for the 36 yard field goal. It was good. Then he kicked off to Miami. Sooners Never saw the ball again, game over. Oklahoma loses by 1.

    My thinking is this. Whether you go for it or kick the field goal, your team still needs to stop the other team. It doesn’t matter if you are successful or not. The better call was to go for it. I think.

  • JPHurricane


    Oklahoma had 4th and 11, with 4 and a half minutes left. Wonder what the odds of making a 4th and 11 are? I also wonder what the odds are had they failed, that OU fans everywhere would be all over him for that. Bottom line is the defense has to make a stop and 4:30 minutes is plenty to get the ball back and kick a FG to win it.

  • JPHurricane


    It truly would be a miracle if Wichita State was in that situation with Florida. Mainly because they haven’t played football at WSU since 1987 when they dropped it.

  • Your test perhaps confuses two forms of decision support: a) a propensity problem; b) a stochastic optimization problem (a problem with a binary outcome). This is the classic situation in which one may be, on average, correct, but so what?

    In quantitative finance, these may be shown as a) a pricing problem (what is the probabilistic outcome); b) a default problem (what happens if I’m wrong where the penalty for being wrong is obliteration). In short, it’s a stochastic optimization problem because if you go for it and miss, you have lost (the loan has defaulted, the game is over). If you simply calculate probabilities, on average you will be ahead, except that today you may be dead (you have lost).

    So, a couple of non-financial analogies.

    A. You must walk across the Platte River. While the Platte River, on average (probabilistically) may be 12 inches deep, it turns out you can drown in the Platte if you think the average is the specific reality of the ford you are attempting today at this time. Of course, it is not. You wouldn’t risk your life based on an average outcome expectation. Or, as we quants say, You can drown in 12 inches of water.

    B. You are flying a plane and approaching a cold front and a line of level 4 thunderstorms. Typically, you’ve managed to transition through these lines, and on average you know that most people do. Maybe 5 out of 100 lose control and come apart and die. But on average, *95% of the time* people are fine. Guess what: if you fly a few thousand hours, you are already dead. It’s just a matter of time. This is a stochastic optimization problem because it’s meaningless to be, on average, correct if you are dead today.

    Therefore, you kick the field goal because a more likely outcome of the lower-probability decision is … game-death. The propensity model doesn’t help you calibrate the risk of being *game-dead*. You live to find yourself in a decision with more rational factors to manage. Raheem Morris was trying to think this way, but it turns out he can’t think abstractly and like many people, totally undervalued future contingency.

    Hence if losing the game is an absolute negative, discard the propensity modeling and do like the mortgage engineers do: build a good stochastic optimization tool, and manage against catastrophe.

  • Or, to coaches losing is dying. So they fly around thunderstorms under the assumption they’ll find better weather, if they’re still alive. Of course, Mr. Morris flew from thunderstorm into a tropical low, but then, what is he, 33? There’s a reason fighter pilots are 25; they undervalue future contingency.

  • Or, as my favorite coach (Ferentz) would say,

    “Well, kinda tough deal. Tough deal. Have to make the call, no one else is there to hold your hand. Gotta take the points and move on. Liked our chances once the field was level. Something like that. Very tough deal, do it again. Take the points, everybody gets the same shot in OT. Sure, half of you would have a better idea, but I’m from Pittsburgh, live in Iowa. Our state: put hay in the barn. Can’t remember when I was unhappy with points and still breathing.”

  • Linus

    Ok, I realize that I was an idiot. I knew I should have paid more attention in math class.

  • cerebral

    JPHurricane, thats exactly my point. The Oklahoma defense needed to make a stop regardless of the decision and outcome.

    OU field goal good, OU needs the ball back for another FG
    OU field goal no good, Ou needs ball back for a TD
    OU go for it make it, OU up 3, need a stop to win the game
    OU go for it miss it, OU down 4 still, need a stop to for a TD

    why not try going for it, its the best probablity. You got to concider not getting the ball back anymore;

  • Ryan


    I believe your stochastic analogy is flawed in that catastrophe avoidance is only advantageous if there is value to be gained in the time between avoiding the potential catastrophe and the end result. All college football games result in a win or loss. Unless you have reason to predict your odds will improve in the future (eg., you believe your athletes are less susceptible to fatigue) I don’t see the value to delaying the decision.

  • Bellanca: Thanks for the comments. I definitely understand the concept where the average can be misleading because of a kind of black swan/instant death scenario. I’m sure there are ones that can slip past me, but I’m not sure whether any of these did. (Other than my admittedly unrealistic probabilities for my hypo, which most got right — you throw the pass.)

    I definitely buy that many of the popular 4th down analyses overlook the sort of “instant death” risk — i.e. that going for it on 4th might on average be better in terms of points, but if you go for it and fail the game is likely over, whereas punting, to use the poker term, gives you at least some “outs,” and thus is actually desirable.

    Anyway I’m glad we can all agree that Raheem Morris is insane.

  • Cliff events, probabilities, and unknowable externalities.

    I know this is all in fun, but if we’re going to analogize via quantitative finance, I think we need to be careful. By labeling a football game loss as a black swan event, which it is not, we eliminate discussion. Someone always loses in every game; therefore a loss is not an unknowable externality, which is what a black swan event is.


    a) a game loss is not a ‘black swan’ event — it’s an expected outcome that is a *cliff event*. 9/11 was a black swan event — an event that, literally, could not be modeled. Russia defaulting on its national debt: black swan event (cf. Long Term Capital). The electricity going off in the stadium before Wisconsin can finish beating Nevada — black swan event. Somebody must lose every game, however. It’s a tautology: a compound proposition. Team A will win and if so, Team B will lose. Just as there will always be individual mortgages that default. Therefore one models credit default (cliff event) — an expected event — differently than one *prices* (measures the probability of a price) the credit.

    I think an interesting question to ask in looking at your puzzle is this: how is the FG attempt/TD attempt decision altered if the moment occurs at the end of the first half? Because this changes context while the cliff event (the end-of-time loss) remains distant.

    If one returns to analogy, consider the following. A small-town bank has been in the family for 100 years. Some wiseguy from Lehman shows up with an offer to sell $5mm of deconstructed subprime mortgage paper that “can’t fail.” The banker must weigh the following choices, which are no different than your end-of-game

    a) the opaque piece of engineered financial security, which on average cash flows, is not rendered worthless by the underlying, actual mortgages — and bank earnings climb. This will *probably* happen. Using a propensity modeling outlook, this is clearly the right decision.

    b) the security fails, as does, actually, Lehman because of underlying default. Who cares if on average Lehman was selling profitable, cash flowing paper? In this specific instance, the small town bank has $5mm of capital wiped out, their capital ratios fall below required thresholds, the regulators move in and seize the place, and the family bank is … dead. Note, that the defaulting security is not itself a black swan event. Mortgages and banks fail all the time.

    The actual mathematical technology used to model price (probability) and default (cliff event), in practice, is profoundly different. That’s because the problems being solved are distinct. I think end-of-game decisioning more closely reflects default, rather than pricing, analysis. It is a stochastic optimization problem, not a probability optimization. Different math, different methods.

    If anything in this scenario is a black swan event, it’s the hiring of a 33 year-old with no coordinator or head coaching experience to run an NFL team. (But really not: sports ownership has proven itself feckless some major percentage of the time.)

  • Ryan, for me to agree with you I’d have to believe that it’s always better to wager 100% of my chips on every hand — because I’m just forestalling the inevitable if I make decisions that avoid risking the cliff event (going bust).

    Now, if I knew my team was physically exhausted or if I knew that I had three key guys sidelined by injury, then I would bet the house and go for it on 4/23. I would have no choice. But that’s obvious, and those conditions were not included in the problem.

  • Eduardo Vieira


    Suppose the same situation of the Mich-Mich St. game on the nfl. The difference in the overtime rules changes your analysis?

    In my opinion, in the NFL I would always go for two. It’s better than lose on the toss and watch the other team kick a 40-yard FG without never touching the ball…

    In college I think you are right. The better team has to diminish variance.


  • Ralph Mahan

    Superb share. However, your design doesn’t print right on this firefox. You might want to investigate that. Could you be using external CSS things?