I'm about to get to the segment of my research methods course covering probability, and I have a new favorite example of the cumulative probability of independent events. Too bad I can't use it in class, given that football is a rather culturally biased source for anecdotes.

Super Bowl viewers may recall that despite a furious New England comeback, the Atlanta Falcons were leading 28-20 with four minutes remaining and in a dominant position – first down at New England's 22 yard line. From here, literally all the Falcons had to do was fall down three times (which would either force New England to spend their timeouts or run 2 precious minutes off the clock), kick a simple 40-yard field goal, and return the ball to New England down 11 points with little time left. In other words, a Falcon victory was virtually guaranteed.

How guaranteed? Well, consider if Atlanta ran the simplest of plays on 1st, 2nd, and 3rd down: a run straight up the middle by very excellent running back Devonta Freeman. It didn't matter if he gained yards or not. Running the clock and, crucially, NOT fumbling the ball away were all that mattered. Fortunately for Atlanta, Freeman carried the ball 227 times and caught 54 passes this season with all of one fumble, so we can calculate his odds of running the play without fumbling as 1 – 1/(227+54), or 99.64%. To calculate the odds of running the play three times (independent events) without fumbling, we cube that figure, (0.9964)3 = 98.92%. Assuming that Freeman would actually be trying much harder than usual to avoid fumbling at the expense of trying to gain yards, this is probably a serious underestimate to the likelihood of success. But let's stick with it.

On fourth down, Falcons kicker Matt Bryant would appear to kick a field goal of just under or over 40 yards. This season he made 95% (19/20) of kicks under 40 yards, and 97% (28/29) under 50. The 41 year old veteran has made 300 field goals in the NFL over 15 years, so presumably nerves wouldn't have drastically altered his performance. But for the sake of being conservative, let's say his odds were 92% (his total season average). 98.92% x 92% = 91%. In other words, by doing nothing but what was obvious, the Falcons had at least a 91% chance of taking an 11 point lead and essentially guaranteeing victory.

Instead, Atlanta got too cute. On 1st down Freeman carried the ball for a short loss. On second down, Atlanta passed for baffling reasons. QB Matt Ryan was sacked, losing 12 yards and making a potential field goal very long. Then they passed again, this time drawing a very obvious holding penalty and losing 10 more yards. Now, no field goal attempt was possible. The rest is history.

Consider what they did there. Leave aside for a moment the 30% chance of a pass being incomplete and stopping the clock, which would be bad (helping New England) but not fatal. QB Ryan had 1.3% of his passes intercepted, was sacked 6.5% of the time he attempted to pass, and the Falcons performed near the NFL average of an offensive penalty on 1 of every 10 plays (10%). The sum of those (17.8%) is the probability that something really, really bad could happen on a pass attempt. That leaves an 82.2% chance that things will be alright on a pass attempt. Counting Freeman's first down run (0.9964), we then multiply by (0.822) x (0.822) for the second and third down passes, giving us 67.3% probability of these three plays being run without "something bad" happening. Multiply that by Bryant's 92% chance of making a field goal, and we see that the plays Atlanta actually ran gave them only a 61.94% chance of getting that crucial 11-point lead.

NFL coaches may not be rocket scientists but most could tell you that 91% is greater than about 62%. And remember, 91% is an extremely low, conservative estimate.

We see this all the time in football; coaches get too fancy trying to "outsmart" the odds. When it works, they're praised for being Bold. But math is going to win more regularly than Guts or Boldness or anything else.

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16 Responses to “NPF: FALCONS vs. PROBABILITY”

  1. democommie Says:

    Why is it NPF? There's a ,0000000000000% chance that it's Friday.

    Is it because it really stands for Non Political Football?

    I would say the odds of ME, if I had used the "NPF" in my post's title, using that second sentence as, "Yeah, that's what I meant.", would be like a Gazillion%.

    Now, as for the gist of it. I never would suspect dickwaddery of MY team's(yes, I've been a Pat's fan since before Trump's first bankrupty) coach but isn't this pretty much what happened to Pete Carroll when the Seahawks playe the pats in SBXXX19? His brain sorta melted in the last 90 seconds of the game. Small coincidence–the Falcon's head coach was Seattle's Defensive Co-ordinator when they gave it up to the Pat's in 2014.

  2. ronzie Says:

    Football is entertainment. Would the audience, most of whom I assume weren't regular fans of either team, have been more entertained if Atlanta had played it safe for those last four minutes? Would they have stayed tuned to the game?

  3. democommie Says:

    @ ronzie:

    In Atlanta, for sure.

    Outside Atlanta, hard to say. I do know a LOT of people who are not Pat's fans, to the extent that they would rather lose a few bucks by betting against them than win a few betting with them. I spent two super bowls in upstate NY watching the Giants beat the Pat's, in both instances on last minute theatrics/heroics. For me it was fine if they lost, if they played well–and I've always felt that way. That they won was nice in that it did shut up a few people that like to remind that Eli won two rings by beating them.

  4. Droppy Says:

    All very true. But I grew up watching Big 10 football (or Big 2, Little 8, as we used to say) when it was "3 yards and a cloud of dust" play in and play out. Very high probability rates and all that, but I spent most games gawking at the cheerleaders.

  5. sluggo Says:

    Putin hacked the Super Bowl. Occam's Razor.

  6. Grendel Says:

    I'm a Falcons fan and this post pains me greatly. Sigh.

  7. Whitt Staircase Says:

    Belichick: the mysterious power to cloud the minds of opposing coaches.
    He has vowed always to use this power for good, never for evil.

  8. Periscope Says:

    Easy to play retrospective statistics football with no mention of confidence intervals and no commentary on the physical condition of the players. Human error is what makes the game worth watching.

  9. TAGinMO Says:

    Honest question, Ed: When you say you can't use this example in class because football is a culturally biased source of anecdotes, is that just a prudential decision on your part? Or are you legitimately concerned that a student would report you to someone in administration and that you'd run afoul of some sort of professorial code of conduct?

  10. democommie Says:

    "Human error is what makes the game worth watching."

    Same as politics–and just as excruciating.

  11. Spiffy McBang Says:

    I was wondering the same thing as TAG. I get how it's culturally biased, but at the same time, if you're trying to get kids to learn how these numbers work in the political realm, it's common to use an example that will make sense to more of them than something politically-based. Football would almost certainly qualify by that standard.

    You might well have even better examples than that, and that's fine, it just seems like this would be ok since it would probably click with a reasonable percentage of the class.

  12. RJB Says:

    @TAG and Spiffy, American football metaphors are not great for education, because the rules and strategies are so complicated. I used such a metaphor to talk about some changes to peer review, a blogger wrote about it here , and I get comments like "Financial economists in Europe and Asia are frantically googling American football to figure out what a field goal is and whether they could publish one." Even though I created a completely football-free video and explanation to address exactly this concern!

  13. Grendel Says:

    @Periscope for a "commentary on the physical condition of the players" how about this… the Falcon's All-Pro center had been playing all day on a fractured leg and his play had deteriorated in the 4th quarter. Their very good right tackle had come out of the game injured and their not-very-good backup tackle was in. It was NOT a time to be depending on pass protection when you didn't have to.

  14. quixote Says:

    Very smart not to use US football examples for "clarification" in class. You'd be leaving out all the students who haven't played football, or at least studied it — most women, most hispanics, almost all foreigners. In our case we're so busy trying to figure out what the words mean, the analogy isn't even in the picture and the usage causes confusion, not clarity.

  15. democommie Says:

    I've been watching pro football for over 50 years. I still have no idea what the infield fly rule means. Is it like an extra point?

    Yeah, I can see where Ed gets to thinking that it's not the best sort of thing to use.

  16. Tom Says:

    #fake statistics