Tied Up in Knots

Apologies for the gap between posts–travel and whatnot. I’ll hopefully have some shiny new content in the future. A narrow-minded, two part post inspired by the Bears game against the Vikings today:

Part I: The line going into the game was pick ’em, meaning no favorite. This means that a tie (very much on the table) would have resulted in a push. Has a tie game ever resulted in a push before?

As it turns out, using Pro Football Reference’s search function, there have been 19 ties since the overtime rule was introduced in the NFL in 1974, and none of them were pick ’em. (Note: PFR only has lines going back to the mid-1970s, so for two games I had to find out if there was a favorite from a Google News archive search.) (EDIT: Based on some search issues I’ve had, PFR may not list any games as pick ’ems. However, all of the lines were at least 2.5 points, so if there’s a recording error it isn’t responsible for this.)

Part II has to do with ties, specifically consecutive ones. Since 1974, unsurprisingly, no team has tied consecutive games. Were the Vikings, who were 24 seconds 1:47 shy of a second tie, the closest?

Only two teams before the Vikes have even had a stretch of two overtime games with one tie, both in 1986. The Eagles won a game on a QB sneak at 8:07 of OT a week before their tie, in a game that seems very odd now–the Raiders fumbled at the Philly 15 and had it taken back to the Raiders’ 4, after which the Eagles had Randall Cunningham punch it in. Given that the coaches today chose to go with field goal tries of 45+ even before 4th down, it’s clear that risk calculations with respect to kicking have changed quite a bit.

As for the other team, the 49ers lost on a field goal less than four minutes into overtime the week before their 1986 tie. Thus, the Vikings seem to have come well closer to consecutive ties than any other team since the merger.

Finally, a crude estimate of the probability a team would tie two consecutive games in a row. (Caveats follow at the end of the piece.) Assuming everything is independent (though realistically it’s not), we figure a tie occurs roughly 0.207% of the time, or roughly 2 ties for every thousand games played. Once again assuming independence (i.e. that a team that has tied once is no more likely to tie than any other), we figure the probability of consecutive ties in any given pair of games to be 0.0004%, or 1 in 232,000. Given the current status of an 32 team league in which each team plays 16 games, there are 480 such pairs of games per year.

Ignoring the fact that a tie has to have two teams (not a huge deal given the small probabilities we’re talking about), we would figure there is about a 0.2% chance that a team in the NFL will have two consecutive ties in a given year, meaning that we’d expect 500 seasons in the current format to be played before we get a streak like that.

I’ll note (warning: dull stuff follows) that there are some probably silly assumptions that went into these calculations, some of which—the ones relating to independence—I’ve already mentioned. I imagine that baseline tie rate is probably wrong, and I imagine it’s high. I can think of two things that would make me underestimate the likelihood of a tie: one is the new rules, which by reducing the amount of sudden death increase the probability that teams tie. The other is that I’ve assumed there’s no heterogeneity across teams in tie rates, and that’s just silly—a team with a bad offense and good defense, i.e. one that plays low scoring games, is more likely to play close games and more likely to have a scoreless OT. Teams that play outside, given the greater difficulty of field goal kicking, probably have a similar effect. Some math using Jensen’s inequality tells us that the heterogeneity will probably increase the likelihood that one team will do it.

However, those two changes will have a much smaller impact, I expect, than that of increasing field goal conversion rates and a dramatic increase in both overall points scored and the amount of passing that occurs, which makes it easier for teams to get more possessions in one OT. Given the extreme rarity of the tie, I don’t know how to empirically verify these suppositions (though I’d love to see a good simulation of these effects, but I don’t know of anyone who has one for this specific a scenario), but I’ll put it this way: I wouldn’t put money down at 400-1 that a team would tie twice in a row in a given year. I don’t even think I’d do it at 1000-1, but I’d certainly think about it.

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2 thoughts on “Tied Up in Knots

  1. Jimmy

    Semi-related question: is there an empirical way of determining whether Trestman should have spent another down or two trying to get Gould in better position to kick that FG?

    Reply
  2. clownhypothesis Post author

    Without needing to do much digging, the answer is that it’s dumb to kick a 47 yarder on 2nd down. The odds of botching two snaps in a row are vanishingly unlikely, so the only reason to sit is that you think there’ll be a turnover or loss of yardage. Since the Bears had a positive expected yardage (somewhere north of 6 yards a play, given that that’s their season rate and they were doing better Sunday than normal), the only reason not to run a play is if the risk of turnover is exceedingly high. The Bears’ turnover rate is in the 3% range (closer to 1% if you restrict to running plays), and a gain of even 4 yards increases the FG% by 5 percentage points in this setting.

    Basically, I would say the Bears should keep running plays until the increase in FG% from their expected gain is lower than their turnover rate. Gould is basically automatic inside 30 yards (missed 2 out of almost 400 kicks in that range if you count PATs), so 15 yards farther in I’d have him kick. From 47 yards, though? Pretty clear you run the play, and probably even another one on 3rd down.

    Reply

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