The bets have been coming in fast and furious during this Super Bowl week.
John Locher/AP Photo
This year’s Super Bowl in Arizona will be the first ever played in a state with legalized gambling. Fans in Glendale will be able to bet while at the game using their phones, and gambling trade groups are projecting 50 million people will wager $16 billion on the Super Bowl — more than double last year’s “handle.”
Handle is the betting industry’s term for the total amount of money wagered on a given sporting event.
“>1 It seems like everybody is in a gambling mood in 2023 — so let’s join them.
This is the fifth year running that I’ll be overanalyzing a prop bet, and in past years I’ve focused on bets that had nothing to do with the actual game. Last year, I analyzed whether bitcoin’s price would fall during the Super Bowl (it did); back in 2019, I looked at whether Gladys Knight would go over 107 seconds with her rendition of the national anthem (she did, just barely). In between, I looked at the most likely opening song in Jennifer Lopez’s halftime show, and which word Amanda Gorman would utter first during the performance of her pregame poem.
I’m sticking to actual football this time around, though, because I found a bet that was too interesting to pass up. One international sportsbook is laying odds on three straight scores by either team in Super Bowl LVII — meaning the Philadelphia Eagles and/or Kansas City Chiefs would score on three consecutive possessions between the two of them
So, for example, three straight possessions consisting of an Eagles TD, a Chiefs TD and an Eagles TD would count, as would the sequence Chiefs TD-Eagles TD-Chiefs TD. But so would a string with a Chiefs TD, a Chiefs INT return TD and an Eagles FG, and so forth.
“>2 — and the current implied probability for “yes” is 66.8 percent.
The actual odds are -201 for Yes, and +150 for No. Those were then 3 Maybe I just don’t pay enough attention to the games, but 67 percent seems surprisingly high. Do two-thirds of NFL games feature a series of three consecutive possessions ending in some score or another? And if so, has it always been this way?
To find out, I pulled up play-by-play data from the open-source data repository nflreadr and identified every instance of a game with at least one series of three straight scoring possessions by any team. The results were surprising (at least to me). Since 2000, there have been 3,317 games that featured back-to-back-to-back scoring possessions, out of 6,159 regular-season and postseason games played. That’s over half of all games (53.9 percent)! And while that’s well shy of the nearly 67 percent implied probability for the Super Bowl prop, it’s still somewhat eyebrow-raising.
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Scoring has skyrocketed in the NFL over the past 20-plus years, so that’s likely a large part of the explanation. Offenses have also changed quite a bit since the turn of the century, moving from two-running back, two-wide receiver formations to having three wide receivers on the field on most snaps. It would make sense if instances of three consecutive scores have increased along with an uptick in scoring and an increased emphasis on passing. And when we look at the data by season, it turns out that’s exactly what we find.
The general trend until this year has been an upward one, tracking fairly well with other measures of offensive efficiency like points per drive. The share of games with three consecutive scores peaked last year at 63.5 percent, though it came crashing all the way down to 54.4 percent this season.
2022 statistics are through the conference championship games.
“>4 That also makes sense: This is the year that offense died in the NFL. But what makes less sense is why this Super Bowl has an implied probability that’s higher than the peak year in our sample.
Perhaps there’s something special about the Super Bowl somehow? If we just look at the big game, 14 of the past 22 Super Bowls (64 percent) had at least one series of back-to-back-to-back possessions resulting in scores. But honestly, that’s a silly comparison that unnecessarily limits the sample. And anyway, even if you insist on limiting the analysis to Super Bowls only, the base rate here is still less than 66.8 percent (the market’s odds on this occurring).
Before concluding that the sportsbook has this prop priced wrong, however, there’s another factor to account for: the offensive strength of these particular teams. The game total for the Super Bowl — the over/under number for combined points that bettors wager on in a given game — is a relatively high 50 points,
As of Feb. 6 at 2 p.m. ET.
“>5 and that seems important. Since my feeble brain can’t keep track of all these variables, I cheated and used a model
The model is a multilevel Bayesian Bernoulli logistic regression model trained on data from 2010-22. The dependent variable was a binary variable for whether a game featured three consecutive scores, and the independent variables were the predicted total points scored in the game according to Vegas odds, game spread (which was positive for if it favored the home team and negative if it favored the away team), a binary variable indicating whether the game was played in the playoffs and the season. I also included a random intercept of season to account for seasonal scoring environments.
“>6 to do all that for me. It accounts for the seasonal effects we saw above, and uses market-derived measures of combined offensive strength.
As it turns out, those game totals do an excellent job of helping predict which games will feature three consecutive scores, and the seasonal adjustments were quite important as well.
Game spread was not a useful predictor, and neither was whether the game occurred during the playoffs. Although the playoffs appeared to have a lower rate of games with three consecutive scores at every “Vegas” total that we could group by, the findings were within the credible intervals, so I can’t conclude that a difference exists.
“>7 But even at a robust total of 50, the model’s estimate of the true odds of three straight scores in Super Bowl LVII stands at 65.6 percent, giving me a nominal edge of 1.2 percentage points.
Because I’m using MCMC, which is subject to some random number generation, the nominal edge differs depending on what seed you set, but the result is fairly similar regardless. These numbers were the most conservative of the several seeds I tried.
“>8 Simply put, a 66.8 percent probability of three straight possessions containing some kind of score is just too damn high.
The last thing to figure out before putting real money on the line is to calculate how much the sportsbook is charging for the privilege of wagering with them. Called the vigorish, or the “vig,” the sportsbook’s profit margin can be calculated from the odds that it lays for each side of a wager. In this case, the sportsbook is charging a vig of 6.3 percent,
I assume no draws here, and also that the “overround” is evenly distributed between both sides of the wager, which 9 so I need to subtract that from my edge.
When I do, the edge disappears. The sportsbook’s vig of 6.3 percentage points crushes my edge of 1.2 percentage points, leaving an expected value of -5.2 percentage points, showing just how tough it is to beat the house on these prop bets.
Again, these numbers differed slightly according to which random seed I set for my model, but that adds further support for the difficulty.
“>10 Still, after all this work, I’m placing the darn bet.
There are a few other unfortunate downsides to this wager. One obvious bummer is that on top of the bet being negative EV, I’m still an underdog. It’s more likely than not that I’ll lose. There’s also a bit of ambiguity in the way the bet is worded — simply, “3 straight scores by either team” — which is open to interpretation. (However, I looked into alternative interpretations — such as the next three scores of a game being by the same team — and their observed frequencies were so low that the sportsbook’s line made even less sense.)
The other big downside is that it forces me to root against a wildly entertaining game filled with scoring, and that stinks. Incidentally, that’s often why recreational gamblers avoid bets like unders (and why those unders remain a perennial value): They aren’t very fun wagers to place.
I have a narrow path through the forest that leads to fun, though. I’ll still be rooting for Showtime Patrick Mahomes and speedy Jalen Hurts to run up the score and light up the desert with explosive plays. I just request, humbly, that they take every other drive off while doing so.
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