ESPN.com columnist Bill Simmons and fellow sports gambling addict Cousin Sal had their annual Super Bowl prop bets podcast where they discussed the best gambling deals of this Sunday’s Super Bowl (if gambling were legal, *ahem*). Aside: if you haven’t checked out the list of potential bets for the Super Bowl, you should (how long will Christina Aguilera hold the word “brave” in the National Anthem? over/under is at 6 seconds).
Anyway, one of Simmons’ prime suggestions was the bet of 100/1 for the number of total points scored being in the 71-75 range and 150/1 in the 76-80 range. So you plunk 10 bucks on each of those and a $20 bet could net you $1000 or more in the event it’s a high scoring game. The logic Simmons mentioned was this: “if these teams played 100 games, they would score over 70 points at least once.” That totally makes sense to me. In fact, the two teams playing in the Super Bowl, Green Bay and Pittsburgh, played in 2009 and scored a total of 83 points (which, strangely enough is too much for the bets he suggested). But if you wanted insurance against that you could put another $10 down on the higher point total range, but it’s starting to add up.
Again, this makes total sense to me. It seems like every other week in the NFL there’s some wacky game that sees both teams score over 35 points. Why, it happened just a couple weeks ago. And while it’s not likely to happen, it sometimes does, and at 100/1 odds that’s some pretty good winnings.
But is it good math?
There’s a few ways we could approach this mathematically. If we buy into both point ranges to cover 71-80, the mean payout is 1/125, meaning we bet one dollar and get 125 back. Now, let’s look at all the scores of every NFL game this past season.
We find that only 10 regular season games and the 1 aforementioned playoff game featured a score above 70 points. Of those games, one exceeded 80 points.
There are 32 teams in the NFL and each team plays 16 games.
32 teams x 16 games/team = 512 regular season games.
There have been 10 postseason games thus far.
So in a total of 520 games, 9 games have been between 71 and 80 points.
10 games / 520 games = 0.0192
Or, 1.9% of all games end with a score in the target mark.
Digging a bit deeper, 3 of those 10 games were in the 76-80 bracket, yielding a payout of 1/150, 7 in the 71-75 bracket, yielding a payout of 1/100. So the winnings would skew slightly toward the 1/100 ratio, but either way, this looks like a pretty good bet over the 2010 season.
So could we expect 1 out of every 100 games between these teams to end up in the 71-80 range? It seems reasonable to me.
There’s one huge caveat though: the Super Bowl isn’t just a regular game. And I mean that in a bad way. Anyone that watches football can attest: Super Bowl teams look flat. No Super Bowl game has ever exceeded 70 total points. I don’t know if it’s the two-week layoff or the extra rust or whatever, but teams take a while to warm up. At least that’s the way it seems to me.
Take last year’s Super Bowl, for example: two of the most prolific offenses (and hapless defenses) only combined for 48 points – and that was artificially inflated by a defensive touchdown.
Still, with the high powered Green Bay offense and the “fast” turf of Cowboy Stadium, I’m not sure you’d drop all the way from almost a 2% chance of hitting to less than a 1% chance of hitting due solely to the Super Bowl “rust” that teams seem to suffer from.
What do you think? Is this a suckers bet? Is it too good to be true?
emergent math 
First off, you have no idea how happy this blog posting makes me! One of my day-dreams is teaching an interdisciplinary statistics, psychology, and language arts (I’m an English guy so I need to wedge myself in there somewhere) course and do all PBL/gambling projects (and maybe co-author/edit a textbook with Simmons)
So I think it depends on your betting rational. I think your analysis above supports Simmons’ claim in the pod that (to paraphrase) “If they played the game 100 times, at least once they’d be over 70 at least once – so it is a good value bet” – even with the fact that the layoff + pressure would seem to push scores down. (I like the comparison of this seasons’ scores – if you look at the history of Superbowl Scoring we already have 1 of 44 games reaching the 70pt threshold so it definitely seems in play).
On the flip side, I’ve been thinking a lot about the “Sharps vs. Squares” conversation he had with Chad Millman. This feels like one of those “more satisfying to cheer FOR something than against” scenarios. So while it may be probable that if they played the game 100x the score would exceed 70 at least once, they aren’t playing it 100x. Since they are just playing it once, the Sharp money would seem to go against this.
Thanks for the posting!
I think a fun class activity would be to give students a printout of the Super Bowl prop bets and tell them they have $100 to spend on bets. At the end of the class, they have to tell which bets they are taking and why.
Some students would be engaged by football statistics. Others by NBA stats (note the cross-sports bets). Others by things like Christina Aguilera and Fergie bets.
It might be frowned on: introducing kids into gambling. But hey, it worked in The Wire.
Bad bet. High-scoring games are rarely between teams that are evenly matched – usually one dominates to run up the score. Also, you need at least one team to have a not terribly strong defense, and likely both…but it doesn’t seem likely that a team gets to the Superbowl with a weak defense.
Drew’s point about the odds are great – it is THAT game that must be played 100 times to get one over 70 pts… BUT… even that statement is a bad extrapolation using a probability. It is more likely that if that game were played 1,000,000 times, then 10,000 of them, more or less, would breach the 70 pt mark. The 100/1 is an average, right? It could be the second game out of a series of 100 that 70 pts is reached. It could take 200 games before the threshold is crossed.
Kiss your $20 goodbye.
My gut agrees with Kevin that it’s a bad bet: there’s a reason that SBs have been relatively low scoring (or at least, that’s why my confirmation bias is telling me).
But my brain thinks it is an excellent bet. I can’t imagine that the “SB letdown” would cut the potential for 70+ points in half. Which is what it would have to do to make it a bad bet (~2% 70+ point games in regular season versus 1% for the “cutoff point” to make it a bad bet).
I also think that using past Super Bowls as an indicator of future Super Bowls is probably a bit dicey: there have only been 45 SBs. That’s a pretty small sample size, equivalent to less than 3 weeks of the regular season’s worth of games.
Let me phrase it this way: how confident are you that the next 55 Super Bowls will *all* have less than 70 points. That’s a bet I’m NOT willing to take.
One other thing that might need to be considered. The first 70+ point game of the 2010 NFL season until week 8 (BAL-BUF). That’s probably significant as teams start wearing down around then, particularly defenses, and injuries take place.
The SB, with that two week layoff, are a bit more “recharged” and perhaps scoring could be surpressed.
I wonder if anyone wants to go back through NFL history and see how many games were 70+points in the first week of the season.
So part of what I love about the Vegas angle is that because of the money involved, people setting the lines have some of the best information and analysis going. The other part of what we are leaving out is that the odds are not set at 100 to 1 because that’s what Vegas thinks is the most likely probability. Rather, that’s the mark that will get the most balanced betting. Since it is psychologically more fun to bet FOR something to happen than for it not to happen, it is likely that the actual odds for the score being over 70 combined are actually even worse.
I love the idea of looking for inefficiencies in markets like this (not that I am knowledgeable enough to). Ideas like “if the Packers win, it is REALLY likely that Rogers will be the MVP, so if I want to bet Green Bay, I am better off betting Rogers for MVP and getting those odds.” With the above – I wonder if the above line could be a part of an overall package of bets that would provide the greatest likelihood of coming out with a decent return (i.e. could you bet the above with some other items to form a safe hedge?)
I guess this is sort of the idea behind giving students $100 as a project. Since all it does is snow here, maybe I’ll try to put together a set before the game…
That’s a great idea. Re: rodgers as mvp vs. Packers winning. If you put something together email me and I’ll give it its own post. I kind of wish I had thought of this sooner and I could have put together something more robust. I’ll have to remember this come NCAA tourney time…