Economists (I am one) have historically been trained to believe in the efficiency of markets. The simplest way to think of this is that market prices capture all relevant information. Of course, this is sometimes not quite right, or even close to right. All the mortgage-backed securities that helped bring down our economy were horrendously mispriced, for example, despite lots of people seeing the warning signs. Even then, people betting against those securities provided information about their true value. They were just drowned out for too long by people clamoring to buy that worthless stuff.

The sports betting market, though, is a case that we might actually expect to work better. Unlike mortgage-backed securities, everyone making a wager in Las Vegas is incentivized to get the price right. There’s nobody who’s pushing a bad wager on their clients, for example. ^[1]These perverse incentives have been going on a long time, too. Check out Michael Lewis’s Liar’s Poker for fascinating stories of investment bankers pushing junk on their clients. Therefore, we might expect efficient markets to mostly work in Vegas and that the odds would converge to the correct number.

Mostly, it seems like that’s what’s going on. Whatever information is not contained in the initial odds may be quickly corrected as people swoop in to take advantage. I’ve experienced this first-hand. Last year, I went to Vegas about a week after the first season win-totals for 2013 came out. I found the numbers online and came up with this list of wagers I was interested in.

So I left for Vegas planning to bet 1/3 of my money on the Seahawks to go over 10 wins (betting $120 to win $100), 1/3 on the Chiefs over 6.5, 1/6 on the Colts under 8.5, and 1/6 on the Cardinals over 5.5. As you might have guessed, I never got the chance. By the time I arrived, the Seahawks were at 10.5 and the odds were up to -150 (needed to bet $150 to win $100). The Chiefs had moved even more. I didn’t record exactly how far it moved, so I don’t know the exact number. I think they were at 7.5 in at least one sportsbook. By the time the season started, they were at 7.5 and you had to lay $160 to win $100 on the over, and a different book listed them at 8.

Alas, this story doesn’t have the happy ending it would have if I’d gotten in on the IPO. I didn’t bet on either the Seahawks or the Chiefs because I decided the price had moved too much. The Cardinals and Colts prices stayed put, so I made those bets. I was too late. A potential nice win became a wash. ^[2]Obviously, the Seahawks and Chiefs bets would actually still have worked out well had I jumped in at the less attractive prices.

The movements in those Seahawks and Chiefs lines likely reflected efficient markets at work. Those initial numbers that looked so appealing to me caused money to crash in to take advantage. What did the bettors see? Probably the same things I saw. On the Seahawks, it was basically that they’d been #1 in DVOA in 2012. More simply, they had an estimated win total based on that DVOA that was substantially better than their actual wins in 2012. ^[3]For details on estimated wins and DVOA, see here. My research suggested that teams like the Seahawks tended to beat their win total most of the time of the following year. For the Chiefs, I was mainly attracted by their extremely easy schedule and likelihood of bouncing back from a two-win season.

The Seahawks’ situation was one that seemed more likely to perhaps be mispriced, in general. It was at least feasible that teams with misleading win/loss records would mean opportunities. To see if that was the case, I collected data on season wins lines from 2003-2013, with two years (’05 and’07) not included. I combined that data with Football Outsiders’ estimated win totals from the previous year. Even though those numbers are a great way to measure previous performance, we still might not expect them to have much predictive power given the Vegas lines, which incorporate all the free agent signings, injuries, and the draft. Still, FO’s numbers do have some predictive power that would have been profitable to utilize, at least in the past.

Betting on Underachieving Teams by DVOA

Football Outsiders reports a team’s estimated wins, which is close to using DVOA to predict what would have happened against an average schedule in a given year. Every year, there are teams that substantially outperform or underperform their estimated wins. The 2012 Colts were the biggest deviation in the sample, winning 4.8 games more than their 6.2 estimated wins.

Looking first at teams that underachieved, winning at least one game less in the previous season than their estimated win total according to DVOA, have there been opportunities to win by betting on these teams? The data seem to suggest the answer has been yes. The table below summarizes the outcome of betting $100 on the over for every team that had estimated wins at least one higher than their actual wins in the previous year.

If you had made these bets over the nine years in the data, you would have won a total of $881, or an average of about $13.50 on the 65 bets you would have made. You would have won 39 bets, lost 25, and pushed on 1. ^[4]Note that the 2003 Jets do not count in these calculations since they were off the board in my data.

It’s a little hard to tell if things have changed over time, but you would have particularly done well in the early years of the data. The graph below summarizes the profit or loss from betting on these estimated win underachievers for each year in the data.

From this, it at least seems possible that there were more opportunities to bet on teams like the 2013 Seahawks in the past. On the 28 bets from 2003-2008, you would have won about $27 per $100 bet, compared to only $3 since 2008. Of course, this result depends on how you divide the data and we’re dealing with small samples. Still, the previously successful strategy has not worked in three of the last five years.

Betting on Overachieving Teams by DVOA

If betting on teams that underperformed compared to their expected wins has made money in the past, how about betting against teams that won more than would have been expected based on their play? Things actually look pretty different here. Betting against teams like the 2012 Colts actually hasn’t worked, on average, going back to 2003. These kinds of teams definitely do worse the previous year, but that regression is baked into the price so that there’s been no opportunity there.

The table below summarizes all the outcomes from betting $100 on the under for all teams that won at least one game more than their estimated wins in the previous year.

If you’d followed this strategy, you would have lost about $3 per $100 bet since 2003. This loss is almost entirely because of Vegas’s commission on the bets. You would have won 31 bets, lost 32, and pushed on 4, by betting this way.

And there’s little reason to think that much has changed over time, either. The graph below shows the trend in profitability of betting against these likely-regression teams. As before, it’s a little hard to say, but I think the most reasonable reading of the graph is that betting against the overachievers has consistently lost a small amount of money over time.

2014 Win Totals: Learning from the Past

The first thing I remember thinking when I saw the 2014 lines was that there was almost nothing that looked appealing. ^[5]See here for the complete set of initial lines and his comparisons of those lines to projections using 2013 DVOA I thought the Packers and Patriots looked appealing at 10 and that the Jags looked appealing at 4.5. I didn’t see any unders that excited me. The most amazing thing was how much regression the oddsmakers built in. Houston opened at 8.5 at the Cantor sportsbooks in March. ^[6]The Superbook had them at 7.5 in May. Really? For a 2-14 team? That’s a huge adjustment, but perhaps not surprising now that investment bankers are making the lines at some of the sportsbooks. And then there is the team with the biggest gap between 2013 estimated and actual wins. The Falcons had 6.5 estimated wins compared to their actual four. Again, the price already seems to build in the expected rebound in 2014 wins. The Falcons opened at eight wins, similar to where the Lions ended up last year after a four-win season.

I think the market is likely pricing all of these things close to correctly now. I also think it’s pretty likely that there was a window of opportunity to profit within the last ten years. The strategy of betting on teams that either underperformed in the win column or against those that overperformed would have, on average, yielded about $5 in profit for every $100 bet over the last ten years, with all of that coming from betting on the underperforming teams. Betting just on the underperformers would have yielded $13 in profit, although I think the greater success there may be about random chance rather than something special about underperforming teams relative to overperforming ones.

By the way, give me a time machine, and here’s my favorite bet in the data: the 2004 San Diego Chargers. They had four wins in 2003, but 6.1 estimated wins. Somehow, they went off at 4.5 wins, with -115 the line on the over. I find it pretty hard to believe that line would be anything below 5.5 today. As the data suggest if they cannot quite prove, the market probably just does not provide these kinds of enticing opportunities anymore.