How to Beat the Over-Under

Note: A follow-up to the results of the 2007 season can be found here.

Just in time for the beginning of the season, I think we've cracked the code on beating the Vegas over-under lines. Prompted by a recent comment from Tarr, I did some additional analysis. Although this is not a gambling site, I realize a lot of people are interested in it, and many people would at least be interested in how to beat conventional wisdom.

I only had the last two seasons of data available, and although I'd prefer to have more, the results are convincing.

In my past several months of researching NFL win-loss records, I've noted two overwhelming phenomena:

1. The NFL is impossible to predict before the season starts. And,
2. Regression to the mean rules the day.

In practical terms, expert predictions, including the consensus Las Vegas over-under predictions, are bad primarily because they underestimate the annual tendency for bad teams to improve their records and good teams to worsen their records. Expert predictions stink--that's the good news.

The bad news is our own predictions usually stink worse. Sometimes people get lucky and outguess Vegas or the experts, but over time, luck will catch up to you. So the trick is to take advantage of Vegas' flaws by applying the two lessons above, all the while ignoring our own predictions. Here's how:

1. Take the under on teams predicted to finish with 9.5 wins or more.
2. Take the over on teams predicted to finish with 6.5 wins or less.

And here's why:

1. Of the 18 teams predicted to have 9.5 wins or more, 13 finished the season under, and 5 finished over.
2. Of the 15 teams predicted to have 6.5 wins or fewer, 11 finished the season over, and 5 finished under.

Using these two rules, the '9.5 or more' teams would have yielded a net of 13-5=8 winning bets, and the '6.5 wins or fewer' teams would have yielded 11-4=7 winning bets.

I am not a gambler at all, so forgive me if I mess this up. In the last 2 years, if you bet \$110 on each game according to these rules, you'd have placed 18+15=33 bets for a total of \$3300. For each loss, you'd receive nothing, but for each of the 24 wins, you'd get back \$210 (\$110 + \$100) for a total of \$5040. Your net winnings would be \$1740. That's a 152% return on your "investment" over two years.

This analysis is based on only two years of data. However, of the 33 observations included, the chance of being correct by chance 24 or more times is p=0.0068. To statisticians, that means it's significant. To gamblers, it means it's a safe bet. But if anyone has over-under data from years prior to 2005, I can include it in the analysis to increase the confidence level.

The lesson here is if you're going to gamble, don't bet on your own dumb guesses. Bet against the dumb guesses of everyone else. Take the over on stupidity.

The table below lists each team's actual wins, pre-season over-under lines, and the error of the over-under predictions. The system's correct predictions are in green and its incorrect guesses are in red.

 Year Team Wins Over-Under O-U Error 2005 IND 14 11.5 -3 2005 PHI 6 11.5 6 2006 IND 12 11.5 -1 2005 NE 10 10.5 1 2006 NE 12 10.5 -2 2006 SS 9 10.5 2 2006 DEN 9 10 1 2005 ATL 8 9.5 2 2005 BAL 6 9.5 4 2005 CAR 11 9.5 -2 2005 MIN 9 9.5 1 2005 NYJ 4 9.5 6 2005 PIT 11 9.5 -2 2006 CAR 8 9.5 2 2006 DAL 9 9.5 1 2006 JAX 8 9.5 2 2006 KC 9 9.5 1 2006 NYG 8 9.5 2 2006 PIT 8 9.5 2 2006 CHI 13 9 -4 2006 CIN 8 9 1 2006 MIA 6 9 3 2006 SD 14 9 -5 2006 WAS 5 9 4 2005 BUF 5 8.5 4 2005 DAL 9 8.5 -1 2005 DEN 13 8.5 -5 2005 DET 5 8.5 4 2005 JAX 12 8.5 -4 2005 KC 10 8.5 -2 2005 SS 13 8.5 -5 2005 STL 6 8.5 3 2006 ARI 5 8.5 4 2006 MIN 6 8.5 3 2006 PHI 10 8.5 -2 2006 TB 4 8.5 5 2005 SD 9 8 -1 2006 ATL 7 8 1 2005 ARI 5 7.5 3 2005 CIN 11 7.5 -4 2005 GB 4 7.5 4 2005 HOU 2 7.5 6 2005 NO 3 7.5 5 2005 OAK 4 7.5 4 2005 WAS 10 7.5 -3 2006 BAL 13 7.5 -6 2006 NO 10 7 -3 2006 STL 8 7 -1 2005 CHI 11 6.5 -5 2005 NYG 11 6.5 -5 2005 TB 11 6.5 -5 2005 TEN 4 6.5 3 2006 BUF 7 6.5 -1 2006 CLE 4 6.5 3 2006 DET 3 6.5 4 2006 GB 8 6 -2 2006 OAK 2 6 4 2005 MIA 9 5.5 -4 2006 HOU 6 5.5 -1 2006 NYJ 10 5.5 -5 2006 TEN 8 5.5 -3 2006 SF 7 5 -2 2005 CLE 6 4.5 -2 2005 SF 4 4.5 1

14 Responses to “How to Beat the Over-Under”

1. Chip says:

You need to factor in the vig. During the season, it's usually used to manage the action to equalize both sides of a bet. Given the unpredictability of forecasting mean season wins, the vig is very large on NFL futures. To bet the over on CLE's season wins (5.5), requires laying 150 to win 100. You can see how wide the vig is on your bets:

TEAM O/U TEAM
CLE 5.5 -150
BUF 6.0 -110
DET 6.0 -135
HOU 6.5 -110
MIN 6.5 -160

TEAM O/U TEAM
DEN 9.5 Even
CHI 10.0 -115
IND 10.5 Even
SD 10.5 110
NE 11.5 -110

It is still a money making strategy though:

TEAM O/U Over Bet Win E(win)
CLE 5.5 -150 150 100 73.3
BUF 6.0 -110 110 100 73.3
DET 6.0 -135 135 100 73.3
HOU 6.5 -110 110 100 73.3
MIN 6.5 -160 160 100 73.3
Sum: 665 500 366.7

Under Bet Win E(win)
DEN 9.5 Even 100 100 72.2
CHI 10.0 -115 115 100 72.2
IND 10.5 Even 100 100 72.2
SD 10.5 110 100 110 79.4
NE 11.5 -110 110 100 72.2
Sum: 525 510 368.3

Total Over Under
Wagers: 1190 665 525
Winnings: 735 367 368
ROC: 62% 55% 70%

2. Brian Burke says:

Chip-You're right. That makes a big difference. I had assumed it's always 110 to win 100, but I guess that's just for individual game bets against the spread.

I noticed that the number of games that meet my criteria are diminishing over recent years. In 2005 there were 18 teams, 2006 had 15 teams, and this year, depending on your source, there are only 11 teams (your list, which I'd trust more than my own, has only 10). Pehaps the handicappers are learning, or maybe someone has published this trend before. And with fewer the games to bet on, the higher the risk/reward factor is for an individual year.

Also, this sytem requires a leap of faith. You can't cherry pick which teams to bet on. For example, you can't say, "Naah, no way CLE wins 6 games in the AFC North!" You need to spread your chips on ALL the games that meet the criteria.

3. Brian Burke says:

Just noticed a couple things. The O-U Error column rounds the error. The accuracy of the results doesn't change, just the appearance of the table.

Also, there isn't a single instance of Vegas predicting a team's actual number of wins in the past 2 years. A lot of them are X.5 predictions, but still, I'd expect a few direct hits.

4. Anonymous says:

Coincidentally, I just bet on the Patriots under 11.5 and the Saints under 9.5 ... both bets offering better than even money.

I should check if the line changed on TradeSports in response to this post. How many readers do you have, Brian? :)

Nope, no change.

BTW, Buffalo at over 5.5 is a 3 to 2 favorite.

5. Tarr says:

Well, you certainly CAN cherry pick your bets, and only take a few of the extreme O/Us. But if we assume that you have no special predictive powers, then all this does is increase your variance.

6. Brian Burke says:

I get about 500 per day, but it's growing daily.

Tarr-True. I guess it depends on your risk tolerance. But since there are only 10 or 11 teams that fit the criteria, I'd spread my chips out. But that's just me.

7. Anonymous says:

"Breaking the Code" needs more than TWO years worth of data. LOL!

I'd say at least ten years.

And, every so often there's a sea change. Could be a rules modification (like instant replay which mollified some of the home field advantage) or the 2 pt option after a TD that has a major effect across the board.

Plus, for most gamblers the length of a football season is WAY too long to hold a bet in order to make a profit.

Nonetheless, I'll give you your props if your hypothesis holds up over ten years.

Try the goldsheets or something for historic data. Or maybe even contact pinnaclesports.com who's been offering this kind of line for the past ten years (without tipping your hand of course.)

Finally, should you be right, the books WILL adjust.

8. Brian Burke says:

You're right for not trusting any gambling system. I wouldn't either. But although it's only 2 years of data, it's 64 teams. It's also statistically significant. The chances of being correct 24 out of 33 times just by chance are incredibly small.

I might agree we're seeing the market slowly adjust for this phenomenon. In the past 3 years the number of teams with over-unders above 9.5 or under 6 are steadily decreasing.

9. Tarr says:

Of course, those who set the lines aren't really concerned with whether the lines are actually the minimum error estimate. They care about maximizing their profits. As long as they are getting plenty of action taking the over on inflated overs and the unders on depressed unders, they will continue to use those lines.

Which is to say, until what is written here becomes common knowledge among those who place bets, the lines will stay like they are, and there may be room for smart gamblers to find an edge.

10. Brian Burke says:

I did some more homework on this. I found a website that had done somewhat similar research and had historical over-under data from 1996-2005.

Using the system as proposed, a bettor would have won 86 out of 148 of his bets, a rate of over 58%.

Although not the 70% rate over the past two years, it would remain a safe and lucrative system. I'm guessing most professional gamblers would sell their soul for a 58% winning rate over a 10 year period.

Data from: http://www.twominutewarning.com/season-win-bets2.htm

Also, if you go with 6 instead of 6.5 for the overs, you'd improve to 61% correct over the '96-'05 period.

11. Anonymous says:

I have to comment on this, you must consider all variables involved, there were 17 new head coaches over the last two years, which means that close to 1/3 of the teams could not be predicted becuase no one knew what a coach might do in certain situations, they could only project that they would lose, but two years ago, you had the Jets and Saints kickin butt with first year head coaches,last year started the season with playoff teams having new head coaches,this year there are only 4 new head coaches, and in my oppinion the vegas total wins for each team will not be off by that much. The four teams with new head coaches may be worth using your theory, and I like Miami to surpass their projected win total of 5.5..nice work though, keep it up, the key is to beat Vegas before they beat you..Mike Hillin vegasflyer.net

12. Samson Himpachni says:

Awesome find!

Keep up the great work!

13. Unknown says:

GOOD JOB THANKS! GOOD JOB

14. Anonymous says:

knowledge is power and research is the key