NO, SPORTS BOOKS DID NOT GET KILLED DURING THE NFL SEASON

race & sports book (Photo credit: fictures)

It happens every season. One Sunday, favorites will dominate the card. And, like clockwork, media reports will surface detailing how sports books “got killed” while gamblers cashed winner after winner.

But here’s the deal: Nevada sports books haven’t had a losing football season, ever. Period.

The worst year Nevada books had handling football bets was 1992. They made $19.8M which was 2.69% of the $735M bet on football in Nevada books that year. Since then, Nevada books have never made less than $30M in any year handling football bets.

Their best year was 2006 when bettors were particularly terrible and lost 8.02% of the $1.13 billion they bet on football games (NFL and NCAA), providing sports books with gross revenue of $91.1M from football betting. That led to the most profitable year ever for Nevada sports books as they made $288M.

Now, the LA Times published a story on how bad sports books are faring during this NFL season. From the article:

The result is what one Las Vegas sports bookmaker called a “staggering” financial hit from the NFL regular season, as bettors handed Nevada sports books their worst year in memory.
Did the article cite any actual numbers? Nope. So we will. And these figures are directly from the Nevada Gaming Commission, in case you’re curious.

Through the first 10 months of 2012, Nevada sports books have handled $1.28 billion in wagers – a record amount. And books have ‘won’ $96.8M. During the first 10 months of 2011, books ‘won’ only $37.4M so this year’s first 10 months represent a 158% growth rate over 2011.

More specifically, sports books won $44M on football bets in the quarter ending October 31, 2012. Yes, you read that correctly. The LA Times has a story about how sports books are getting killed when, in fact, sports books won more money in football bets during August, September and October than they won in all sports combined during the entire 2011 calendar year.

The LA Times also points out that books are getting “killed” because favorites are covering the spread. Well, underdogs covered 52% of the games during this NFL season.

Unfortunately, Deadspin has parroted this LA Times story without actually adding any data or refuting any of the inaccurate assessments. And Deadspin even managed to add this stunningly inaccurate zinger:

Occasionally sportsbooks will shift lines based on lopsided action, but they do their damnedest to avoid it.
So, as you read more and more of these articles, remember reality: Nevada sports books don’t lose money because bettors are winning too much. It doesn’t happen.

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The Dangers of Over-betting and Over-Estimating your Edge

Gambling (Photo credit: sincerelyhiten)

These graphs illustrate the long term power of using Kelly sizing to increase one's bankroll over time, and beg the question, 'if Kelly betting will lead to such incredible returns, then betting double or triple Kelly must lead to even higher returns!' Referred to as 'over betting,' this misguided notion is one of the reasons that so many +EV sports bettors go broke just like their square compatriots. It turns out that someone betting 1.5 Kelly has the same expected growth as someone betting 0.5 Kelly, but with tremendously wilder upswings and downswings, and much more risk. Betting 2 Kelly actually has the same expected return as not betting at all: exactly zero, and betting more than two Kelly has a negative long term expected growth even if you are making positive expected value bets, and your bankroll will eventually fall to zero! In conclusion, Kelly sizing is in fact, as has been stated several times, the point at which return is exactly optimal.

Another important point to consider is that the dangers of over-estimating and over-betting your edge are not restricted to Kelly Betting. Flat bettors or even bettors who gamble 'however much they feel like' on a given trip to the casino frequently over-estimate and over-bet as well. Generally, bettors this unsophisticated are over-betting no matter what they do; they have zero edge at best, and probably a negative edge expectation, and shouldn't even be betting in the first place. Yet, many advantageous cappers or bettors who buy my picks can unwittingly over-bet as well.


In addition to the dangers of over betting, the Kelly Criterion also has large swings compared to flat betting. For example, a given positive expectation wager that compounds at 10% per time unit will eventually double, and of course grow to infinity. However, since the swings with Kelly betting are so large, the initial bankroll actually has a 1/3 chance of being cut to half its initial value at some point before doubling. To an academic, this is immaterial, since they can keep their eyes on the long run expected growth. However, to investors who are often investing money for a shorter period of time and expecting immediate and consistent returns, this relatively high short term risk and volatility is unacceptable.

However, because variance is exponentially related to return, we find that cutting the bet size in half causes only a nominal reduction in expected growth, but square roots the variance. In other words, if we were to bet one half Kelly unit on our 10% per time unit (with full Kelly) proposition, we would grow our funds at a slightly slower rate of 7.5% per time unit while our risk/variance/volatility would be the square root of what it was previously. To use the previous example, we would now fall to 50% of our starting bankroll only 1/9 (rather than 1/3) of the time before doubling it - a much more tolerable level of risk for the average investor.

Betting one half Kelly unit instead of a full unit also helps prevent accidental over betting when we may have overestimated our edge, and we have already examined how destructive this can be. For example, if a bettor estimates his win percentage to be 58%, he would accordingly bet 11.8% (at 10:11) of his bankroll following full Kelly sizing. But, suppose that despite correctly picking a winner, the bettor had incorrectly assessed the real win percentage, and the side he picked would in fact be a winner only 55%, rather than 58% of the time. In this case, he should have bet only 5.5% of his bankroll, and since he overestimated his edge by 3% he actually over bet and wagered more than 2.1 Kelly. This will result in a negative expected growth despite the fact that the bet was still positive expected value, and would win 55% of the time. However, if the bettor instead followed a policy of betting ½ Kelly, overestimating win percentages is not nearly so dangerous. In this case, the win percentage miscalculation would have caused him to mistakenly bet twice the determined appropriate bet size… and he would have bet 1.0 Kelly instead of ½ Kelly, causing himself no harm whatsoever.

Full Kelly wagering is optimal when you know the odds exactly (as might a card counter who is aware of precisely which cards remain), but is too dangerous when positive expectation wagers are less certain.  Bettors are well advised to halve or even third their bet sizes to cut down immensely on volatility while sacrificing relatively little expected growth.

Talk to any career bookie, and you will find a shocking truth: many (maybe even as high as 20% or 30%) sports bettors actually win over 50% of their games in the long run. However, their concepts of money management are so poor that almost all of them over bet wildly, driving their long term expectation to zero, and they all end up completely broke. The following anecdote, which could be any one of a million different bettors, illustrates the dangers of over betting:

"This guy Archie came into my book on the first week of September and bet about $1k on ten different NFL games. He ended up going 9-1, and turned his $10k into $18k. (n.b. we are ignoring vig for the sake of simple calculations) I knew he would be back though, and sure enough he was there the following week, betting $2k on nine different NFL games and totals. He got hot again, and went 7-2, and his $10k had now grown to $28k in just two weeks. I wasn't worried though, because the story is always the same with these guys. In week three, he came in with 7 more 'locks' and put $4k on each game, only to go 1-6, losing three of the games in the last minute. Frustrated with his bad luck, he put all of his remaining $8k on the Monday Night Under, which busted when the Broncos scored a meaningless touchdown in the final minute. Three weeks after he started, Archie was broke."

Archie is a prototypical gambler with absolutely no investment discipline. He started out with $10k, went 17-10 (63%) and ended up broke. Rampant over betting is a great way to empty your pockets while winning two thirds of your games. If Archie had just flat bet $500 per game the whole way through, he would've turned his $10k into $13.5k in three weeks. If he had bet 5% of his bankroll on each sequential game, he would have run his $10k up to $18.7k, and then slid in week 3 to finish at $13.7k, netting a $3.7k profit, albeit with some big swings. Does this story sound familiar? It should - it describes about 90% of the gamblers you'll find at any given time in a Las Vegas sportsbook.

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