Variance and Its Effect on Sports Bettors

Sports bettors are as subject to the whims of variance as any other gamblers, and that includes casino gamblers and poker players. It might take different forms, but variance is the factor that confuses otherwise smart people into thinking that they’re winning or losing gamblers. (Yeah, and confirmation bias has something to do with that, too, but that’s another blog post.)

In probability, variance is the tendency for short-term results to vary from the mathematically expected results. For example, if you’re playing roulette, and you make 20 bets on 20 spins, you could easily see red come up 16 times and black only come up 4 times. The mathematically predicted results would look more like red coming up 9 times, black coming up 9 times, and green coming up once or twice.

If the roulette wheel isn’t biased, and if you continued to bet on spins until the end of time, eventually the actual results would resemble the mathematical prediction. In fact, the closer the number of spins gets to infinity, the closer the results should get to the prediction. This is called “the Law of Large Numbers.”

When you’re placing bets on something like a spin of the roulette wheel, you might feel like your hunches are paying off.

Really what you’re seeing, though, is just variance.

Variance in Sports Betting Is a Double-Edged Sword

The trick with sports betting is to be able to pick winners against the point spread often enough to overcome the vig. The vig, or vigorish, is the extra amount you must wager to place a bet. Usually, a book requires you to risk $110 to win $100. That extra $10 you’re risking is where the book makes its money.

If you win 50% of the time and lose 50% of the time, you’ll eventually go broke. Think about it like this:

• If you make 1000 bets of $100 each, and you win 500 of them, your winnings are $50,000.
• But on the 500 bets you lost, your losses are $55,000.
• Your net loss on those 1000 bets is $5000, or $5 per bet on average.
• That $5 is the vig in action.

Now let’s say you’re good at handicapping, and you can find a profitable bet 53% of the time. What does that do to your numbers?

• Now you win 530 of those bets for $100 each, for $53,000 in winnings.
• You lose 470 of those bets for $110 each, for $51,700.
• You’ve profited $1300 over 1000 bets, or $1.30 per bet.

But even if your bets should win 53% of the time in the long run because of your skill as a handicapper, in the short run, you can lose a huge percentage of bets.

It’s easy for a skilled sports bettor to have a bad week and lose 7 or 8 bets out of 10. If this theoretical sports bettor doesn’t have a large enough bankroll to ride out this variance, he could go broke before the Law of Large Numbers catches up with him.

On the other hand, you might easily be lousy at picking winners against the spread. You might only expect to win 48% or 49% of the time just because you make bad decisions.

But you might easily win 7 or 8 bets out of 10 in a week. You might decide, based on this, that you have a working system, or that you’re really smart. If you keep betting badly, eventually the Law of Large Numbers will catch up with you, and you’ll lose money. It’s inevitable.

That’s why I say short-term variance is a double-edge sword. You can be a short-term winner, but you can also go broke in the short run even if you’re making positive expectation decisions.

A Simple Example of Variance

About 3 years ago, I met a beautiful who, for some reason, was interested in me. To get my attention, she got my phone number and email address, and she asked me to help her with her “pick’em pool” at work. All we had to do was pick who was going to win each game, regardless of the point spread.

That should have been easy, right?

After all, we know who the underdogs are, so if we just take all the favorites that week, we should have a good shot at doing respectably, at least.

So one would think, anyway.

As it turns out, even with some thoughtful consideration, my picks that week were awful. I was wrong about 14 of the 16 games. She would have fared better had she flipped a coin.

Any time an underdog outright wins a game, that’s an example of variance in sports betting. And it happens far more often than most people expect.

Major League Baseball is the most volatile popular sport in the United States in this regard. The underdog wins about 42% of the time in a professional baseball game. The National Hockey League is almost as bad. The underdog wins about 40% of the time.

Professional football and basketball are less volatile, but the results are still surprisingly high. The underdog wins an NFL game outright about 33% of the time, and in the NBA, the percentage is about 30%.

Keep in mind, this is the win percentage for a straight win that doesn’t account for the point spread. Take the point spread into account, and the numbers change even more dramatically.

I’m glad that young woman didn’t really care whether she won that football pool or not, because we had some fun together for a while. But she never asked me for help with her football pool at work again, either.

Betting on the underdog alone isn’t a surefire way to get a long-term edge on sports betting.
But it’s a good place to start.

It’s also a way to embrace variance.

Winning Streaks, Losing Streaks, and Variance

Variance is also one of the reasons teams go on winning or losing streaks. You’ll see winning and losing streaks in purely random games of chance, and plenty of people think they have predictive value. Of course, a pair of dice has no memory, so they don’t know if they’re on a winning streak or not.

Sports teams are somewhat different, though, because the players do have memories. When a team is on a winning streak, you’ll sometimes hear people talk about how they’re playing with “Big Mo” on their team. That’s a nickname for the concept of “momentum,” which is a real thing in sports betting.

But not all winning streaks or losing streaks have anything to do with the actual behavior or attitudes of the players on the team. Often, a winning streak or a losing streak is just an example of good luck or bad luck. And let’s face it, those expressions—“good luck” and “bad luck”—are just synonyms for the word “variance.”

Streaks are less likely to happen in football games because the teams only play a handful of games each season. The sample set is so small that it’s hard to see a big streak going.

But think about how many games there are in a season of professional baseball. When you’re looking at a team’s performance over 162 games, it’s almost impossible to NOT see a winning or losing streak in there somewhere.

The thing about streaks, though, is that they’re usually only visible in hindsight, and it’s hard to predict when they’re going to begin and end.

Protecting Yourself from the Whims of Variance When Betting on Sports

Remember earlier how I mentioned that you could easily go broke betting on sports just because of variance and bad luck?

There’s a way to protect yourself from variance, but it only works if you’re a winning sports bettor. If you’re an average (losing) sports bettor, it doesn’t matter what you do—you’ll eventually lose all your money.

Since variance is a short term thing, your goal as a winning sports bettor is to not put enough money into action on a single game to seriously reduce the size of your bankroll.

By limiting the size of your bets this way, you make sure that your bankroll is preserved long enough that your long-term expectation can start to be fulfilled. You can’t take advantage of the Law of Large Numbers if you go broke before you make a large number of bets.

Limiting the size of your bets preserves your bankroll through the variance-caused losing streaks that are inevitable.

Another Way of Looking at Variance

You can look at the amount you win or lose over each week of a season of NFL betting to get an average win or loss number. An average is just a total divided by the number of repetitions. In an NFL season, that’s 16 weeks.

Let’s assume you place a $100 bet every week for 16 weeks, and your results look like this:

You lost $770 total during weeks 1-7. But then in weeks 8-16, you win $900. Your net win for the season is $130.

Since you won $130 over 16 weeks, your average win per game is about $8.13.

But during no week did you win $8.13.

You either won $100, which was a big difference between the average win of $8.13, or lose $110, which is also a big difference between the average win of $8.13.

In fact, over a single week, it’s impossible to see a win or loss of just $8.13. That’s variance.

You can’t even see that kind of average over 2 weeks.

Those averages only show up over the course of multiple games.

In fact, 16 bets isn’t a large sample size at all. It’s entirely possible that the sports bettor in this example is making bad bets and just got lucky for the season.

The long run doesn’t even start to kick in until 100 bets, and you can’t really count on any of these results until you start getting into 1000 bets or more.

Any sample size smaller than that is just too likely to be a result of variance.

If you’re good at sports betting, you can consider it a type of investing. I’ve written blog posts on that subject before. How does the variance in sports betting compare to that of the stock market, though?

In general, sports betting results are far more volatile than stock market results. You can expect see variance of at least 10 times what you’d see if you invested in the stock market.

The more games you bet on, the lower the effect of variance will be on your results.

Conclusion

Variance is one of those aspects of probability that everyone who bets should understand. It’s just as important to a sports bettor as it is to a professional blackjack or poker player.

But you don’t see as much coverage of the subject when people write about sports betting.

Some of that’s based on the fact that the outcomes of sporting events are affected by chance, but they’re not ENTIRELY determined by chance.

You can protect yourself from short-term variance in 2 ways:

• 1. Keep the ratio of bet sizes versus your bankroll small—1% or 2% of your bankroll is plenty to bet.
• 2. Make lots of bets. The fewer bets you make, the more effect luck will have on your results.

I hope you enjoyed this introduction to the subject of variance in sports betting.