Sports Betting Math

Most people who want to place bets on sports are fans to begin with. It isn’t unheard of for a gambler to place some sports bets, especially during big games like the Super Bowl or the NCAA basketball Final Four, but for the most part, sports bettors are sports fans looking to use their knowledge of a game or of a game’s players to earn a little extra cash. Being a fan of a particular sport, a team, a college or professional squad—these are all precursors to placing sports bet. Sports betting is also a way for a fan to get in on the action of the game, with something more than self-respect at stake.

All gambling is mathematics, even games of chance. If you understand the math behind the game, you understand the game and can give yourself an advantage. For many games, like penny slots or poorly placed roulette bets, are so bad that smart bettors earn their advantage by avoiding them altogether. In sports betting, the math is more complicated. Depending on your favorite sport, you may need to think about things like bye weeks, underdogs, quarterback ratings, and injuries with the same fervor other connoisseurs reserve for fancy winces.

So how difficult is sports betting math? The math behind placing a winning bet is fairly complicated, but the way to stay ahead of the bookmaker is rather straightforward. If you collect on 52.4% of your bets, you’ll break even. We’ll have more details on that number later, including why it takes more than 50% wins to break even, but first some general knowledge about sports gambling and the numbers behind it.

Sports Betting Basics

The easiest way to demonstrate the math behind a sports bet is to make up an example. Let’s say you and your buddy walk into a casino, each with $200 burning a hole in your pocket. There’s a big game on tonight, the Cowboys and the Redskins, so you wander into the sportsbook to check up on the latest news about the game. While you’re sitting there, you see the wagering board, with some funny numbers on it. It looks like this:

428 Cowboys +175
429 Redskins -4 -200 38

Some of this is easy enough to read. The Redskins -4 means the Redskins are favored to win and must do so by at least 5 points for a bet on the ‘Skins to pay out. The next number (-200) is the moneyline, in this case the Redskins are a 2/1 favorite. The last number (38) is the total, the over/under of the expected number of points scored in the game.

More on Placing Sports Bets

Look at that over/under number, in this case 38. If you or your buddy thinks this is going to be a particularly high or low scoring game, based on your knowledge of the team’s offenses and defenses, or information about a hurt player or bad playing conditions, you can place a wager on the total of points scored.

So how is a guy supposed to know how to literally lay down a sports bet? You need to know three things:

*the type of bet you want to make
*the number of the corresponding team you have chosen and
*the amount you wish to wager

Knowing all that beforehand gives the ticket writer the details he needs to write the ticket without having to bend over backwards to process your bet.

Tipping and Sports Betting

We haven’t even gotten to the meat of the sports math yet, and we’re already talking about tipping the staff behind the window? Yep. Here’s why.

If you place two $100 bets, and you win, you’ll collect $440. You should consider leaving a tip around five percent of your winnings. Yes, that’s a $22 tip, but you just made a huge win, and surely you can spring for a twenty-spot for the guy who helped you win it. If you tip around the five percent mark regularly, when you win, you’re way more likely to get free drinks, which is about all you’re going to get comp-wise at the sportsbook.

So, back to the basic math of sports betting. You and your buddy, after much deliberation, decide to each place a $100 bet on your favorite team. What now?

To bet on the Redskins using the point spread, your bet is called “laying the points.” For your bet to pay off, the ‘Skins have to win by five or more to cover the spread. Remember, if the ‘Skins win by exactly four, the game is a push, and both sides recoup their bet. Another alternative is called “taking the points” with the Cowboys. That means the Cowboys have to lose by three or less for your bet to win, or if the Cowboys win outright. So you and your buddy go up to place your $100 bet, and you find out that the standard straight bet at any bookie pays 11/10. That means you have to bet $110 if you want to win $100. You and your buddy pay the bookie $110 and sit down with drinks to watch your bets come in.

These are deceptively simple bets. Deceptively because they make it look like the outcome of the football game is like the outcome of picking marbles out of a bag. Put one black marble and two white marbles in a bag, pull one out at random, and there’s your football game. After all, the odds are the same: 2/1 for white.

But we, as sports fans, know that the mathematics of a sporting event is much more complex. Sports bettors deeply involved in their hobby will subscribe to weather bulletins from major cities that take part in their sport, making huge wagering decisions based on a few mph of wind in one direction or another. Then there’s the unknown—does a player get hurt in the first quarter? Does weather become a factor? Is a particular player “in the zone?”

How Do Bookies Make a Profit?

Just as we finish ruminating on the concept of the difficult math at play in the background of major sporting events, we’re going to turn right back towards the simpler side of sports betting. Bookies make a profit because of vigorish. What’s vigorish?

Look at the above example again. You and your buddy each paid $10 to the bookie to place your bet. That’s what the standard 11/10 odds in sports betting are all about. You bet the Cowboys and your buddy bet the Redskins, a total of $220 bet. The sportsbook has to pay back $210 to the winner, leaving a nice $10 profit no matter what happens on the football field. That $10 built-in profit is called the vigorish, and it’s the final monkey wrench in the gears of sports betting.

Obviously, sportsbooks are going to take more than two bets on any game, but this example is for simplicity’s sake. Looking at the total number of bets on different games over the course of a week and adjusting the moneyline and other numbers is another way the bookie makes a profit. Adjusting the odds a tiny percentage point in either direction will affect the balance of beats and make the book more likely to turn a profit no matter what.

Essentially, a bookie is a person who holds on to money from bettors then pays them if they win and keeps their money if they don’t. That’s what the job is boiled down to its essence.

When a bookie sets odds for games, he will build what bookies call an “over round” into his set of odds. Another slang term used for this formula is “the juice.” For the sake of simplicity, let’s look at a boxing match where both contenders are equally talented, of equal stature, etc. Since they both have an equal chance of winning, a casual bet may be even money. You put $20 on one guy; your friend puts $20 on the other. Whichever fighter wins awards the bettor with the total of $40.

Bookies don’t offer even money like friends in a casual betting situation. In the above example, with two evenly matched boxers, a smart bookie will offer 5/6 odds for each. That way, a $10 winning bet would only return $8.30 plus your stake. What does this do for the bookmaker? He can float an equal amount of money on both fighters, winning no matter which fighter actually wins. If they take $1,000 worth of bets on one boxer and $1,000 on the other, the bookie would take in $1,000 but only have to pay out $830, for a guaranteed $170 profit regardless of the outcome.

Bookies look at the weight of their books all the time and adjust odds and other factors to make sure their books balance. Though it isn’t possible to completely balance a book, bookies that go too far out on one side run the risk of losing money, and losing money in gambling is the fastest way to find yourself in another industry. All of these factors are why bookies generally root for the underdog—too many favorites winning in a sport with a short season (such as the NFL) can cause a bookmaker to lose money, while a bunch of upsets (like you generally see in college football) is a guaranteed profit for the bookmaker.

The short answer here is that bookies making money has nothing at all to do with your betting. It is almost unheard of for a single customer to be allowed to place enough bets to sink a single book all on his own. High rollers in sports betting get special privileges in terms of their maximum bet size, but these privileges often change with the bettor’s luck—maximums get raised after the bettor sees big losses and decreased (sharply) when the bettor starts to get lucky.

In short, a sportsbook’s profits aren’t necessarily impacted directly by the way an individual bet is called. Unlike casino games or slot machines, where it’s you against the house, sports bettors fuel the bookmaker’s business and only rarely is an individual bettor betting against the bookie.

Sports Betting Odds

Remember at the beginning when we talked about the magic number necessary to guarantee a break-even week in sports betting? If you read enough about sports betting, you’ll hear this number repeated often: 52.4%. If a bettor can win 52.4% of his bets, he’ll break even. Where does that number come from?

When betting the spread, you get odds of -110. Sometimes, sportsbooks will offer a -105 line as a promotion or to welcome new business. But for the most part, if you’re betting the spread, you’re getting -110.

We draw that 52.4% break even number right out of the odds. -110 is equivalent to 11/10. That means if you bet 21 games, you’d have to win eleven of them and lose ten of them to break completely even. Even at -105, you’d still have to win an astounding 51.2% of the time just to break even.

If you don’t trust the basic math behind this break-even principle, look at another real-world example. Let’s say you get really into sports betting after your Cowboys cream the Redskins and you go home with a nice fat wallet. You then bet on the next 10 Cowboys games, winning six times and losing four times. That 60% betting record (with the odds of -110 that is traditional for against the spread bets in football) will leave you with a profit of $160. Think about it—your $600 profit from your 6 winning bets minus the $440 you lost on losing bets leaves $160. It took you $1,100 to win $160, meaning you have to bet $6.87 to win $1 on average. So you see the small differences between a 52.4% winning rate and a 60% winning rate—inside those 7.3 percentage points lies hundreds of dollars in profit.

Now imagine instead that you lost one of those six winning bets, leaving you with a 50% betting record. You spent a total of $1,100, won $500, and lost $550. That means overall your 50% record drained your wallet by $50. That’s where the vigorish will get you. Not even winning half the time is good enough to break even in sports betting.

Professional Sports Bettors

Believe it or not, some people really do bet on sports for a living. Maybe they work part time at a sportsbook or in some other marginal job in the casino industry, but there is a group of gamblers who bet on sports for their life’s work. With all the math swirling around in our heads after the last bit of the article, it’s hard to imagine anyone wanting to do this for a living.

If you know that a 52.4% record will mean you break even, the simplest way to turn sports betting into a career is to bet enough so that a 53% winning record will bring in the kind of money you want to make.

Another example. After your successful Cowboys experiment, you decide to invest $10,000 in sports gambling over the first four months of the following football season. That $10,000 is set aside to win or lose in sportsbooks.

You plan on betting on 160 games during your investment period. You dream of a 55% winning record because your win-loss with a 55% winning record would give you an 88-72 record. That’s an expected profit of +8.8 units. How did we get to that number? To calculate your units, subtract the total of your losses (multiplied by 1.1 to include the vig) from your wins and you’ll get your unit profit.

Placing $460 bets on each of these games, a number pulled from some quick and dirty math about how much you could afford to bet in a single week’s NFL play without blowing your bankroll, would result in a $4,048 profit if you maintain that 55% winning record. Turning $10,000 into $14,048 in just four months is an investment return of 40.48%. I dare you to ask your bank for that kind of return on your savings account.

But that’s all assuming you can pick the winner 55% of the time. Do your research, look into the records of professional sports gamblers. 55%, while not impossible, would place you among the elite sports bettors in the country, if not the world.

Professional sports bettors have to worry about variance more than any other type of gambler. Working against the forces of variance means managing your bankroll over the course of the season to avoid the negative possibilities that could totally empty your wagering account. Professional sports bettors have the time and resources necessary to calculate these variances, and there are even a few pieces of software out there that can help you figure out your ideal bet in the face of negative variance. But the bottom line is that professional sports bettors would dream of having a 55% winning record, simply because it guarantees you’re beating the house.

Pro bettors make their money on bets that sportsbooks offer that give them even the slightest betting advantage. The key to becoming a profitable sports bettor is being able to find advantages, opportunities where the line a book is offering is vulnerable.

This is why many long-term sports bettors are math freaks. Good sports bettors understand statistics, particularly what are called inferential statistics, though any higher math will help when it comes time to place a bet.

Here is what a professional baseball bettor might do in his head. After looking over statistics from MLB (kept religiously by all sorts of bloggers, data archives, and magazines) between the years 2000-2010, he notices a particular statistic pop out. For example: when the home team starts a left-handed pitcher the day after a loss, that team wins 59% of the time. Good sports bettors can do this sort of math in their head or very quickly on paper. From that bit of information comes a new betting theory—look for game situations that mirror the above example and bet on them. That means he’ll only bet games where the home team starts a left-handed pitcher the day after a loss. Does he just jump in and start betting based on this back of the napkin math? No way. More statistical analysis is required—he may find that this was a fluke for that particular decade and isn’t a trustworthy statistics, or he may find an even more advantageous bet based on his original theory.

Pro sports bettors also keep near-obsessive records of their bets. Obviously, no edge in sports betting lasts longer than a single game. Taking proper records will also help you test theories, like the above one about left-handed pitchers and losses. Without taking good records, no sports bettor’s bankroll will last very long.

What Is a Good Record for Sports Bettors?

So, at the end of the day, what could you call a “good” record for a sports bettor? Most casual gamblers looking into sports betting see a pro advertising his 1100-900 record and shake their head a little. How could such an abysmal record be something to be proud of? That’s a 55% winning percentage, and it indicates to those in the know that this bettor is actually turning a profit placing bets on sports.

A good record for a sports bettor is any record equal to or larger than 52.4%, because that number or anything higher means you’re not losing money. A 53% winning record, while not impressive on paper, means you’re actually beating the sportsbook and putting money back in your pocket. Ask your friends that play the slots or play online poker how often they end up putting money back in their pocket.

A -110 wager, standard for spread bets in the NFL, gives the house a built-in advantage of 10%. It means that even if you do win, and you line up to collect your $100, some sucker behind you just spent $10 to hand the casino $100.

A good record for sports bettors is any record that ensures they at least break-even. If you bet 16 games this NFL season and you won 9 and lost 7, you probably made money. And taking money away from a casino is always something to be proud of.