More About Odds And Hold

In my last article, I talked about how to read the American Odds format that is most popular in the US and told you to convert all odds directly to break-even percentages before trying to use them.

In this article I’ll cover a few other important points about odds that are fundamental to learning to bet sports intelligently.

Decimal and Fractional Odds

We Americans like to be different. We like our inches and pounds and pints and Fahrenheit. The rest of the world thinks we’re a bit nuts.

It shouldn’t come as a surprise that the rest of the world thinks we’re a bit nuts about how we do sports betting as well. Instead of the American odds system, they tend to use two other systems called decimal and fractional odds. You may see these formats here as well, so it’s worth a few paragraphs to become familiar with them.

Decimal odds are quoted as a single number, such as 1.9 or 2.5 or 6. What that number means is it’s the amount that you’ll collect from a winning $1 bet—including the amount of your bet. So if you bet $1 at 2.5, you will receive $2.50 from a winning bet—your original $1 plus $1.50 in winnings.

Therefore, 2 represents an even money bet. Numbers between 1 and 2 represent favorites. And numbers over 2 represent underdogs. The “standard” -110 in American is 1.91 in decimal. And +230 would be 3.3.

A nice feature of decimal odds is that to find the break-even percentage you just take the reciprocal. The break-even percentage of 1.91 is 1 / 1.91 = 52.4 percent. The break even percentage of 3.3 is 1 / 3.3 = 30 percent. And so on. You don’t have to mess with different formulas for plus and minus numbers.

You’re probably already familiar with fractional odds. If you see something like 7/4 odds, it means if you bet 4 (the denominator) you stand to win 7 (the numerator). In American, 7/4 is +175. In decimal it’s 2.75. You would represent -110 as 10/11 in fractional odds.

More On Hold

The book makes money via the hold—a spread between what they will buy a bet for and what they sell it for.

If you’re like most sports bettors and don’t really have any ability to find the good bets among the sea of bad bets on offer, then it’s easy to estimate how much you expect to lose on each bet by looking at the size of this spread.

The first thing to note is that at almost all sportsbooks, this hold is shockingly large when compared to other gambling games like blackjack, video poker, craps, and even a relatively player-unfriendly game like roulette. Let’s take the “standard” hold where either side of a roughly 50:50 bet is priced at -110.

The break-even percentage of -110 is 110/210 = 52.4 percent. The overround is the sum of the break-even percentages for all options, and therefore in this case 104.8 percent. Because this number is more than 100 percent, it indicates the sportsbook has an advantage on a randomly selected bet.

If you were to bet randomly, you can estimate the percentage of your bet that will return to you on average by taking the reciprocal of the overround (written as a decimal like 1.048 for 104.8 percent). In this case it’s 1 / 1.048 = 0.954 or 95.4 percent of your bet will be returned to you. Therefore, the sportsbook will hold about 4.6 percent of your total bet.

So, if you were to make a total of $10,000 in bets at a sportsbook at -110 odds for all the bets, and you were to make the bets randomly with no skill at finding good (or particularly bad) bets, you’d lose on average about $460.

Except, not quite. This math assumes you never push your bet. Since sportsbooks return the full bet on a push, the sportsbook hold drops as push frequency increases.

Compare a bet at -3.5 on an NFL game to one at -3. The -3.5 bet never pushes, so it’s priced at -110 the hold is 4.6 percent.

The -3 bet will push, however. For the sake of argument let’s say it pushes 10 percent of the time. If you bet $110 with no advantage at -110 on -3, then 45 percent of the time you lose $110, 45 percent you win $100, and 10 percent of the time you get your money back for a $0 win. The average outcome for your $110 then is
EV = 0.45 * -$110 + 0.45 * $100 + 0.1 * $0 = -$4.50

which is an average loss of 4.5/110 = 4.1 percent of your bet.

The chance to push the bet on three points dropped the average house hold from 4.6 percent to 4.1 percent. If you’re making random bets into a sportsbook, the chance to push helps you. If you have an edge, it hurts you. Either way, you should be aware of it.
Finally, most American books hang different holds on different markets—and often will have different holds from game to game even in the same sport on the same day.

One reason this happens is thanks to the quirks of that old American Odds system. Books often calculate their hold in terms of “cents” of American odds. In NHL, for example, you might get “20 cent lines.”

If the two teams are evenly matched, they might each get priced at -110, and the average hold would be the 4.6 percent we calculated above.
But if one team is a favorite, they might get priced at -150 and the underdog at “20 cents worse” or +130.

The first step here is to calculate break-even percentages. The -150 break-even is 150 / 250 = 60 percent. The +130 break-even is 100 / 230 = 43.5 percent. The overround is 60 percent + 43.5 percent = 103.5 percent. The return to player is the reciprocal or 1 / 1.035 = 96.6 percent and therefore the hold is 3.4 percent.

That’s a lot lower than the 4.6 percent hold at -110 on each side.

Books know all about this effect, obviously, so they will only give you a break like this to a point. After a while they will switch to “30 cent” lines such as -200 and +170. And then they will add more and more cents like -300 and +250 as one side becomes a bigger and bigger favorite.

Again, working in cents is imprecise, and if you want to get serious about betting sports, you should calculate hold percentages in all these markets for yourself until they become second nature. If you want to win, the difference between a 3 percent and a 5 percent hold is very significant.

As an exercise, try to calculate the hold in the -200/170 and -300/250 markets using the method I outlined.

Once you get into this, you’ll see the huge disparity in hold percentages. You might see a -160/+150 market in MLB (a 1.5 percent hold) or a -120/-120 market on a prop (an 8.3 percent hold). Figuring out the hold in every market is the first step in finding good bets. ♠

Ed’s newest book, The Course: Serious Hold ‘Em Strategy For Smart Players is available now at his website edmillerpoker.com. You can also find original articles and instructional videos by Ed at the training site redchippoker.com.