Why is something 1/6 and something else 1/25? Why is something that was last week 1/5 is 1/15 this week? I’ve seen these “odds” change in the newspapers for horse racing, football, and other sports. I have never understood this. I watched some YouTube videos to try to make heads or tails from it but it’s left me in the same.
In: Mathematics
So the thing is that betting odds don’t actually reflect the peobability that you will win. They reflect the amount you will win if you win the bet. There are three types of odds.
The first, the one you reference, is “fractional odds.” In this case, the odds are presented as winnings/bet. So if the odds are 6/1, then for every dollar you bet, you get six back on a win. If the odds are 1/6, then for every six dollars you bet you win 1 back . The closer the fraction is to 1, the more likely the bet is to win.
The second is “decimal odds.” This one is easier to understand. It is just take the bet, multiply it by the odds, and that’s your payout. If the decimal odds are 7.0, then whatever you bet is paid out seven times over. If the decimal odds are 1.167, then whatever you bet is paid out 1.167 times over. The closer to 1.0, the better the bet is, the more likely the bet is to win.
The third type is “money line,” and it is the most confusing. Money line odds are a positive or negative number, and they actually mean different things. A positive number is the amount of money you will win if you bet $100, while a negative number is the amount of money you need to bet in order to win $100. (But in either case, you get your original bet back if you win.) So if the odds are +600, then you would bet $100 to win $600 for a total payout of $700. If the odds are -600 then that means you would bet $600 to win $100 for a total of $700. The negative numbers are the ones that are most likely to win.
Now, if you are really math saavy, you may have noticed that all the odds I listed were the same. So why the difference? Well, all of them are made this way to obscure the actual odds. Because saying 6/1 or 6.0 or +500 sounds like a much more enticing deal than 14.29% and 1/6 or 1.167 or -600 or 85.71%. (These percentages are called the “implied odds and are found by dividing 1 by the decimal odds and multiplying it by 100%.)
Now you might also note something else here they add up to 0 in this case and 100%. But if you look at the moneyline odds for the two teams competing in the Superbowl today (February 11th, 2024) the 49ers are at -130 or a decimal odds of 1.77 and the Chiefs are at +110 or a decimal odds of 2.1. Those add up to a total of -20 and an implied odds of 56.52% and 47.62%, which is a total of 104.14%. Which doesn’t make sense? How can there be more than a 100% chance? Well, the answer is that they are skewing the odds to manipulate the expectation values.
So, the expectation value is how much money you can expect to get from a given bet. The equation for the expecation value is E=WP-C, where W is the winnings you get, P is the probability you win, C is the cost, and E is the amount you can expect to win from the average result. In other words, let’s say that the game was played 10,000 times, and each time you bet $100 on the Chiefs. You would win 4762 of those bets and get $210 for each of those 4762 victories. But would that offset the cost for the 5238 losses? Well E=210(0.4762)-100, which gives an expectation value of E=0.002, so you will actually win $0.002 per game. For the 49ers, the expectation value is $0.0404 per game. But this is only true if the odds are ACTUALLY the present odds. But they aren’t. If the odds that the 49ers will actually win is lower than 56.50% and the odds that the Chiefs will win is lower than 47.62% the. You will have a negative expectation value. So if the actual odds are 56% for the 49ers and 44% for the 49ers than the average better will lose money.
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