Sunday, November 1, 2020

Published November 01, 2020 by with 10 comments

How Do American Betting Odds Convert to Percent Chance?

If you've looked at betting odds, you've probably seen something like +140 and -175. What % chance does that imply for each participant?

Definition

First, what do those numbers mean? A -175 means 'you win $100 for each $175 that you bet' and a +140 means 'you win $140 for each $100 that you bet'.

Example

Now, consider a matchup that's 60% chance for A and 40% chance for B. What does that convert to?

Assuming no cost to bet, if there were 10 matches and you bet $100 on A each time, you'd put in $1000 and expect to get out $1000. Since A wins 60% of the time, you'd get 6 payouts and they would sum to $1000 (since you lose the bet on the 40% where A loses). Each bet would pay out $167, and subtracting off the initial $100 means a profit of $67. Thus, a $100 bet on A yields a profit of $67 when A wins which means that to get a profit of $100 you'd bet 100/.67, or $150. From the definition above, that means that a 60% chance of winning is a line of -150.

Doing the same with the 40% one, you'd get 4 payouts that sum to $1000, so $250 per payout and a profit of $150. You bet $100, and profit $150 on a win, so the line is +150.

Thus, a 60/40 matchup corresponds to a line of -150/+150. The general equation for the logic above is:

  • favorite: American line = - 100/[( 1/percent - 1)]
  • underdog: American line = 100*[( 1/percent - 1)]
Going the other direction:

  • favorite: percent = 1/[(100/-American) + 1]
  • underdog: percent = 1/[(American/100) + 1]

Real Life

It's not quite this easy. The person offering the bets (bookie) needs to make money. Imagine in the above that the person offering the bet wants to make $10 for every $100 bet. How does that change things?

Consider bets on A. You make 10 bets on A. A wins 60% of the time, so you should get $1000 back like before except that you pay $10 per bet so you get $900 back. 6 payout that give $900 means $150 per payout and subtracting initial investment means $50 profit. That means you'd bet 100/0.5, or $200 for each $100 profit which means the line is -200.

For B...4 payouts gets $900, so $225 payout per win which is $125 profit per win after subtracting initial investment. $125 profit on a $100 bet means +125 is the line.

How can you factor out this $10 cost (margin)?

You get a line of -200/+125 to start and want to see what the margin is on this. It's actually easy from what we did earlier. Simply convert these lines to the percentage versions, and add them together. Taking these specific numbers:
  • -200 => 66.67%
  • +125 => 44.44%
  • sum = 111.11%
That is, for every $100 that is bet, the bookie gets $11.11 (or in the earlier terms, for every $90 that is bet you pay an additional $10).

Finally...how do you get the implied chance of each option winning from odds that have the margin factored in like these? Simply divide each percentage by the sum.
  • favorite: 66.67% / 1.1111 = 60%
  • underdog: 44.44% / 1.1111 = 40%
And we recovered the original odds.



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