## Wednesday, May 05, 2010

### Converting From A Win Percentage To A Money Line

I was recently asked if there was a formula for converting a win percentage to a Money Line. For example, if we think a team has a 65% chance of winning a game, what would the "fair" money line be for that game?

Money lines are generally given as a negative number for the favorite and a positive number for the underdog. There are cases that both teams will be listed with a negative number if the odds are very even and there is juice on the game. A site that has a dime juice, will have the money line listed as -105/-105 on a 50/50 game. Without the juice, both teams would be listed as +100 or -100 (same thing).

Now back to our request for a formula for converting from win percentage to money line. Since the favorite will be listed as a negative number and the underdog as a positive number, we have to use two similar but slightly different formulas. One for the favorite and one for the underdog.

Depending on what type of juice you’d be expecting you’d add/subtract an offset in. With a dime juice you’d subtract a nickel (from -150 to -155) from the favorite and subtract a nickel from the dog too (+150 to +145). Let's ignore the juice for now, as it can easily be added in at the end of the process.

P = Probability of the team winning
X = Money Line (not adjusted for juice)

Favorites: X = -100P / (1 – P)

Underdog X = (100 – 100P) / P

Example, Team A has a 65% chance of winning and Team B has a 35% chance of winning.

ML for Team A would be:
= (-100 * .65) / (1 – .65)
= -65 / .35
= -185.7

ML for Team B would be:
= (100 – (100 * .35)) / .35
= (100 – 35) / .35
= 65 / .35
= +185.7

Let's round it off a little bit and call this a -186/+186 game. So if a team was listed on the money line as -186 favorite (with no juice) they would have a 65% chance of winning according to the money line. If you were to add a dime juice to this line you would end up with something like -191/+181. But keep in mind that juice tends to increase as a team becomes a larger and larger favorite.

Feel free to use my handy Money Line to Win Percentage Calculator, via Google Docs.