Quick question about betting lines and odds

I do understand the -x (favorite) / +y (underdog) aspect of betting lines and what that means. I don’t understand how you calculate someone as being, say, a “5 to 1 underdog” based on those numbers.

For example, if team/fighter X is -300 and the opponent is +200, how much of a favorite (as in an x to 1 favorite) is X? How do you calculate that?

This has been bugging me for a while. Thanks.

X being quoted at -300, meaning the punter must bet $300 to win $100, makes X a 1 to 3 favourite to win the event.

A negative odds (-X) quote can be substituted into “100 to X.” Thus -300 means “100 to 300” or “1 to 3”. His chance, if the bet were “fair” would be 3/4, i.e. 300/(300+100) or 75%.

A positive odds (+X) quote can be substituted into “X to 100”. Thus +200 means “200 to 100” or “2 to 1” or, if the bet were “fair” 1/3 chance of winning, i.e. 100/(200+100) or 33%.

These two probabilities, 75% and 33% sum to more than 100%. This is due to the bookmaker’s vigorish. To estimate the actual chance the favorite will win, you need to average 75% and 67% (1 - 33%). A simple arithmetic mean is not the proper average for this, but in this case it may be “close enough for government work.” The bookie’s market is predicting the favorite is 71% to win.

But don’t the odds take into account both numbers?

For example if one fight, fighter A is -200 and fighter B is +200 and in another fight, fighter A is -200 and fighter B is +400 aren’t the “x to 1 favorite” odds for fighter A different in both fights?

I figured maybe you add the absolute value between them. Like if a fighter is -500 and the other is +500 it would be 10 to 1 favorite (and 1 in 10 underdog). But that doesn’t seem to be how it works when i hear people say what the odds are based on the two lines.

I’m not a gambler, but I used to listen to a sports talk show that dealt with gambling a bunch.

Basically, the -x/+y numbers aren’t odds of who is going to win. They are weightings done by the book makers to try to even out the betting. The people running the gambling location want half the bets to be on one side, and half the bets to be on the other side. They win either way. So they set up the payoffs to try to even things out.

Neither of these situations would occur in the real world.

The -200/+200 fight translates to odds of 1 to 2 (1/2) for the favourite and 2 to 1 (2/1) for the second favourite. The probabilities are therefore 67% and 33% respectively. Unlike the original example, which gives the layer a margin (vigorish) of 8%, there is no profit for him in this scenario because the book is dead round at 100%.

The -200/+400 fight is even more unrealistic. This translates to odds of 1/2 the favourite and 4/1 the second favourite. Punters looking at this market could bet $200 @ 1/2 and $60 @4/1 thus collecting $300 for a stake of $260 whatever the result of the contest. Here the layer is just giving money away and would be out of business in very short order.

I realize my examples don’t include the vig. It would be more like -160/+140 or something like that. I was just trying to keep the numbers simple for purposes of the example.

So if the line is -340/+260 by what odds is the favorite the favorite? Don’t you have to take the +260 into account in making that “x to 1” calculation? You don’t just look at the -340, right?