A question of line logic

[TraderMike]

In a sport if the total is on an integer, say 6 for the sake of this example, what is the proper procedure for measuring the probability a certain outcome. For example, if the line reads:

Over 6 -105
under 6 -105

If your calculated chances of the game going over is 55% and under is 30%, would you simply subtract the chances of the outcome being a push from 100 so that we get (100-15), or 85%, then calculate the ratio of the of both the over and under separately as a proportion of 85% so that we get the following:

Over: (55/85)= 64.5%
Under: (30/85)= 35%

(approximations of course)

Should these numbers then be used to compare against the the posted lines of -105 for both wagers for determining any possible wagers?

I know this was winded and please let me know if I can clarify my question if it is unclear. Thank you.

 

[IrishTim]

Not sure I understand your question. I think you're after the implied winning percentage of a given bet. If there was an easy way to calculate the probability of a certain outcome in sports, we'd all be making bank.

For you're example, you have the over and under of 6 both with a vig of -105.

You need to use the payout/juice to determine the implied winning percentage, not the number. The easiest way to estimate this is to take the average of the 2 payouts. In this case, the average of -105 and -105 is obviously 105. Then you divide that number (105) by the number + 100 (105+100 = 205) and this gives you the implied winning percentage.

So you have 105/205 = .512, so you're implied winning percentage on either the over or under 6 at a price of -105 is 51.2%.

If you calculate the game going over 55% of the time, you believe you have 3.8% edge over the book, which--if true--will make you money long-term. The question, of course, is how accurate is the 55% you came up with. Hope this helps.

 

[TraderMike]

Thank you for taking the time to answer the question. However, my question was more aimed at deciphering your implied edge over the book, given that your calculated probability is greater is greater than the implied probability given by the book. In essence, when dealing with an integer total number, like 5 or 6 in hockey, do you essentially want to calculate the chances of the game beating the total or pushing when deciding whether or not to make the play.

 

[bdmcleod]

I understand what you're saying and the answer is no. Sort of.

If P is a proposition stating all the possible outcomes in a certain situation ("Either A, or B, or C, etc"), then Pr(P) = 1. And in this case there are 3 outcomes. over, under, 6.

Conversely if you are stating a total of 1, then you need to account for all the possible outcomes. You didn't because you didn't consider 6 in your
Over: (55/85)= 64.5%
Under: (30/85)= 35%

What you could say is
If money is going to be changing hands,
Over: (55/85)= 64.5%
Under: (30/85)= 35%

Because you eliminated the zero-sum possible outcome.

 

[TraderMike]

When you put it that way, if money exchanges hands then the probability of the two outcomes is x and y, it makes it more clear. In these circumstances remove the zero sum outcomes.Thanks for the response.