Edge calculation problem for Props today.

[red_falcon]

Hi PLP,

Is PLPlayer updated?? Please check if a payout of 1.70 at 57.3% does indeed come out as 19.9%, I have -2.59%.....

Red.

[ProlinePlayer]

You're overlooking that the loss probability is only 20.2%

PLP

[lonewarrior]

Hello PLP. Actually I have the same question. You calculated 79.8% chance of at least 2.0 SOG with 57.3% chance of more than 2.0. It means there is a 22.5% chance it lands on 2.0 exactly.

Shouldn't be the edge represent the amount of money one would win in a long run? A push doesn't win anything unless a tie is a win too when betting on the over. For people that bet on over, they want 3+ and for under they want 0 or 1. Landing on 2 doesn't do either side any good in terms of profit.

I can be wrong and hope you can help us. Thanks a lot and GL!

[MattyKGB]

A push is actually more than 50% as good as a win because the win pays 1.70 and the push pays 1.00.

FWIW my numbers are significantly different from PLP's and I'm passing on this card. I hope for your sake that I'm wrong!

[ProlinePlayer]

lol

my program is now making the same error in calculating the ev for the game.

It seems to get it right when it first grabs the lines from the OLG but if the program is stopped and restarted (like when I was vacuming and accidently unplugged the computer) then it does not seem to handle the pushes for props correctly.

Will fix in the morning.

PLP

[Opportunist]

I am impressed that you vacuum, somehow I didn't see that in you.

[richhhh]

What type of vacuum do you have? upright?canister?bagless?

[mlansky]

I am impressed that you vacuum, somehow I didn't see that in you.

Haha Opportunist..funny, I thought the exact same thing!

[ProlinePlayer]

I am impressed that you vacuum, somehow I didn't see that in you.

lol

[ProlinePlayer]

There's an old thread in the theory section somewhere dating back to just after the start of the hockey season where this is discussed at great length. The topic is calculating edges for NHL pointspread games - include or ignore the push probability. In previous times this was not really a big issue, although pushes in CBB and football were possible they did not have a signifiicant effect on any calculations. With the higher probabilities of pushes in hockey this matter needed to be considered.

I'll describe both methods here. But first I want to point out that what you're doing does not fall into either group. You're not ignoring the pushes - you're treating them as losses. They may not be wins but they certainly are not the same as a loss.


WinProb : 57.3%
LossProb 20.2%
PushProb 22.5%

1/ Ignoring the pushes.
I myself always thought this was very reasonable approach. Simple, since they don't affect our bottom line just toss them out. But in order to do that you must also take them out of the total pool of results. The easiest way to do that is to recalculate what percent of games you win out of the total games with no pushes.

If we exclude pushes we have a total pool of 57.3 + 20.2 = 77.5
Out of those you win 57.3 of the total pool or as a percentage = (57.3 / 77.5) * 100 = 73.9%
With a payout of 1.70 this gives an edge of (1.70 * 73.9) - 100 = +25.63


2/ Include the pushes
If we accept that the pushes are real results which cannot just be ignored than the edge calculation goes like so
Edge = (57.3 * 1.70) + (22.5 * 1.00) - 100 = +19.91



So those are the two choices here. I originally argued that either method was acceptable but I personally preferred method 1. A few members did agree but some of our best math minds like MattyKgb and Dilbert were on the other side and believed that 2 was correct and method 1 was wrong.
In the end, Matty and Dilbert's arguments were very convincing (surprise). After listening to their arguments and rethinking things I now have no doubts that you have to include the pushes. They are real results and can not just be ignored.


I'll try to explain why throwing out the pushes is wrong.
First of all, it turns out that if you're betting games straight up, then my thought that either method is acceptable, is actually quite accurate. Assuming that after calculating the edge your next step is to calculate the Kelly bet size, then the thing is both methods, when entered into a Kelly formula, produce the same $$ result.

But if betting parlays things are a lot different and excluding the pushes will create misleading results. I'll try to explain why but my explanataion is going to sound a bit muddled so I hope it will make sense in the end.
I'll try by giving an example using the above game. Let's assume a 3 team parlay and the other 2 games are not so great and actually have a combined ev of -20%, not real I know but it will serve to demonstrate the issues.
If we'd used method 1 (ignore push) we would now have a 3 teamer with the above game offsetting the -20 for a net edge of approx. +5%. However using method 2 (all games count), the +19% would not be enough and we'd still have a negative ev parlays.
Which is right?
Method 2. The fallacy with using method 1 is that we are treating the parlay as if the +25 will offset the negative value of the rest. However in many cases the above game will result in a push and all we're left with is the other 2 parts and their -20%. This has not been accounted for in the +25% ev. I know I haven't explained this very well, but what I've tried to illustrate here is that the pushes do affect the ev of the parlay and for that reason they cannot be ignored.


Hope this helps,

PLP