Calculating Edge for Pointspread

[ProlinePlayer]

You've probably noticed that I've changed up the way OLG Pointspread games are displayed on the web site. If a push is possible the win probabilities are now shown as Visit / Push / Home.

My question is how would you go about calculating the edge for a play based on the game's probabilities. The question probably has no one right answer has the whole concept is in the case of pointspread a bit artificial at best. Due to the nature of the game you really need to break down completed parlays for accurate edge values. But as a simple method I've tried to provide values here just for quick comparisons of different plays.

To start I've always used an assumption of 4 team parlays and a payout of 1.78 per game as basis for calculating the edge. However adding in the push creates new problems.

The simple way (this is done for even number totals) would be to ignore the push and just do the math based on the win loss probability.
For example game 47 tonight has the following probabilities visit 43.4, push 25.7, home 30.9. A simple calculation of the edge would be (.434 * 0.78) - .309 = +2.9%.
This however accepts the push as a zero result and ignores it in the calculations. But we all know that this is not what really happens and that the push games do represent a loss in value.

So this is what I'm trying now. When the game pushes it means that the 4-teamer, which we are basing our numbers on, drops to a 3-teamer. This means that the other 3 games in the parlay all have a drop in payouts from 1.78 to 1.71, or a drop of .0683 * 3 in payout value.

So I've included this as the loss for push games.
The above game's edge would now be (.434 * 0.78) - (.257 * .0683 * 3) - .309 = -2.3%

So do you guys think this is a reasonable way of calculating the game's edge? Or have any better suggestions?

Thanks,

PLP

[MattyKGB]

Here's what I would do...it doesn't quite jive with my math in the other thread, not quite sure why.

Suppose you've won the first 3 games paying 1.778 each (10^[1/4]), and the 4th game is the one with the push line.

Your cumulative odds on the first 3 games are 10^(3/4) = 5.623.
A push on the 4th game will reduce the payout from 5.623 to 5 - a ratio of 5/5.623 = 0.889.

So, outcomes are:
Win - 0.434 prob x 1.778 payout
Push - 0.257 prob x 0.889 payout
Loss - 0.309 prob x 0 payout

Total EV = +0.03%. This is the edge I would use.

Side note - why did you pick 4 gamers as the basis for the PS edge calculations on your site? I'd think that 5 games are much more commonly played by edge players in Ontario. 4 gamers are sub-optimal in most (not all, but most) cases because you are passing up a chance to add a 5th leg at marginal odds of 20/10 = 2.00. Even if your 5th leg has 50.1% win probability, you've still increased your edge by adding it.

[MattyKGB]

Repeating my calculation using a 5-gamer instead of a 4-gamer:

"Old method" edge = 0.434 x (20^1/5) + 0.257 x 1 - 1 = +4.71%

"New method" edge = 0.434 x (20^1/5) + 0.257 x (10 / [20^4/5]) - 1 = +2.41%.

So by this logic it looks like the push line reduces the edge on a 5-gamer by around 2.3 percentage points per game.

If you wanted to figure out an "edge-equivalent" probability to stick into parlaymaker or another rotation calculator (like mine!), I'd start with the +2.41% edge and work backwards:

1.0241 / (20^1/5) = 0.5625

A straight win probability (with no push possibility) of 56.25% would give you the same +2.41% edge. So you could say that a 43.4% win + 25.7% push proposition is equivalent to a 56.25% win + no push proposition.

Now here's the weird part (and this may explain my result in the other thread...although, again, I didn't sleep much last night so I could have royally screwed up somewhere!):

If you take the win probability + half of the push probability, you get .434 + .257/2 = exactly 56.25%!

So (I think!!!) you can skip all this math and just take the win probability + half of the push probability, consider that to be the new win probability in a no-push scenario and off you go. That's what I did in the other thread to calculate the 25.7098% edge.

Am I missing something?

[sharpasitgets]

Consider event 68 today.

Would you agree that the odds of Anaheim to win 2+ and the Rangers to win, describes the non-push scenario? If so then it would follow:

Rangers win 0.434
Anaheim Win 2+=0.308
Odds of Anaheim win 2+: Rangers win = 1:1.41

Rangers win Probability in non-push out comes= 1-(1/2.41)=58.5%.

Isn’t 56.25% the probability of covering +1?

[MattyKGB]

As PLP and others have pointed out, you can't just pretend the push doesn't exist because it is a real event with a non-zero probability and a quantifiable impact (it reduces the payout on the other games in your parlay).

[sharpasitgets]

I think I am getting lost in semantics. I would approach the above problem as follows:

Involved in a 4 team parlay.

Edge of a settled scenario=0.743*((1.78/1.711)-1) = 2.95%
Edge adjustment given push=-0.257*((5.623/5)-1) = -3.20%
Edge of a settled scenario+ Edge adjustment given push=-0.25%

Involved in a 5 team parlay.

Edge of a settled scenario=0.743*((1.82/1.711)-1) = 4.71%
Edge adjustment given push=-0.257*((10.985/10)-1) = -2.53%
Edge of a settled scenario+ Edge adjustment given push=2.18%

Assuming the other games are involved in the parlays are not also push games and they are all even plays…..

[ProlinePlayer]

Side note - why did you pick 4 gamers as the basis for the PS edge calculations on your site? I'd think that 5 games are much more commonly played by edge players in Ontario. 4 gamers are sub-optimal in most (not all, but most) cases because you are passing up a chance to add a 5th leg at marginal odds of 20/10 = 2.00. Even if your 5th leg has 50.1% win probability, you've still increased your edge by adding it.

Why not 7? 8?

I think that it was a simple case of using 4 because it was the lowest parlay size that was a reasonable consideration. But I do agree with you about 5 teams. I've always believed that 5 teams (and more) is the best way to play. And since I think most others would agree as well I'll follow through on your suggestion and change the OLG page to use 5 teams as the default payout for pointspread.

PLP

[ProlinePlayer]

"New method" edge = 0.434 x (20^1/5) + 0.257 x (10 / [20^4/5]) - 1 = +2.41%.

Thanks matttykgb,

I've used this method to adjust the edge for push lines on OLG pointspread

PLP