Confirming my Understanding of Kelly -diverted-

cschaps · 07-09-2008, 01:09 PM

Hello,

I am new to the forum. I have been reading at length the threads on the Kelly Criterion. I would appreciate it if someone would confirm my understanding. Here is how I think it is supposed to work.

Example:

Bankroll = $10,000

7/9 - Cardinals (+142) vs. Phillies (-152)

Cardinals:
Probability - 100/242 = 41.3%
Decimal Odds - 1+(142/100) = 2.42
Edge - .413 * 2.42 - 1 = -.05%

Phillies:
Probability - 152/252 = 60.3%
Decimal Odds - 1+ (100/152) = 1.66
Edge - .603 * 1.66 - 1 = .098%

Combined Probability - 41.3% + 60.3% = 101.60

New Info:

Cardinals:
New Probability - 41.3/101.60 = 40.65%
New Edge = .4065 * 2.42 - 1 = -.016

Phillies:
New Probability - 60.3/101.60 = 59.35%
New Edge - .5935 * 1.66 - 1 = -.014

Questions:

Do I base edge on
1) the calculated probability that includes vig (Cardinals -.05, Phillies .098)?
2) the calculated probability that does not include vig (Cardinals -.016 Phillies -.014)?
3) on a probability I would get from another source (i.e. espn.com)?

I am thinking it has to be the 3rd option. So assuming that is the case I would only wager if the following criteria are met:

1. If the probability of winning for either team found on espn.com, for example, is greater than the implied probability calculated.
2. If the probability of winning for each team taken from espn.com and their respective lines create a positive edge. Of course if they both have positive edges, I would choose the team with the higher edge.

Am I understanding this correctly?

So assuming the edge on the Phillies tonight is 3% and the line is -152 (this means I am relying on a probability of (1+
.03)/1.66 = 62.05% chance that the Phillies will win, the amount I would wager would be:
.03 (Edge)/1.66 (Odds) - 1 = 4.5% of $10,000, which is $450.

Again I would appreciate an confirmation that I am understanding all of this.

Thanks in advance!

cschaps

Ganchrow · 07-09-2008, 03:50 PM

Quote:

Originally Posted by cschaps

Example:

Bankroll = $10,000

7/9 - Cardinals (+142) vs. Phillies (-152)

Cardinals:
Probability - 100/242 = 41.3%
Decimal Odds - 1+(142/100) = 2.42
Edge - .413 * 2.42 - 1 = -.05%

This is just rounding error. "Edge" calculated in this manner will be definition always be exactly 0.

"Edge" = 100/242 * 2.42 - 1 = 0

Quote:

Originally Posted by cschaps

Phillies:
Probability - 152/252 = 60.3%
Decimal Odds - 1+ (100/152) = 1.66
Edge - .603 * 1.66 - 1 = .098%

"Edge" = 152/252 * 252/152 = 0

The implied probability of a money line is by definition the probability that implies zero edge.

See An introduction to betting lines and percentages and An introduction to expectations and theoretical hold.

Quote:

Originally Posted by cschaps

Do I base edge on
1) the calculated probability that includes vig (Cardinals -.05, Phillies .098)?

No. This would always imply 0 edge and hence no bet (unless hedging).

Quote:

Originally Posted by cschaps

2) the calculated probability that does not include vig (Cardinals -.016 Phillies -.014)?

No. This would always imply negative edge and hence no bet (unless hedging).

Quote:

Originally Posted by cschaps

3) on a probability I would get from another source (i.e. espn.com)?

Yes. Although ESPN.com might not be the most accurate source of such estimates.

Quote:

Originally Posted by cschaps

1. If the probability of winning for either team found on espn.com, for example, is greater than the implied probability calculated.
2. If the probability of winning for each team taken from espn.com and their respective lines create a positive edge. Of course if they both have positive edges, I would choose the team with the higher edge.

Am I understanding this correctly?

You place a bet if the Kelly stake is > 0. This will be the case if and only if (once again, ignoring hedging) edge > 0.

Unless a scalping opportunity existed there'd be no way for there to be a positive edge
on both a team and its opponent.

Quote:

Originally Posted by cschaps

So assuming the edge on the Phillies tonight is 3% and the line is -152 (this means I am relying on a probability of (1+
.03)/1.66 = 62.05% chance that the Phillies will win, the amount I would wager would be:
.03 (Edge)/1.66 (Odds) - 1 = 4.5% of $10,000, which is $450.

If you were a full Kelly bettor then yes, exactly.

cschaps · 07-09-2008, 04:49 PM

Thanks for the quick response, Ganchrow.

So the edge should always be calculated using a probability determined through an outside handicapping strategy?

If so, what handicapping strategy do you recommend?

And that outside probability would need to be higher than the implied probability to create an edge greater than 0, right?

Thanks again for taking the time to help me understand!

cschaps

Ganchrow · 07-09-2008, 05:12 PM

Quote:

Originally Posted by cschaps

So the edge should always be calculated using a probability determined through an outside handicapping strategy?

Exactly.

Quote:

Originally Posted by cschaps

If so, what handicapping strategy do you recommend

Naturally, the one that works best.

That's the million-dollar question.

Quote:

Originally Posted by cschaps

And that outside probability would need to be higher than the implied probability to create an edge greater than 0, right?

You got it.