Based on the 2007 paper, Algorithms of Optimal Allocation of Bets on Many Simultaneous Events by Chris Whitrow, the Kelly criterion for the bets should be used for multiple simultaneous bets (like betting on football games that are playing at the same time) when the number of bets is small. In other words you should use the Kelly bets for instances where the total percentage of the bets is not near your whole bank roll. As you number of bets increases, and the sum of the bets approaches 100% of your bankroll you should bet the percent of the better's edge.

The better's edge is
your probably of getting the bet right minus the book probability
which is measured as the 1 / (book odds + 1). For instance, in a
college football game where I predict I have a 60% probability of
being right and the house had 100/110 odds on game, the book
probability would be 1/(100/110 + 1) = 0.524. The better's edge in
this instance would be 0.60 – 0.524 = 0.076 or 7.6%. So, I would be
7.6% of my bankroll on the game.

Also, according to
Whitrow's computer models for optimal performance if the percentage
of bets is greater than 100% of your bankroll scale the bets so they
are under your bankroll limit based on the better's edge.

This conclusion from
the paper is based on empirical evidence and not theory where the
author did not know why this observation was happening. The empirical
evidence and model was convincing, and I will use this system for my
bets.

#### How will it work in practice

For simplicity, let
us say I have $1000 in my bankroll for the picks for October 3, 2014
and October 4, 2014.

On October 3, my
prediction algorithm picked 2 games with an advantageous
probabilities:

- Syracuse +2.5 vs Louisville at a 75% probability of being correct with a 48% Kelly criterion
- San Diego State +3.0 at Fresno State at a 54.55% probability of being correct with a 5% Kelly criterion

By adding up the
Kelly bets, 48% + 5% = 53%, the total bet of the payroll does not get
close to 100% of my bankroll, so according to the paper's author
Kelly betting is optimal.

On October 4, my
prediction algorithm picks 20 games where I have an advantage, where
the sum of the probabilities,

.48+.48+.40+.33+.33+.27+.25+.19+.17+.16+.1+.1+.08+.06+.05+.04+.03+.03+.02+.01=3.58
or 358%, obviously, I cannot bet over 100% of my bankroll. For this
situation, the author's paper concludes that the optimal would be
percentage of the bankroll approximately the better's edge. So, using
the better's edge as the percent of bankroll to bet is advised.

Given
the better's edge values from October 4,

.23+.23+.19+.16+.16+.14+.13+.12+.09+.08+.08+.05+.05+.04+.03+.02+.01+.01+.01
= 1.83 or 183% of bankroll which is still not possible. The author
then recommends scaling the bets, so the values are less than 100% of
bankroll or if you want to be more conservative less than the percent
of bankroll you want to bet at a given time. I am comfortable betting
on all the bets recommended by the algorithm due to the very low
probability they will all be wrong. The scaled bets would become

0.12 0.12 0.10
0.08 0.08 0.07 0.07 0.06 0.04 0.04 0.04 0.02 0.02 0.01
0.01 0.01

respectively for the
first 14 games, and I will drop off the ones below 1%. Using this
metric my total betting of my bankroll would be 88%.

This is system I
tried for this Friday and Saturday of Week 6, I have not modeled it
my algorithm yet, but I thought I would take a leap of faith, and
model it later.

I really enjoyed reading your article. I found this as an informative and interesting post, so I think it is very useful and knowledgeable. I would like to thank you for the effort you have made in writing this article.

ReplyDeleteThis post is on Algorithms based sports by Dr.Wag`s Picks.He has Optimized Betting and Horse Racing Odds for Multiple Games at the Same Time.Thanks for an interesting post keep sharing more info related it.

ReplyDeleteFor +2.5 decimal odds (1.5-1 fractional odds), with 0.75 probability, does not the Kelly criterion yield (1.5*0.75 - 0.25)/1.5 = 0.58 ?

ReplyDeleteWhere does the 0.48 come from?

I was assuming -110 in US odds, or a 0.91 return a winning bet and +2.5 was the against the spread line. Where the equation would be ((0.91 * .75) - 0.25)/0.91. which would be .475.

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