The Kelly criterion optimises the expected return on a series of identical, sequential bets. The criterion gives the ideal ratio of the bank roll that should be placed on a bet.
If a single bet has a positive outcome with objective probability p and a negative outcome with probability q=1−p, then the Kelly criterion is given by κ=αwp−αlqαwαl, where αw is the multiplies of the amount of stake that is won in the case of a win and αl the amount proportional to the stake that is lost. Many exchanges, such as Betfair, use the decimal odds system. When backing a selection in the decimal system, the losing amount is the stake itself, so αl=1, and the winning multiplier is the quoted price P−1. Additionally, commisions are typically proportional to winnings, which further reduce the potential winnings.
The kelly_back_dec
and kelly_lay_dec
functions allow for a quick calculation of the Kelly criterion given the true probability, the quoted price and a commision percentage.
library(RKelly)
# A bet to back at price 2.1 and objective probability of 0.5 and 5% commision
kelly_back_dec(price = 2.1, p=0.5, commision_rate = 0.05)
#> [1] 0.0215311
The same applies for lay bets where αw=1 and αl=P−1.
# A bet to lay at price 1.9 and objective probability of 0.5 and 5% commision
kelly_lay_dec(price = 1.9, p = 0.5, commision_rate = 0.05)
#> [1] 0.02923977
A negative Kelly criterion means that the bet is not favored by the model and should be avoided.
kelly_back_dec(price = 1.9, p=0.5, commision_rate = 0.0)
#> [1] -0.05555556
Use at your own risk. More detailed derivations can be found here. here/