Probability Score as a Predictor of Profitability: Part 2

In the previous blog I came up with some rules of thumb (rule of thumbs?) for determining what probability score was necessary to be profitable when following a Kelly-staking or a Level-staking approach, and what probability score was necessary to favour one form of staking over the other.

Briefly, we found that, when the overround is 106%, Bookie Bias is -1%, Bookie Sigma is 5%, and when the distribution of Home team probabilities broadly mirrors the historical distribution from 1999 to the present, then:

1. If the Probability Score is less than 0.035 per game then Kelly-staking will tend to be unprofitable 
2. If the Probability Score is less than 0.014 per game then Level-staking will be unprofitable 
3. If the Probability Score is less than 0.072 per game then Level-staking is superior to Kelly-staking

Taken together these rules suggest that, when facing a bookie of the type described, a punter should avoid betting if her probability scoring is under 0.014 per game, Level-stake if it's between 0.014 and 0.072, and Kelly-stake otherwise.

For this blog we'll determine how these rules would change if the punter was faced with a slightly more talented and greedier bookmaker, specifically, one with an overround of 107.5%, a bias of 0% and a sigma of 5%.

In this wagering environment the rules become:

1. If the Probability Score is less than 0.075 per game then Kelly-staking will tend to be unprofitable 
2. If the Probability Score is less than 0.080 per game then Level-staking will be unprofitable 
3. If the Probability Score is less than 0.074 per game then Level-staking is superior to Kelly-staking (but is generally unprofitable)

Taken together these rules suggest that, when facing a bookie of the type now described, a punter should avoid betting if her probability scoring is under 0.075 per game and Kelly-stake otherwise. Level-staking is never preferred in this wagering environment because Level-staking is more profitable than Kelly-staking only for the range of probability scores for which neither Level-staking nor Kelly-staking tends to be profitable.

Essentially, the increase in the talent and greed of the bookmaker has eliminated the range of probability scores for which Level-staking is superior and increased the minimum required probability score to make Kelly-staking profitable from 0.072 to 0.075 per game.