Best Odds Guaranteed

The Question

A lot of bookmakers offer what is called BOG or Best Odds Guaranteed. It means if you take an Early Price (EP) on a horse and the Starting Price (SP) is greater than the price you took, then you are payed at the better odds. Grammatically, it should be marketed as "BETTER" Odds Guaranteed and not "BEST" Odds Guaranteed but let's ignore that and investigate if this offer gives value to the punter and how much value.

The Data

I have been collecting price data on and off for horse races over the past year. The result is that I have a set of data for prices on all horses at different times of the day for a subset of all races ran last year. I have filtered this data to find the price available on Bet365 for each horse where I have recorded a price between the hours of 10am and 11am.  Since this data was collected ad hoc I don't have data for every horse, but the horses where I do have data, the data is accurate.

I have collected a second set of data fr…