I am not a Kelly man, but I can tell you how I back test Kelly in this case. I use a program to go back to each previous day and run the model for that day. I then use the odds for that day to compute the model's expected return for a variety of wagers. For those with positive expected returns I generate a pseudo wager using Kelly (or whatever bet sizing method I am testing). The program then grades the wager based on the actual results. I then analyze the returns of these pseudo wagers. It's quite simple to back test.