What are the bankroll implications if we keep the bet size and edge constant but vary the odds? The chart below plots the probability of various drawdowns (from starting bankroll) when a bettor places 1,000 1 unit bets at various odds, with an edge of 4%. Each series of 1,000 wagers was simulated 10,000 times.
Recall that when betting at odds of 2.0, there was a 17.4% chance of being down 20 units at some stage through a series of 1,000 bets. At odds of 5.0, the chance of a 20 unit drawdown increases to just under 60%. With an identical stake, edge and expected return from a series of bets, predominantly backing favourites or longshots has drastically different bankroll implications in terms of variance.
Understanding what type of bettor you are is therefore critical to dealing with the inevitable swings you will experience.
To quantify this variance, consider again a series of 1,000 bets. By varying the odds (implied probability from 10% to 90%) and edge, the chart below plots the standard deviation of returns.
We can see clearly that variance increases as the odds lengthen (or as implied probability decreases), in line with the analysis above. From the chart above, making 1,000 1 unit bets with 10% edge has a standard deviation of 6.5% if all bets are made at 5.0 compared to 2.5% betting at 1.67. In both cases the expected return is +100 units (+10%).
An interesting result is that for odds shorter than 2.0, as edge (and thus expected return) increases, standard deviation actually decreases. Finding an increasing edge in odds shorter than 2.0 is rewarded not only by the increase in expected return but with a reduction in variance.