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Variance and the Importance of Sound Bankroll Management
Two of the most common questions we receive in relation to horse racing investing are:
- “How much can you expect to win?” and,
- “If your tips are so good why do you go on a losing streak?”
Let’s break this down into several parts. As an example, we may price a horse at $4 (25% chance of winning), but the horse is $5 (20% chance of winning) with the bookmakers. When this situation occurs, we may determine this to be a suitable investment. Tips are only provided when the rated price is shorter than the odds available in the market. This is the basis of punting profitably.
The mathematical definition of expectation is the sum of probabilities of an outcome, multiplied by the “payoff” when that outcome occurs. In the examples to follow, the payoff is the amount that you either win or lose.
If you were to bet 1 unit at $5 with a horse that we rate at $4, this means 25% of the time you will win $4, and the remaining 75% of the time you will lose your $1 investment. Mathematically, the expectation is: (4 x 0.25) + (0.75 x -1) = 1 - 0.75 = 0.25. So for each unit you bet, you expect to receive a profit of 0.25, or a profit on turnover of 25%. If you bet $100 a unit, on average you will receive $25 of profit on each bet. Given the number of bets we provide, and the effect of compounding, profits can grow very quickly.
Where the expectation is a positive number, the terminology is ‘+EV’ (Positive Expected Value). Obviously, and clearly, the better the odds you get for an event the higher your expectation. If you managed to find a bookie offering $5.50 instead of $5, your expectation would be (4.5 x 0.25) + (0.75 x -1) = 37.5%. That is a huge difference and demonstrates the importance of having access to as many bookmakers as possible, and meticulously finding the best odds on offer. In addition, bookies offer sign up bonuses of up to $500 which both reduce your initial risk as well as giving added impetus to your bankroll growth.
Obviously, however, if you only bet once you aren’t going to receive a profit of 25%; You will either win and receive a 400% return on your investment, or you will lose, resulting in the loss of your entire investment or a profit of -100%. As you can see, both of these outcomes are significantly different from the expectation of a profit of 25%. The varying results you get away from the expectation is called variance.
The more events you bet on (mathematically speaking an increase in sample size), the less variance there is. As the sample size increases, the actual return will trend to the expected return. This is why you will not see a return of 25% after one event, but you will start seeing it after 100 events or more.
Looking into variance another way, let’s say that you and a friend toss a coin. If it comes up tails, you get $2. If it comes up heads, you need to pay your friend $1. Obviously this is a great bet for you, but you are going to lose 50% of the time. There will be stretches where heads comes up numerous times in a row and as a high percentage of a specified sample (say, 8 out of 10 tosses). This is natural statistical variation and is unavoidable.
The coin example also demonstrates the importance of having a bankroll and managing it appropriately. Imagine if you only had $1 - you have a 50% chance of going bust after just one toss (and this doesn’t include the probability of winning the first toss but then going bust after a run of heads that your bankroll cannot sustain) and missing out on what would be highly profitable betting situation – what a waste!
Clearly, the larger your bankroll, the smaller the chance you have of going bust. At the same time, if you bet too small a percentage of your bankroll per event you will be unnecessarily giving up potential profits without making a meaningful reduction in risk. An important concept here is that there are only a finite number of events to place a bet on.
Back to the coin example; imagine you could only engage in 10 tosses. If you bet a tiny percentage of your bankroll, you could be sure you wouldn’t go bust but you could also be certain that you would make little profit relative to your bankroll. The aim here is to outlay as much as possible while still removing, or greatly mitigating, the risk of going bust (depending on your risk tolerance). This is a fine balancing act and falls under the realms of a concept called maximizing ‘+EG’ (Positive Expected Growth), and is a central tenet of astute bankroll management.
At Winning Edge Investments, we structure our bankroll and betting amounts to try and minimise the chance of going bust while still allowing the ability to make significant profits relative to the bankroll outlay. Essentially we have produced strategies that are optimal on the risk/return scale.
What this all means, is that Horse Racing investing is a long-term exercise.
In the short term, variance leads to fluctuations in betting results. But in the long term, the ability to pick winners & place bets on +EV situations will ensure sustainable profits.
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