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Staking: Fixed Or Variable?

There is some debate about whether it is better to follow a fixed staking strategy or a variable staking strategy.

To be clear, what we are discussing here is fixed staking returns a variable amount, the amount depending on the price, while variable staking returns a fixed amount, with the stake depending on the price.

The assumption here is that your selections have a positive expectancy (an edge in other words) and that your edge is not known accurately enough for you to be able to stake using Kelly, which is proven to be the optimal staking strategy.

Unfortunately the nature of sports betting means that we often don’t know exactly what our edge is, so a broader approach to choosing our staking method is required.

Fixed Staking

Fixed stake betting is simple – you put one unit on a selection at whatever price, and your profit will vary. If you are backing at odds-on, your profit will be less than your stake. If you are backing at evens, your profit will be equal to your stake, and if you are backing at odds-against, your profit will exceed your stake.

Profit = Decimal Odds – Stake

Examples:

At odds-on, 1 unit staked at odds of 1.50 (or 2/1 on) returns 1.5 units which is a profit of 0.5 units.

At evens (2.0), 1 unit staked returns 2 units, a profit of 1 unit.

At odds-against (3.0, 2-1), 1 unit staked returns 3 units, a profit of 2 units.

Variable Staking

Variable stake betting is almost as simple – you put a stake on to return a profit of one unit. Incidentally, the notion that variable staking is somehow more sophisticated, or for more experienced investors, is palpable nonsense. Anyone who is capable of calculating value is more than capable of calculating the stake required for a fixed return.

Stake = Profit / (Decimal Odds – 1)

To return a profit of 1 unit, the stake will be the reciprocal of the decimal odds minus one.

Examples:

At odds-on, at a price of 1.50 (or 2/1 on) the stake would be 2 units, 1 / (1.5 – 1).

At evens (2.0), 1 unit staked returns 2 units, a profit of 1 unit.

At odds-against (3.0, 2-1), 0.5 units staked returns 1.5 units, a profit of 1 unit.

For Better Or Worse

Having established the basic terms and definitions, the question now turns to the discussion on which method is better.

The answer is that you need a definition of ‘better’ and that it depends.

If you are interested in two or three outcome events, where the range of odds is relatively narrow, then my opinion is that it really makes little difference in the long run.

If you are looking for a method to use in a sport such as horse racing, and have selections at longer prices, then you are better off using the variable staking approach.

Better off in what way? Many of us might consider ‘better off’ to mean applying the strategy that maximises our profits. However, even with a positive expectancy (edge) on our selections, the possibility of losing our bank exists, so protecting against this is also important.

The mathematics prove that variable staking reduces the probability of going bankrupt, but the benefits of variable staking are found when betting at longer odds, i.e. where the losing sequences are likely to be considerable, and the possibility of busting your bank is higher.

An Example: Betting On Soccer

For a sport like soccer, or at least in the two or three outcome markets in that sport, the benefits are minimal at best given that the likelihood of bankruptcy is much smaller assuming your stake size is reasonable relative to your bank and selections do not consist of frequent long-shots.

If your bank is headed to bankruptcy while staking sensibly at the lower odds found in soccer, you might want to reconsider whether or not you still have an edge on your selections.

For sports where the range of odds is relatively narrow, what difference does it make whether you bet a fixed stake or for a fixed return?

A few simple experiments will show that the differences depend on the following assumptions and factors:

If we look at the prices more typical in soccer, (perhaps 1.3 to 4.0 would cover the majority of them), and adjust the various parameters, we see some interesting results.

For example, if you have 100 bets at 14 odds-on prices (1.3 to 1.95), 100 bets at evens and 100 bets at odds-against from 2.1 to 3.6 and assume an edge of 5%, your 2,900 bets will result in a profit of 145 points to level staking, (risking 1 point) and a profit of 173.34 points using variable staking (to win 1 point). Your outlay will total 2,900 points and 3,467 points respectively and your ROI is, unsurprisingly, exactly 5%.

  Fixed Stakes P/L ROI% Variable Stakes P/L ROI% F/V
Total 2900 +145.00 5.00% 3467 +173.34 5.00% 83.65%
Odds-On 1400 +70.00 5.00% 2529 +126.44 5.00% 55.36%
Evens 100 +5.00 5.00% 100 +5.00 5.00% 100.00%
Against 1400 +70.00 5.00% 838 +41.90 5.00% 167.06%

The differences between the two staking methods are clear. At odds-on, variable staking leads to greater profits, and odds-against fixed staking is more profitable. Obviously at evens, the two staking types are identical.

However, this example has a higher volume of bets at the higher prices, so to see a more realistic example we can make the increments at odds-on 0.05 and re-run the numbers.

Now across 35 prices, we stake (fixed) 3,500 points and variable 3,695 points and profit by 175 points or 184.74 points respectively. When we are betting more at odds-on, variable staking performs better, because at odds-on we are staking more, but the ROI is still the same at 5%.

It is often argued that edges are harder to find at odds-on, so another experiment we can try is to determine the effect on our returns of using a smaller edge starting at 1% for 1.3 and increasing to 4.4% at the 4.0 price.

The fixed staking now returns a profit of 94.5 points (2.7% ROI) while the variable staking returns 75.44 points (2.04%).

Conclusion

These are very general and broad examples, and the results will be different for every individual depending on the prices, the size of your edge, and the volume of bets at each price, but the conclusion is that for football betting, there is no proven benefit for variable staking than for level staking.

If you want to see how returns will vary for yourself, put together a spreadsheet and play with the numbers.

 

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