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15. Using The Kelly Formula

You may have heard how using Kelly's "magic" formula for calculating the next stake will maximise the return to your original Base Bank. It will, if (a) you have a solid advantage over the Bookie and (b) you use the formula properly!

Before you could ever be in the position to use the Kelly formula properly, you must make sure you understand all its components and how they fit together. Then, when you apply it correctly, you will discover something quite amazing in the situation where you haven't got the right "advantage" compared to the "Odds" on offer - it will simply give you a negative answer as the next "stake"! A negative answer means that you should not bet using the Kelly formula, because you stand no chance at all of increasing your original Base Bank.

The straight, unmodified "sports betting" version of the Kelly Criterion formula calculates the amount to stake on your next bet as a proportion of your current Betting Bank. The current Betting Bank is simply your original Base Bank plus your Kelly winnings and minus your Kelly losses to date. The actual proportion of the Betting Bank to stake (which is a "constant" to be applied throughout the entire duration of what you have established to be a full betting "cycle") is calculated as follows:

PROPORTION OF BANK TO STAKE = (Probs x (Odds + 1) - 1) / Odds
Probs = Your previous successes over the total number of Value Bets placed (expressed as a percentage to 2 decimal places)
Odds = The Bookie's Non-Decimal Odds (expressed as a decimal number to 2 places)

Properly applied, the Kelly method of stake calculation is meant to be used for a particular series of related bets, and it tells you the exact proportion of the Bank you should use. It should never be applied to a mixture of different betting scenarios, but some self-styled betting "gurus" will encourage you to do so, simply because they don't know any better. No matter how tempting they make it sound, don't make the mistake of following in their footsteps, because that approach is truly a "kamikaze" one.

A fundamental key to utilising the Kelly formula to its greatest potential is that you need to establish the minimum length of the betting "cycle" required to maximise the returns. This need not be a long cycle at all, but you must be very sure that you know exactly what it is.

Let's look at a practical example where, say, you have established that on average you have a 75% probability of picking the winner where the Non-Decimal Odds average 0.36 (4/11). In such a case the Kelly formula will tell you that you should bet 5.56% of the Bank on every bet; and that value is an absolute constant and must not be changed for that series of bets under any circumstances whatsoever.

However, to establish your minimum betting cycle in the above case it is not simply a matter of saying that, since you have a 75% chance of winning, you need 4 bets minimum so that you will get 3 of them right. Betting never works like that. Instead, what you ideally need to do is to establish just how many times in a row it has been possible to lose in the past before you reached the 75% success target. You only need a few early losses, and it then could be quite some time before you reach your target! For example, 6 losses out of 23 bets will mean than you must win the next bet to have achieved a 75% success rate. And each additional loss makes it harder to catch up on the losses to the Bank, because the actual amount staked (not the percentage) is being reduced each time!

Let me now describe the safest strategy we know of for successful Kelly betting. First, we establish which betting scenario made us the most money last season and the season before. We then calculate our success rate over a "core" 40 weeks duration only for both years, and we apply that as our maximum "probability". Next, we establish the average non-Decimal Odds on offer for our winners across both seasons, and we plug both those factors into the Kelly formula to see the proportion of the Bank we should be staking each week.

You need to be aware of just how sensitive the Kelly formula answer is to even a very small change in the probability! For example, if you drop the above 75% probability to just 72.50%, then the Kelly answer for the proportion to bet is MINUS 1.03% (in other words, don't bet - because you don't have an advantage). It is therefore imperative that you establish that you have at least a 10% "advantage" over the Bookie, so that you have adequate leeway if your probability is not as reliable as you had hoped. In practice, therefore, the "advantage" is what you will probably need to calculate separately for each and every individual bet (so it will be an ongoing process, not a one-off exercise). If a particular intended bet has less than a 10% advantage, drop it!

You may think it would be possible simply to select an Odds value (or a limited range for the Odds) that will ensure that your advantage never alters, but that would be very dangerous, because the selected Bookie's over-round may change, thus altering the true (fair) probability used by the Bookie (and thus your "advantage"). So you must watch this point carefully! The reality is that the "match" over-round may seem beneficial, but the "result type" over-round is a killer (as it usually is where a "favourite" is concerned).

Using the above formula where you have established that you have a 10% minimum advantage and a 75% probability of winning, you could lose the first 30 bets out of 120 and yet still turn ₤1,000 into its maximum amount of around ₤9,000, just as long as you managed to achieve the 66 wins that ensured your 75% track record overall. If you only managed 62 wins you would still have a slight increase over your starting bank. Losing 30 straight bets with a 10% advantage and a genuine 55% win probability is a 1 in 25,000 million chance!

You must remember, however, that even the Kelly formula is subject to the Law of Averages (properly, the Law of Large Numbers), so much so that many aficionados recommend halving the figure that the unmodified Kelly soccwer betting formula gives you as the amount for your next stake. The main reason for doing so is not due to any flaw in the Kelly Criterion formula itself (it is a very sound device), but due to (i) the probable unreliability of the calculation of your "advantage" and (ii) the fact that last season's success rate may not be replicated this season (as the performance of most known Selection Systems has been found to fluctuate significantly from season to season).

If both the advantage and the success rate are found wanting, you will lose all your money using the Kelly formula, whether or not you halve the stake! Our advice therefore is for you to test how you are doing over the first few months of a new season before applying the Kelly formula, to see if both your supposed advantage and your success rate are holding up.

Despite that last statement, in view of the fact that use of the unmodified Kelly formula can cause heavy losses if you have over-estimated your betting advantage, an alternative formula has been concocted that will limit the stakes to about half that derived from use of the unmodified formula. It has also been generated to simplify remembering the formula, and now reads:

ADV = your Advantage (expressed as a percentage)
ODDS = the Bookie's Non-Decimal Odds

One further modification, which reduces the stake even further, is to use the Decimal Odds as the divider in the above alternative formula.

Having explained why the alternative formulae have been introduced, we wish to make it clear that we cannot see their usefulness, because they negate the whole purpose of the Kelly formula (which is to maximise your returns from the Odds on offer, where you have confidence in your advantage and success rate).

If you feel that you need to use a watered down Kelly formula stake level, then we suggest that you haven't got the strength to make the play in the first place; you must obviously feel that either your advantage or your success rate is weak. If either is true, you would be very unwise to employ the Kelly formula. If you are sure on both points however, then the Kelly formula is absolutely the best solution there is for maximising your returns. But do make doubly sure that you can really trust your Selection System, otherwise mistakes will cost you dearly.

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Last Updated: 20-Jan-2017 08:20 GMT
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