14. Making Sense Of The Kelly Criterion

The Kelly Criterion is a staking method that is outstandingly brilliant when the advantage is on your side, but otherwise is completely dysfunctional! It takes its name from a certain John L Kelly from the USA (who worked for AT&T's Bell Laboratory). He was nobody's fool, as researching into his mathematical formula will show you. But, following the formula's modification to allow the "optimum" value of a Bettor's next stake to be calculated "with precision", the Kelly Criterion has picked up an army of detractors.

The original formula was never intended for gambling. Its application was of a technical nature, designed principally for use in the field of communications engineering. However, some other talented people picked up on its potential and adapted it for use with stock market trading (to calculate the investment to be placed on each transaction), after which it was then adapted to sports betting.

The basic Kelly formula was constructed to take account of the fact that for certain activities (such as the received strength of a signal sent over a long distance) the outcome is variable from "test to test" or "event to event". What Kelly concentrated on was how to capitalise on knowing what the "average" outcome would be where that outcome had a high level of reliability (for soccer betting that translates to "edge" or "advantage").

The beauty and strength of the modified Kelly formula for soccer betting lies in the fact that, if you have correctly established that you have an advantage over the course of a whole season because your reliability is high compared to the level of Odds on offer, then you can lose the amount you thought you would lose almost anywhere in the sequence (up to a maximum of about 30 straight losses), yet you will still receive the maximum return by or before the end of the season. The Kelly formula does this by use of a proportional staking algorithm derived from the application of calculus, adjusting the level of the stake each time according to the amount remaining in your bank.

The major problem in the application of the Kelly formula is that people ignore the fact that they must - absolutely must - establish that they have a genuine advantage first! Without that as the basis, using the Kelly formula will undoubtedly bankrupt you (although perhaps not as fast as some other Staking Plans such as the Martingale).

The Kelly Criterion's bad reputation has arisen largely because certain self-styled "betting gurus" apply it in a totally inappropriate way, completely unaware of their error. These are the ones who make statements such as "Your advantage is what you think the chances of a win are compared to what the Bookie thinks." Such a statement is absolute nonsense, showing that the concept of "advantage" has not only been totally misunderstood but not even grasped at the most basic of levels.

Another good example of where the Kelly Criterion is maligned is where the "gurus" warn you that sometimes the Kelly formula will tell you to bet more than 25% of your current Bank. The reality is that such a situation could only occur where you have a highly reliable chance of winning (60% minimum chance) on a long-term basis, and where the Decimal Odds offered are at least 2.15! Do you honestly think that scenario is likely with soccer betting? [Don't listen to those charlatans who try to tell you that they can provide you Asian Handicap predictions that will achieve that goal!]

The two examples above of the blind leading the blind typify 99% of the advice given to punters on how to use the Kelly formula for soccer betting. Is it any wonder then that the Kelly concept has such a bad name?

Now, there are many websites that will take you step-by-step through the maths leading to the culmination of that final "magic" Kelly Criterion formula, although most of them are very hard for the average person to follow due to the calculus involved. We are not going to attempt the same thing here because, for those who have the maths knowledge and the desire to prove the formula's validity for themselves, all they have to do is type the words "Kelly Criterion Football Betting" into a good search engine.

Here, we simply intend to tell you why we consider the Kelly Criterion to be a very well constructed mechanism (perhaps, even, a stroke of pure genius). Particularly, we will concentrate on explaining why the Kelly formula works and what its potential problems are.

In essence, the Kelly Criterion as modified for sports betting is a proportional staking formula, which adjusts the level of the stake for each successive bet according to the amount remaining in the Betting Bank. It is "unbeatable" when calculating what the value of your next stake should be in a situation where you know for sure that you have an advantage. However, if you cannot establish that you have the advantage, then the Kelly Criterion is totally inapplicable, because its "magic" formula will not be able to return a valid (positive) answer - in fact, it will give you a negative figure.

Many people have written off the Kelly Criterion as a "kamikaze" staking method primarily because they have completely understood this need for a real advantage to be present. But what could possibly be wrong with a formula that, in effect, GUARANTEES that, provided you are correct with your estimation of your betting advantage, you will be able to maximise the increase to your starting Base Bank? Well, the rub is there in that last proviso, because (a) how do you know you have an advantage at all, and (b) how can you be sure that your estimation of your advantage is correct? So let's deal with these two issues:

1. To establish that you have an adequate advantage when using the Kelly formula, you first need to be sure that, for each bet, you are looking at something approaching a "Value Bet". The higher your true advantage, the more the chances that you will achieve the desired outcome of making money.
2. Determining a true Value Bet is a 2-stage process: (i) accurately establishing what you think the probability for achieving a given result is, and (ii) establishing what "true" probability the Bookie's Odds translate to.
3. The probabilities that you determine for any given match MUST BE as a result of a statistically-driven and verifiable approach to such determination; anything less and you would be very unwise to employ the Kelly formula. In practise, this means that you must employ a good Selection System that is capable of establishing probabilities to a proven high degree of accuracy, and offering a good "comfort level" (meaning "robustness" must be evidenced in the numbers and the spread of the previously correct predictions - see item 5 below).
4. The probability figure utilised by the Bookie to determine the Odds is established by dividing the Decimal Odds into the number "100". Thus, where Odds of 2.44 are offered for a Home Win, that translates to a probability of 41% of that result being achieved (100/2.44). This would mean that the Bookie thinks that the true (fair) probability (the one you need for comparison when using the Kelly formula) is nearer 35% (where the difference is the allowance built in for the Bookie's "over-round" (the profit margin) of generally between 6.5% and 12.5% on 1X2 betting).
5. Finally, to be sure that your advantage is genuine (and not just wishful thinking on your part), you need to establish your true success rate when picking Value Bets. It is simply a matter of dividing the number of successes by the total number of bets placed, and multiplying by 100. You will only be able to do this properly if you have kept an accurate record of the number of bets placed, and established that the level of the "advantage" in each case is meaningful (that is, it is above the minimum level you wish to operate from). For this exercise to be valid, you also need to ensure that the number of bets placed is large enough to be meaningful (meaning that 6 successes out of 10 bets placed offers nowhere near as strong a "comfort level" as 55 successes out of 100 bets).

Before deciding to use the Kelly formula to calculate your stakes it is also important to fully comprehend the mechanics of the "cycle" that will give you the maximum return in a season, so that you will know when to stop betting within a given betting scenario. Otherwise (assuming you were "spot on" with your estimate of your advantage) you would risk losing what you had had gained, never to recover it!

For example, if you have a reliable track record to show that your average success rate is 30 out of 50 bets (which translates to a 60% probability), but for the past 40 bets you have won 32 times (making 80% accuracy), then you would risk losing most (or even all) of what you have gained if you continued to use the Kelly formula stakes for the remaining 10 bets. So, if you are going to use the Kelly formula, then it is essential that you try this out on a spreadsheet until you fully understand exactly how far any remaining "cycle" must extend to enable you to achieve the optimum return! If you can't do that, then our advice is that you just shouldn't use the Kelly formula at all!