# Is Kelly’s Criterion Effective in Horse Racing Betting?

Experienced punters would suggest that a proper staking plan is as important as finding winners when trying to attain long-term profit. Let’s face it, even the best ‘system’ will have extensive losing runs. If your current method of staking is unable to get you through these rough patches, it is a waste of time because you won’t benefit from the winning runs that make your system worthwhile in the first place!

When you think about it logically, it doesn’t make sense to use flat stakes on every bet regardless of the odds. At least that’s the theory behind the staking method known as Kelly’s Criterion.

**What is Kelly’s Criterion?**

It is a mathematical formula developed by John Kelly in 1956. He created it to help his fellow communications engineers and was not looking to find an edge in sports betting. Nonetheless, Kelly’s Criterion was used on the stock exchange before finally becoming a tool of the gambler.

First and foremost, there **must be an edge **or else the formula recommends no bet. It has been misused by novice punters who try to shoehorn in an edge where none exists. As a result, it is best used by experienced handicappers who have a track record of finding overpriced horses.

Here is the formula:

*f* = (bp – q)/b*

- f* = The fraction of your total betting bank you should wager on the event. For instance, you could bet 1/10 of your £700 bank which means a £70 bet.
- b = Odds in decimal form -1. 4/1 = 5.00 for example. But at 4/1, b = 4.
- p = probability of success.
- q = probability of failure.

**Theoretical & Real-World Examples**

First, I will use a theoretical example using a £500 bank on a horse at odds of 4/1 (or 5.00). This technically equates to a 20% chance of winning. However, you believe the horse’s **true **odds should be 3/1 (or 4.00) which equals a 25% chance of winning. In this example, your edge is 5%. Here is the formula in action:

(p) = 0.25 (probability of winning is 25%).

(q) = 0.75 (probability of losing is 75%).

(b) = 4

= (4*0.25 – 0.75) = (1 – 0.75) = 0.25

f* = 0.25/4 = 0.0625

To determine the right percentage, multiply the final figure x 100. In other words, you should bet 6.25% of your total bankroll. In this example, your bank is £500 so your bet on this event should be £31.25.

**Real World Example Using Profit Recall**

If you have no idea whether a horse is overpriced or not, it is worth checking out Profit Recall. One of its many functions involves a look at the odds a horse **should **be based on a large and complicated set of calculations by The Race Advisor and its software.

In the above example, *Spinart *is given a 13.66% chance of winning the race by Profit Recall which means its odds should be 7.32.

The horse’s odds were 8.2 about 20 minutes before the race which means it is slightly overpriced. If you believe *Spinart *has a chance of winning, here’s how you use Kelly’s Criterion based on a bankroll of £1,000.

(p) = 0.1366

(q) = 0.8634

(b) = 7.2

f* = (7.2*0.1366 – 0.8634)/7.2

f* = (0.98352 – 0.8634 = 0.12012)

f* = (0.12012 / 7.2) = 0.016683

Kelly’s Criterion suggests that you should bet a maximum of 1.67% (rounded up) of your bankroll which equates to £16.70 in this example.

**Is It Useful for Horse Racing?**

There is merit to the idea of using Kelly’s Criterion to get the most out of value bets. Ultimately, the only realistic way of making money long-term is by finding and betting on overpriced horses. Therefore, a horse at Evens is not worth a bet if it has a 47% chance of winning while a horse at 20/1 is worth backing if it has a 7% chance of victory.

Alas, the trick is to find ‘overpriced’ horses in the first place. As Kelly wrote in 1956, the criterion is only valid when the game/investment is played numerous times with the same winning and losing probability every single time. For instance, you know what the odds of betting on black at the roulette wheel (assuming it is always the wheel with one ‘0’) are and also realise that they won’t change. However, the house has the edge so you can’t use Kelly’s Criterion. In horse racing, no two races are ever the same.

Regardless of how knowledgeable you are or how accurate your software is, it is impossible to calculate precise probabilities in horse racing or any sport for that matter. If your percentages are out even slightly, it plays havoc with your bankroll and you can quickly become bust. Kelly’s Criterion also assumes that you can start again if your entire bankroll is lost (going into negative equity).

There is a slight possibility of effectively using Kelly’s Criterion if you are a vastly experienced handicapper. However, there is simply no way to guarantee the complete accuracy of every single race; this is even the case with the Profit Recall software. It is accurate but not perfect and the rigid criteria of the Criterion mean perfection is a must.

If you are a novice, Kelly’s Criterion is a disaster waiting to happen. All it takes is a reasonably small statistical error to ruin everything. For example, if your data suggests a horse has a 40% chance of winning instead of its real chance of 35%, you will end up staking far more than you should. If your data tells you to bet 40% of your bankroll, are you willing to do so? Sensible punters would say ‘NO’ but if you don’t do it, and the probabilities are correct, you don’t get the most out of the formula.

**Final Thoughts on Kelly’s Criterion & Horse Racing**

In the end, you ‘can’ use Kelly’s Criterion for horse racing but it is best to use an ultra-cautious method of betting. For example, rather than adhering to the maximum Kelly stake, you could reduce your stakes and elect to bet half or even quarter of the recommended wager.

Aside from the uncertainty over a bet’s probability of winning or losing, wagers with seemingly large edges require a huge investment. Most betting experts now tell punters to divide their bankroll into units and wager no more than 2% of their entire bank on any single bet.

You could also choose your stakes based on how confident you are rather than relying on flat stakes. After all, it is statistically a bad idea to bet the same amount on a 33/1 shot than on a 2/1 shot. Why? Since 2010, horses at SP odds of exactly 2/1 have won 30.29% of their races, not far off the ‘right’ figure of 33.33%. Meanwhile, horses at exactly 33/1 SP have won just 1.39% of races, way below the ‘correct’ figure of 2.94%.

When you perform further calculations, you can see that 33/1 shots win less than half as often as they ‘should’ while 2/1 horses win slightly over 90% of the races they are ‘supposed to’. It stands to reason that on average, shorter odds horses represent a better overall value which is why a flat stakes strategy is not always the right idea.

Hi there

Thanks for your article. One of the better ones explaining how to use the Kelly criterion.

However (and I may be mistaken here)…

In the Spinart example you have (b) = 7.2 should it be 7.32?

I am trying to understand the application and the 7.2 has thrown me. Is it the price currently trading (8.2) less one? Or is it a typo?

Regards

Aidan

Hi Aidan,

Spinart’s odds are 8.2. However, in Kelly’s Criterion, you subtract 1 from the odds, so in this case the b figure is 7.2.

The 7.32 figure comes from the fact that Profit Recall gave it s 13.66% chance of winning. As its ‘true’ odds (according to PR) of winning are below the odds offered by the exchange, we have an edge.

I hope this explains things!