How much of a losing run can you expect when you make a series of bets? In this article Garry Robinson talks to a mathematician who has examined all aspects of this vital betting factor.

GR: (Garry Robinson): The mythical average punter is always on the lookout for the average losing run of any system. Is it possible to actually find out the likely run of outs a punter can expect?

TA: (The Turf Accountant): Let's look at losing runs from a purely mathematical viewpoint. Taking a strike rate of 50 per cent for example, the average losing run, by definition, is two, and if that would occur in order we would have simply winner/ loser/ winner/ loser and so on. A simple double-up staking plan would ensure a comfortable profit. Alas, it doesn't happen as easily as that.

GR: I know that, and so does every other punter, so what's the worst run we can expect?

TA: No mathematician is going to make an unqualified statement about a maximum run of outs in relation to a given strike rate without the qualifications of the sample size. The mathematical probabilities suggest that the longest run of outs for a 50 per cent strike rate will be:

4 in a sample size of 10
8 in a sample size of 100
12 in a sample size of 1000 etc.

It's a simple matter of adding 4 to the run of outs for each power of 10. In my "Theory of Mathematics for the Punter" I usually use a sample size of 5000, on the basis that the average punter would have around 500 bets per year, and would consider the longest run of outs that is mathematically probable once in 10 years. Since the probability of the occurrence is once in 10 years, we can assume it would happen within five years from any random point.

GR: Or not happen at all?

TA: You'd have to be lucky. I won't bore you with the details but there is a formula that I have used to calculate the likely losing runs that an average punter might strike in two years of punting. As you can see from the chart, the losing runs get proportionately longer as the sample size increases, particularly for the poorer strike rates.

Sample Size

Strike Rate 101001000
10%1 winner in ten21*4466
12.5%1 winner in eight 17*35 53
16.7%1 winner in six 12*2639
20%1 winner in five1021 32
25%1 winner in four81726
33%1 winner in three 61219
50%1 winner in two4812

* There is a strong possibility of no winners at all in this sample size.

GR: It does make one take a second look, doesn't it?

TA: The reason that this chart is much more pessimistic as any you will see elsewhere, is that the table normally presented to represent the probable longest run of outs is usually really only a table of the average expectation of runs of outs. It is a distinctly different proposition, as any punter who has experienced the worse than average run of outs, knows to his sorrow.

GR: I think I know what you mean. I was researching a system based on the first two favourites recently. We all know that the winner will come from this pair around 50 per cent of the time, but on this occasion I encountered a losing run of 16 races.

TA: Yes, it's true. Compare the 1000 column to any two years you have experienced with any system you can name and I think you'd agree that the run of cuts shown there is far more realistic.

GR: There are two lessons to be learnt here. The first is to find a suitably cautious staking plan and the second is that a long losing run does not mean that there is anything wrong with the system you're using, as we are dealing purely with probabilities here.

TA: The strike rate for favourites is about 33 per cent. The longest run of cuts usually expected is about eight to 10, not the 19 suggested here. Would a punter backing favourites long term be safe with a staking plan that busted after nine losses? Or would he be better off with one that could sustain a losing run of 19 or more?

GR: That argument answers itself. Is there anything the average punter can do to improve his chances of coming out a winner?

TA: Garry, the message is clear. The way to reduce losing runs is to improve your selection plan. If you can effectively eliminate those horses that, logically, shouldn't win, your strike rate will go up and your losing runs come down.

By Garry Robinson