Greg Gordon's Betting Experiment part 2

In the last article we looked at some basic performance measures to assess how Greg's stable of tipsters were doing. In this article we'll look at how we can use some of this information to formulate a staking strategy.

"Choose the bookie with the best prices, and if using an exchange, look for the lowest commission."

In previous newsletters we have looked at the influence of singles versus doubles betting, fixed-profits versus fixed-stakes betting and how the commission rate at an exchange impacts on your profitability. We have no need to rehash these old arguments - suffice to say, for our purposes we'll adopt the following maxims:

1. Choose the bookie with the best prices, and if using an exchange, look for the lowest commission
2. Bet singles rather than doubles (or higher multiples)
3. Use fixed profits staking rather than fixed stakes

Our next consideration is how much to stake. To answer this, we'll look at each of the services individually and then look at how to combine the results of these individual studies into a coherent staking plan. The first thing we will need to bear in mind when we look at this question is that if we stake too much we run a very high risk of bankruptcy, while if we stake too little we just make less profit than we might otherwise. In other words, it is better to be prudent with our staking initially.

"We should also bear in mind that anything over 10% is exceptional."

We also have to consider that we don't have a huge amount of information, statistically speaking, about the services Greg is using. What we do have is the information from our sample, as shown in the table in the last article. The first thing we can do with this information is to compare it to the published performance on the tipsters websites - if it is comparable, we can probably have some more confidence that this (sample) figure is closer to the underlying long-term performance of the service. We should also bear in mind that anything over 10% is exceptional, and we should certainly be sceptical about any service claiming over 20% yield in the long-term - are the bookies that wrong?

Looking through the figures, the performance of the Sport4profit Singles club claimed on their website shows approximately 16% yield - so we can be fairly confident in the 14% we have obtained in our sample. It is not so easy to see how the Sport4Profit Golf bets have fared from the information presented, other than to see that they have noted a recent downturn on their results page. What we do here is up to the individual, but if I had confidence in the tipsters behind the system then I might assign a low 'theoretical' yield to the system (e.g. 2%) and monitor it closely. Others may wish to just paper trial this service for a while longer.
The Steve Lewis Hamilton site is strangely reluctant to provide hard figures - very odd considering their stunning performance! Our results indicate that it is almost certainly a profitable system (there is a 99.8% chance that it is fundamentally profitable as we saw last time!), but how representative is our sample? What I'd be inclined to do here is to use some basic statistical theory, namely the binomial distribution to estimate a figure that we can be confident in (to some specified level). Those not mathematically inclined may want to skip the next paragraph and just accept the figure I quote now of 53%!

The binomial theorem says that for a sample of n bets, at strike rate p, the expected number of winners is given by n times p. Further the standard deviation in this figure is given by sqrt(n.p.q) where sqrt is the "square root" and q=1-p. The shape of the probability distribution means that 95% of the data will be contained in an interval 1.96 times this standard deviation on either side of the expected value - that is we can estimate a "95% confidence interval" of the number of winners, by adding/subtracting 1.96 times the standard deviation figure above to the expected value. Other confidence intervals will have different 'z-values', e.g. 95% has a 'z-value' of 1.96, while 50% has a 'z-value' of 0.67. From here it is fairly easy to get a confidence interval for the yield. In this example I'm going to use a 50% confidence interval - that is I'll be 50% confident that the long-term yield is somewhere between the values I calculate. n in this case is 78 while p = 26/76. The standard deviation is therefore 4.16. I can be 50% confident that long-term I could expect between 23 and 29 winners for a sample of this size. This gives an interval of 53% to 90% on the yield. We'll take the lower value - still an extraordinary performance!

"This gives an interval of 53% to 90% on the yield. We'll take the lower value - still an extraordinary performance!"

A quick scan of some figures on The Mathematician's site shows claimed past performance of 30%+ yield. In this light we can be happy enough with the yield from our sample of 10%.

Finally Greg's own figures show a non-too-shabby yield of 21%. A 50% confidence interval here would give 9% to 33% for the yield figure. Because it's Greg and because it's Christmas, I'm going to give him an extra 1% and call it 10%!

So for our risk analyis we will use the following figures:

Service	Av. Odds	Strike Rate, %	Yield, %	Bets per month	Units profit per month
Sport4Profit - Golf	8.1	12.6%	2%	18	0.36
Sport4Profit - Singles	1.8	62.5%	14%	7	0.98
SLH Private	5.2	29.7%	53%	11	5.83
SLH Premium	3.0	35.3%	5%	2	0.1
The Mathematician	3.6	30.6%	10%	7	0.7
Gregs Football	3.2	34.4%	10%	10	1

Our next step is to consider what level of risk we are comfortable with. We can use a handy little tool to do this analysis for us. What I am going to do is assume a level of risk that I am comfortable with - in this case the risk of losing half my bank in a 100 bet sequence to be less than 5%, and evaluate the stake size that conforms to this risk profile. The results are:

Service	Stake Size, %
Sport4Profit - Golf	3%
Sport4Profit - Singles	6%
SLH Private	4%
SLH Premium	2%
The Mathematician	2%
Gregs Football	2%

Of course we are using several services in parallel, so we need to reduce these stakes. The way I am going to do is to weight the total staked by the units profit per month. This gives me the following stakes, based upon a notional £10,000 starting bank:

Service	Stake Size, £
Sport4Profit - Golf	£12
Sport4Profit - Singles	£66
SLH Private	£260
SLH Premium	£2
The Mathematician	£16
Gregs Football	£22

I'll expect to make £1600 per month from the above staking plan - a very nice return, with a good balance between risk and return!
Of course we'll need to watch our performances carefully and update our staking once we have enough data to have more confidence in the performance figures.

In the next article I'll look at putting together a basic checklist for setting out on such an adventure.