How do I know if I have a winning system?

It is impossible to give a definitive answer to these questions, but what we can do is to use the science of statistics to estimate the probability that we have a winning (or losing if that is the question) system.

Most statisticians will, as a rule of thumb, look for 99% 'certainty' before they have a confidence in a system, so we will adopt that stance too. However, exactly the same priniciples apply for 95%, 99.9% or any other 'certainty level' that you desire to use.

Most statisticians will look for 99% 'certainty' before they have a confidence in a system

1) Estimate, or calculate the overround on the bets that you have made.

This will vary from sport to sport, and will strongly depend on how much shopping around you do for the best prices. To take an example - if you bet on the 1X2 market for English Premiership football, an individual bookie will typcially have an overround in the region of 11%. If you select from a range (e.g. 5 or 6) of bookies, you will normally bring this down to circa 5%. Lets assume for the rest of our example that the overround is 5%

2) Calculate the average odds at which you have bet.

Lets say 2.31 for our example

3) Multiply the odds above by the overround e.g. 2.31*1.05 (5% overround) to get the 'bookies fair odds'. In this case that gives us a value of 2.43

4) Invert the answer from (3) above to get the 'bookies true chance'

i.e. the probability of winning as estimated by the bookmaker. In this case 0.412, i.e. 41.2% chance. This is effectively the 'strike rate' that the bookie would expect you to have on the market.

5) Multiply the answer from (4) above by the number of bets made.

Lets say we have made 165 bets, we would get an answer of 165*0.412=68.03. This is the number of winning bets that the bookie would expect you to have, assuming you had guessed randomly (according to the odds offered). 68.03 winners from 165 bets, means that the balance, 96.97 bets, were losers.

6) Note the actual number of winning and losing bets that you had

lets say 75 and 90.

7) Use the 'Chitest' function in Excel to evaluate the following: CHITEST(A1:A2,B1:B2) where cells A1 & A2 contain the actual number of winning and losing bets (i.e. 75 and 90 respectively in our example), and cells B1 and B2 contain the estimated number of winners and losers, i.e. 68.03 and 96.97

"Be extra careful with back-testing as it is extremely easy to data-mine."

8) The answer returned in (7) above, i.e. 0.27, is the probability that the number of winners and losers you obtained is as a result of chance, i.e. just a lucky run. In other words there is a 27% chance that this is just a lucky run, and correspondingly, a 73% chance that you have a winning system.

As stated above, to be any way comfortable with the system (i.e. confident that it is truly a winning system), then 99% is the the 'confidence threshold' that you should be looking at. For 165 bets, 85 winners would be required to achieve this value.

Also, the above analysis assumes that the record above is as a result of live testing. Be extra careful with back-testing as it is extremely easy to (often subconcsiously) 'data-mine' so that you extract some 'rules' related to a lucky run, rather than to a winning system.