mathare
18th January 2004, 17:38
I know quite a few people on this forum run successful systems. I suspect that many others, like myself, have tried to come up with equally good systems. But how do you know whether or not a system is working?
Obviously you can look at strike rates and profit figures. But can you tell when a good system has just had a bad start or conversely when a poor system has had a lucky run at the beginning? I have a pretty solid mathematical background (2 A-levels in maths and a masters degree in theoretical physics) but I understand that most punters don't. So I'm going to try and explain some maths that may help you decide how well your system is working.
Following a few simple steps, we can work out if a system is actually showing progress or whether we could achieve similar results through luck alone.
1) Record every system bet in a spreadsheet. This is essential and you should record at least the profit/loss for each bet and also the total profit/loss on the system to date. NB You can do this using something other than a spreadsheet but you had better be bloody good at maths for the later steps
2) Divide the total profit/loss by the number of system bets to get an average win/loss per bet
3) Calculate the standard deviation of the individual system bet results
4) Work out the standard error by dividing the standard deviation by the square root of the number of system bets
5) Divide the average win/loss by the standard error to get the t-value.
That's the steps to follow, but what does it all mean and what can it tell you?
I'm assuming everyone can understand the averaging in step 2. This just gives us an indication of how successful (or otherwise) an average system bet is. The tricky bit comes in step 3, calculating the standard deviation. This value gives an indication of how much each the profit from each individual bet varies from the average.
The good news is you don't really need to understand what this means too much, you'll just have to trust me on what it means and how it is used. The even better news is that if you are using a spreadsheet then it can calculate the standard deviation for you. If not, you are in for some long, complicated maths that I have no intention of going in to here. If you are using Excel and you're individual bet profits are in column E then entering =stdev(E:E) in a cell on the same page will populate that cell with the standard deviation of you individual system bet results. I'm sure there is also an equivalent in Lotus 1-2-3, Open Office, Star Office or whatever your chosen spreadsheet application is.
That's the tricky bit done and you should be able to complete all 5 steps now. Again, a spreadsheet can be used to help with the maths. They really are very powerful for recording bets and making sense of the data.
At the end of it you have the t-value. What does this mean? Basically, the higher that value the more confident you can be that the profits you seen have been as a result of skill or a viable system rather than just chance. If the value is negative then all it is telling you is that you have made a loss, and you probably knew that anyway. It's only really worth thinking about positive values. If the t-value is 0.7 you can be 75% certain the profits have come from a good system and you haven't just been lucky. With a t-value of 1 you are 80% certain your system is good; a t-value of 2 gives you 95% certainty and a t-value of 3 means 99% certainty.
I have been applying this to some of my systems that I have been developing. I'm not going to publish any results/qualifiers/t-values yet as the systems are still immature, more data is required before I would be happy to publish any figures. The more system bets you have recorded the more data you have and the more accurate and reliable the t-value will be. That said, the data can be obtained for any number of bets and will start to settle down once you have recorded 40 or 50 bets. If it looks poor at that stage it may be worth starting the system again, changing the staking plan or abandoning it all together in favour of something else.
Also the t-value is greatly affected by the staking plan you use with your system because the average win per bet is involved in the calculation. For my systems that use a staking plan I also record profits to level stakes and calculate t-values for both my staking plan and level stakes. A change in staking plan may make a losing system into a winning one but ensure that the reasons behind the plan are sound and that you haven't just changed the plan to suit past data. If I change staking plans on a system I restart my records and work out the t-value after 50 bets using the new plan to see how it has performed. The value of paper-trading systems in a spreadsheet is you can quickly apply a number of staking plans across the same qualifiers and record the profits separately for each.
I hope some of you find this useful. Of course, no amount of maths will turn a rubbish system into one that will make you a million overnight. What I hope this does is encourage anyone paper-trading systems to apply a bit of maths to them to see if the systems look as though they may be profitable long-term.
Now I feel I must apologise for the length of this post. :snooze If anyone has read and understood it all then go and have a well-deserved cup of tea :laugh
Obviously you can look at strike rates and profit figures. But can you tell when a good system has just had a bad start or conversely when a poor system has had a lucky run at the beginning? I have a pretty solid mathematical background (2 A-levels in maths and a masters degree in theoretical physics) but I understand that most punters don't. So I'm going to try and explain some maths that may help you decide how well your system is working.
Following a few simple steps, we can work out if a system is actually showing progress or whether we could achieve similar results through luck alone.
1) Record every system bet in a spreadsheet. This is essential and you should record at least the profit/loss for each bet and also the total profit/loss on the system to date. NB You can do this using something other than a spreadsheet but you had better be bloody good at maths for the later steps
2) Divide the total profit/loss by the number of system bets to get an average win/loss per bet
3) Calculate the standard deviation of the individual system bet results
4) Work out the standard error by dividing the standard deviation by the square root of the number of system bets
5) Divide the average win/loss by the standard error to get the t-value.
That's the steps to follow, but what does it all mean and what can it tell you?
I'm assuming everyone can understand the averaging in step 2. This just gives us an indication of how successful (or otherwise) an average system bet is. The tricky bit comes in step 3, calculating the standard deviation. This value gives an indication of how much each the profit from each individual bet varies from the average.
The good news is you don't really need to understand what this means too much, you'll just have to trust me on what it means and how it is used. The even better news is that if you are using a spreadsheet then it can calculate the standard deviation for you. If not, you are in for some long, complicated maths that I have no intention of going in to here. If you are using Excel and you're individual bet profits are in column E then entering =stdev(E:E) in a cell on the same page will populate that cell with the standard deviation of you individual system bet results. I'm sure there is also an equivalent in Lotus 1-2-3, Open Office, Star Office or whatever your chosen spreadsheet application is.
That's the tricky bit done and you should be able to complete all 5 steps now. Again, a spreadsheet can be used to help with the maths. They really are very powerful for recording bets and making sense of the data.
At the end of it you have the t-value. What does this mean? Basically, the higher that value the more confident you can be that the profits you seen have been as a result of skill or a viable system rather than just chance. If the value is negative then all it is telling you is that you have made a loss, and you probably knew that anyway. It's only really worth thinking about positive values. If the t-value is 0.7 you can be 75% certain the profits have come from a good system and you haven't just been lucky. With a t-value of 1 you are 80% certain your system is good; a t-value of 2 gives you 95% certainty and a t-value of 3 means 99% certainty.
I have been applying this to some of my systems that I have been developing. I'm not going to publish any results/qualifiers/t-values yet as the systems are still immature, more data is required before I would be happy to publish any figures. The more system bets you have recorded the more data you have and the more accurate and reliable the t-value will be. That said, the data can be obtained for any number of bets and will start to settle down once you have recorded 40 or 50 bets. If it looks poor at that stage it may be worth starting the system again, changing the staking plan or abandoning it all together in favour of something else.
Also the t-value is greatly affected by the staking plan you use with your system because the average win per bet is involved in the calculation. For my systems that use a staking plan I also record profits to level stakes and calculate t-values for both my staking plan and level stakes. A change in staking plan may make a losing system into a winning one but ensure that the reasons behind the plan are sound and that you haven't just changed the plan to suit past data. If I change staking plans on a system I restart my records and work out the t-value after 50 bets using the new plan to see how it has performed. The value of paper-trading systems in a spreadsheet is you can quickly apply a number of staking plans across the same qualifiers and record the profits separately for each.
I hope some of you find this useful. Of course, no amount of maths will turn a rubbish system into one that will make you a million overnight. What I hope this does is encourage anyone paper-trading systems to apply a bit of maths to them to see if the systems look as though they may be profitable long-term.
Now I feel I must apologise for the length of this post. :snooze If anyone has read and understood it all then go and have a well-deserved cup of tea :laugh