## Pages

### A Root for Squares

Being on the more sensible side of sports trading I don't get to hear of the wackier ideas that are out there. I am sure I don't have to explain edge and trading in proportion to perceived edge again. Most of you will use some kind of edge based trade sizing mechanism. Even if it is only to increase your trade size as a percentage of an increasing bankroll and to reduce your trade size if your bankroll starts decreasing in size.

Whilst wandering through various websites I noticed a curious trade sizing algorithm called the Square Root System. The system starts out with level stakes trades, which is not the best way of making the most of your edge. If you are lucky enough to have a winning strategy then with this system you increase your future trade size by the square root of your increased bankroll.

For example, if you started with a £100 bankroll, were trading £5 at a time and increased your bankroll to £125 then your new stake size is £5 + sqrt(125-100) = £10. The system also requires the trader to reset the initial bankroll size (maybe £150 in this example) when a target value is reached, otherwise the square roots run away and trade sizes become too large and too risky. As your bankroll continues to grow then you continue to reset your bankroll and increase stakes by the square root when it goes above this new reset value.

If you think this is odd then you can reward yourself with your favourite snack. This system is not as bad as a Martingale as there is no loss chasing. However, as the trade sizing is not based on edge there is bound to be some wild swings in variance. The resetting of the bankroll to keep a lid on size of the square root is not optimised in any way and can lead to large variance in returns creating the opportunity for bankrolls to be wiped out.

Level stakes trading never makes the most of any edge you have so professional traders never use it. In the example above the bankroll has increased by 25% but the trade size has doubled from £5 to £10. What has the square root of your original trade size got to do with your edge? In conclusion the Square Root System is a level stakes system that uses an illogical (no reference to edge) stake increase if the bankroll should grow. Anyone using such a system is obviously too lazy to work out their edge or is not the trading/mathematical/financial genius they purport to be.

Some of the blame for these useless "staking plans" that we see can be laid at the door of bot software vendors who have no trading experience. They just hoover up all the crazy ideas on the web, such as Martingale and Square Root trade sizing, add it to their software and leave it to the buyers of such software to implement and learn the hard way. In my book, Programming for Betfair, I make sure not to give readers all the whistles and bells that are out there because I know I will have created a lot of angry beginner traders.

To all beginner traders I suggest you learn basic maths. Use a spreadsheet to understand edge and variance in returns and the consequences of deviating from edge. You will then understand how important trade sizing is. Not only for making the best of a winning strategy but also to avoid destroying your bankroll from trying to work the strategy too hard. There are no shortcuts to being a winning trader. You either put the work in or you don't and suffer the consequences.

When I see a website like this www.professional-racing-tips.com/staking-plans/square-root-staking-plan.aspx (I do not recommend any of its "staking plans") and see no mention of edge or Kelly Criterion then I know the website is not as "professional" as it purports to be nor the people who read and implement what is on such websites. Without developing your skills to analyse what people tell you to do then are just acting in the dark.

More articles on the Mathematics of Gambling

1. Weird... You mention the square root trading plan James. At one point I was considering using it as it was recommended to me. But as your article points out where is the logic in this plan? I often wondered why you reset your staking once a certain profit target had been reached.

At least with Kelly you can see the logic!!! Staking according to edge seems such a logical plan!

1. You must always question everything.

Just because a friend, trusted source or bloke down the pub recommends something to me does not mean that I will jump at it. I need to see the logic, the maths before I can make a decision about investing my money.

It is obvious that everything involved in the calculation of the Root for Squares trading plan is arbitrary and not based on any consideration of the probability to win or to profit.

More important than resetting your profit target, what has the square root of your bet to do with edge?

Why not the cube root? How about 2/3 * Pi? It's all just a gimmick invented by the clueless.

If anyone reading this article doesn't understand edge then they need to put away their cash and find a new hobby.

2. I think the danger here to a novice is to assume and generalise. Because the plan involves a mathematical equation, I think there is a danger to presume someone has given careful thought to this plan. Furthermore, listed on a site with others such as martingale, Fibonacci etc adds to its presumed integrity. I would say the majority of novices are not maths professors or PhD students therefore do not look at these plans and calculations in detail.

1. "martingale, Fibonacci etc adds to its presumed integrity"

In what way do Martingale and Fibonacci have "integrity"?

Indeed, most novices are not maths professors or PhD students but for their sake I would expect them to have some common sense.