It's all about the variance - part 1

A lot of newcomers to sports trading or betting may imagine that all they have to do is pick winners. They might think that getting as close to a 100% strike rate will guarantee millionaire status. It's just not as simple as that.

For a start, we are going to pick losing bets or make losing trades. Nobody is perfect. Even if we could get close to a 100% success rate we would probably be betting or trading too little to make any serious money.

Risk and reward go hand in hand. The more we are willing to risk then the greater the potential for reward. That doesn't mean we should throw our money round and hope to get lucky. The key to success is money management, balancing risk and reward.

To manage risk we protect our capital from the downside whilst making the most of the upside. We don't even have to have a 50% strike rate to make a profit. All that matters is that when we lose, we lose less than we win.

In the example simulation below (click to enlarge) on RiskSimulator 2, we see a trader who only has a 40% strike rate but who makes twice as much from winning trades as on losing trades.

This simulation models a trader who makes 2% profit on average from a 40% strike rate and who manages to keep his losses down to a 1% average. Intuitively, we know that if the strike rate falls below 33% (1/(2+1) = 0.333) then the trader will make a loss.

Of course, all of these simulations can be calculated mathematically without the need for Monte Carlo methods. The point of the simulation is to show the variance graphically. A lot of novices have difficulty understanding the mathematics of gambling. A graphical representation can often aid the beginner sports bettor/trader.

The formula for expectation will tell you what you need to know about your bets without recourse to a simulation.

Expectation =  (prob of success * return) - (prob of failure * loss)

If the figure is negative then it's a losing system.

For our example simulation the expectation will be

(0.4 * 2) - (0.6 * 1) = 0.2% per bet

The simulation was pretty close (£19.46p average yield) to the expected £20 but we can see clearly in the simulation that we could have made more or less and in some cases there might have been a small drawdown before making a profit. The expectation is based on an infinite series and our betting will tend towards expectation.

In theory when we calculate probabilities we are doing so from a distribution derived from an infinite series. However, we never get to place an infinite number of bets. A few hundred bets will be unlikely to produce smooth distibutions. A simulation helps us to understand short time variance very clearly.

In the example above, although all 100 trials yielded positive returns some were higher than others. The  highest yield was £32.40 and the lowest a little over £7.

However, by trying to lose as little as possible we don't want to be so risk averse as to avoid any losses at all. Doing that can often prevent us from taking the risk of getting the right rewards. It's a matter of balance. Our winning bets or trades must overcompensate us for our losses. Do that and we will always be in profit.

RiskSimulator 2

I am currently working on an improved risk simulator. The simulator will visually depict simulations of betting, trading and staking. The picture above displays the Staking simulator tab, which I am currently working on.

You will notice Martingale and Fibonacci staking options. I am not advocating them as viable staking plans. If the release program has them then it will be to demonstrate that they don't work. However, I expect most of my readership to intelligent enough to have discounted them already so I might remove them as options.


I have written a simple RiskSimulator for level stakes betting. The application permits up to 100,000 bets to be simulated with graphical outputs. The user enters fair and bookmaker/exchange odds, a Monte Carlo simulation handles the rest.

When the simulation is complete the yield, risk of no profit and risk of ruin are output. Also, two charts are output; a time series progression for the bankroll and a histogram of variance.

Although using standard statistical methods such as the binomial distribution will provide more accurate results, the simulator provides a more easy to understand visual representation.

Also, a binomial distribution is based on an infinite number of trials. As nobody bets an infinite number of times a Monte Carlo simulation can show the user the wide variation between what is expected mathematically and what may happen in reality.

Above, we see that the distribution of results in the histogram is not a smooth curve (as one would expect from a binomial distribution) even for 100,000 trials.

Future work will include a StakingSimulator for users to investigate the worth of various staking systems, including level stakes, proportional stakes, Kelly Criterion and guaranteed losers such as Martingale and Fibonacci.

How to Find a Black Cat in a Coal Cellar
Being a technical trader in sports betting markets I have no interest in tipsters. However, I do enjoy reading any mathematical book on sports betting and the mathematics contained in this book are invaluable, even to those who don't use tipsters but develop their own trading and betting strategies.

How to Find a Black Cat in a Coal Cellar is written by Joseph Buchdahl, author also of Fixed Odds Betting, another book I highly recommend. Buchdahl attempts to show those who use tipsers (also called advisories) how to evaluate their performance.Most tipsters, says Buchdahl are either amateurs who don't what they are doing or are fraudsters scamming people for subscription fees.

Although the book is primarily for readers who want to evaluate tipsters, in effect the book is for the evaluation of any systematic approach to betting. Therefore the book is important to anyone who wishes to evaluate their own strategies as if they are tipping bets to themselves.

The first chapter is a description of how various forms of betting work and how the aim is not just to pick winners but winners whose odds give you an edge in the long run. Not news to experienced bettors but you will be surprised how many people still don't understand that just picking a winner is not enough.

You can't predict winners all the time so your winners have to compensate for the losers. Hence, the odds on your winners must be higher than your predicted odds so that you hopefully gain a profit. The first chapter goes on to explain the overround and how that eats into profits. The chapter also covers market inefficiencies such as favourite/long-shot bias, the over-betting of under-dogs and under-betting of favourites.

Finally, the first chapter covers staking and money management. Not exhaustively, as the author covers the subject in more detail in his previous book, Fixed Odds Betting. Needless to say, Buchdahl is against progressive betting systems such as Martingales but he is pro Kelly staking for the maximisation of returns.

In the second chapter we begin to see a methodology for evaluating betting systems be they from tipsters or created by oneself. Again some fairly familiar terms are presented; Return on Investment and Yield. Worth a read for revision, if you think you already know all about it. Many don't.

A positive yield is not necessarily going to make you rich. It's not like a bank account offering 5% per annum and you get all your money back from the government if the bank fails. Buchdahl shows by way of a simple example that even a losing strategy has the potential to yield a profit 30% of the time simply because of variance.

The chapter then proceeds to show the affect of low edge on variance. The lower the edge you have over quoted odds the greater your variance. You could show quite a run of profitable bets even with no edge at all. Worse, you could easily lose your bankroll.

Also shown is that the higher the odds you bet also affects variance. Again, the higher the odds, the higher the variance. Efficient market hypothesis tells us that market odds are close to true and so higher odds win less frequently, adding to the variance if the yield is quite low.

Even if you have two systems that yield 10% profit, if one is betting at higher odds than the other then its variance will be greater than the other and will have a greater chance of losing the bankroll than the other.

The chapter continues by introducing the t-test for statistical significance. Essentially, this is giving the reader a value for the probability that a tipster made their profit through chance and not through skill.

Chapter three covers value for money. Tipster subscription fees are factored into rates of return. Buchdahl looks at what the naive bettor can achieve by themselves and what a tipster can add to that. Arbitrage is covered as a way of guaranteeing success without the fundamental knowledge purportedly known by tipsters. If a tipster cannot beat simple arbitrage then they are no good at their trade. There is also an account of Buchdahl's attempt to win a last man standing competition using value betting.

In chapter four Buchdahl evaluates tipsters and their records. Buchdahl goes through many tipsters and their reported success rates. I won't go through any of it here as the data is in the book and the maths used to evaluate the tipsters has already been mentioned.

The level of unprofessionalism and charlatanism displayed by most tipsters is not unsurprising. Amateurish strategies involving the chasing of losses as an attempt to boost profits are evidenced. The closing down of initially profitable tipster websites, reminiscient of beginner bettors who boast of their skills on blogs that are soon left moribund when the profits start heading south.

In chapter five Buchdahl makes his assessment of tipsters. Most he says, are amateurs, half of whom make a profit but far fewer than that can claim to do so through skill rather than by luck, as has already been shown mathematically. A lot of tipsters "cook the books" and after they have been verified by a tipster evaluation service, such as Buchdahl's own service, profits usually diminish.

Finally, in chapter six Buchdahl show the reader how to professionally go about evaluating tipsters, not just mathematically but carrying out domain checks and web searchers to see if others have reviewed the tipster as legitimate or a flim-flam artist.

My review is not really enough to do justice to this book. There is so much of value to be read. The book will help you to determine which tipsters, if any, are as good as they claim. The book will also improve your own (self-tipping) strategy building.

I recommend that you have Excel or other spreadsheet software close to hand so that you can feed the functions provided into a spreadsheet and experiment with them. You can then have the functions on hand to remind you of the important facts contained in this book.

This book certainly ranks amongst the more important books on sports betting.

Amazon - How to Find a Black Cat in a Coal Cellar

Also recommended - Fixed Odds Betting

Traders: Millions by the Minute - Part 2

Last night the BBC broadcast the second programme in the two-part series entitled Traders: Millions by the Minute. The first programme showed the professionals making millions by the minute, the second programme did not. Instead, with one exception, we got to see amateurs, losing.

The fact is that the vast majority of home traders lose money. In financial trading it is easy to make money in a bull market, you buy and hold. In volatile markets there is the temptation to trade the swings, long and short and with disastrous results.

The problem for financial day traders is that most markets are rigged for the benefit of the professional élite. If the price isn't rigged then the market you trade in will be. Either the price is manipulated or the market you trade in is front run.

Sports trading is a different matter but still, most sports traders are losing traders. Although sports rigging is commonplace and insider trading in horseracing is common too, the playing field is more level between the professional and amateur bettor. Buy and hold lasts only until the end of the event so most trades are very much day trades.

In last night's second programme we saw a house wife making a million but only on paper. When she started using her own money, she lost. A common occurence for traders. The psychological aspects of using your own money are vastly different to paper trading. You will take more risks on paper and may get a long run of success, reinforcing in your mind that you are a good trader. However, that may just be down to luck. After all, a risk taking loser on paper would probably not want to trade with their own money. We got to see a lucky loser on paper, lose it in reality.

When you start using your own money you might be more cautious and the reality of being just another trader snatching pennies in front of a steam roller might be too much to bear. You either give up because you are not going to be as rich as you thought or you take on more risk and blow up.

There was also a team of retirees gambling their pensions on the stock market. They looked and acted professional but even they started to lose money. Again, they found it easy in a bull market and got out of their depth through over-trading a volatile market.

A former antiques dealer knew all the terminology but he just couldn't trade. He was happy to lose money, year after year, to keep him from selling another chest of drawers.

There was a pair from Birmingham but I didn't know what to make of them. Maybe the BBC's usual multi-cult shenanigans in action. We saw the pair in their parents' house plotting to become 'trillionaires' then driving off in a flashy car to drum up business from black footballers. At least they had the sense to risk somebody else's money. At the end of the show, and unlike the other traders, we were not told how they were getting on financially. I suspect they are still living with their parents.

The only winner I could see was a rather narcissistic chap. He had made over a million pounds from day trading and had been given a multi-million pound fund from The City to trade. The narcissist probably has all the skills needed to be a winner; single-minded, self-absorbed with a touch of obsessive personality disorder. His house was immaculately clean, his body immaculately toned in a gym, his Porsche gleaming immaculately in the sunshine. A life dedicated to being good at everything and that includes making money.

BBC iPlayer - Traders: Millions by the Minute

Traders: Millions by the Minute

An interesting two-part documentary series on the BBC this evening, Traders: Millions by the Minute. The series shows us pit, hedge fund, electronic and algo traders at work in Chicago, New York, London and Amsterdam.

Chicago's CBOT is still the scene of pit traders in the grain commodity markets. Although many exchanges throughout the world have gone electronic there is still some liquidity in certain commodities for face-to-face trading.

However, most trading is now done electronically, either by humans at a screen or algorithmically without human intervention. In London we see Amplify Trading, an electronic trading firm, training newcomers with mixed success. I am sure you will notice yourself amongst the trainees, some of whom are scared to trade and others trade too much. A few pass and are given jobs at Amplify or trade on their own accounts.

The hedge fund trader in New York was less interesting, as we mostly see her family and philanthropic life rather than her work. The high-frequency trading in Amsterdam could have been more interesting but a computer trading at the micro-second level probably doesn't make for good television.

All-in-all a fascinating view of people in the world of trading and maybe inspiring to sports traders too. Part two is next week and will concentrate on day traders working from home, which will probably be of more interest to sports traders.

For my readers in the UK I provide a link below to the BBC iPlayer where the series will soon be available to view. In good time I am sure the series will find its way to YouTube and shhhh... BitTorrent, as does everything, eventually.

BBC iPlayer - Traders: Millions by the Minute

Is it time to turn to a bot?

A bot is a virtual robot, which performs simple repetitive tasks for you. Bots are used in trading to perform trades without human interaction.

Whatever online task a bot does, if the task is simple and predicatable then you should be using bots for all of those online tasks and not just in trading.

I recently downloaded SleepBot for my Android phone and it has already made a difference to the quality of my sleep. I have so much more energy when I wake up at 6AM to start trading.

Time means money and wasting time doing things yourself will cost you money in the long run. Bots increase your productivity.

When should you decide to use a bot for your trading? Ask yourself this simple question, "Is my trading algorithmic, predicatable and profitable?" If you can answer 'yes' then you should be delegating tasks to a bot. If your answer is 'no' then you might consider a halt to your trading for obvious reasons.

Why sit in a chair trading one market at a time when one or more bots can be looking at all markets simultaneously? This is called scaling, through which you earn money from multiple sources in parallel. Wealthy people have scalable jobs, the poor do not. Not only that but you are diversifying your risk, which can only be a good thing.

If you find yourself doing the same thing when successfully manual trading then you should have a bot trading for you so that you can earn money elsewhere. If the entry and exit points for your trades are profitable and can be described algorithmically then you should give those trades to a bot whilst you design an entry/exit pair for another market

There is commercial bot software out there but for sports trading I find most of the software useless and so I code my own bots. But do have a trial run with the commercial software and see what it can do for you and what it cannot. Build a list of requirements and see what is out there that will satisfy those requirements. If you can't find what you are looking for then either code your own or pay someone to do it for you. An investment that is sure to pay you a handsome return.

I shall be covering bot trading strategies in a future post.