## Using Expectancy to calculate the probability of profit

## Timing-the-Market versus Time-In-the-Market

Is it possible to time when to start following a tipster who was about to go on a winning streak and predict when to drop them before they hit a losing streak?

I had been looking at using a typical investor’s approach of buy/sell signals when a faster-moving average crosses a slower-moving average. But it just wasn’t working out.

Then I discovered the financial investment insight of “* it’s time IN the market NOT timing the market that’s important*“.

This short article on How to lose £33,000 trying to time the market highlights the issue.

## Problem of joining on a losing month

So if you can’t judge a good time to join a tipster what can you do?

You’d probably not renew your subscription to a tipster if they lost you money in the first month. I think that would be a fairly typical reaction.

But is that the right thing to do?

What if there was a 90% chance of coming out with a small profit if you stuck with them for just one more month?

Or what if there was a 95% chance of making a BIG profit if you stuck with them for two more months?

Would you still jack them in or might you follow them for another month or two?

So rather than trying to time WHEN to join and leave a tipster service what if you had an idea of the probability of coming out with a profit after a certain number of months?

## Finding Positive Expectancy

The table below shows the different profits and losses for different periods of time for a tipster who has been tipping for 30 months.

Consecutive Periods |
Total Periods |
Made Profit |
Made Loss |
%Win Rate |
Avg. Profit |
Avg. Loss |
Expectancy |
Profit Factor |

any 1 month | 30 | 21 | 9 | 70% | 400 | -200 | 220 | 5 |

any 2 months | 29 | 25 | 4 | 85% | 500 | -300 | 380 | 9 |

any 3 months | 28 | 24 | 4 | 85% | 600 | -600 | 420 | 6 |

any 4 months | 27 | 25 | 2 | 95% | 700 | -800 | 625 | 17 |

The first row of data shows that in the 30 one-month periods there were 21 profitable months and 9 losing months – a 70% win rate.

The average profit of a profitable month was 400. The average loss of a losing month was -200.

So you have a 70% chance of making a profit of 400 and a 30% chance of losing 200 – all straightforward so far.

But now we hit our first new term – **Expectancy**.

Financial traders know this as **Trade Expectancy** or Average Profit Per Trade (APPT). You can read a little more about APPT on Investopedia.com

We can use this financial concept of Trade Expectancy in the world of tipsters, tips and betting.

Put simply, the way I see it is for financial traders their concern is the profitable outcome of **one action** (a trade) which happens over a period of time. For sports tipsters and followers, their concern is the profitable outcome of **several actions** (bets) that happen over a period of time. The important common element here is “* outcome over a period of time*“.

If we drop the financial word “Trade” and just talk about Expectancy we can do some calculations around the expected profit/loss over different periods – different numbers of months – of a tipster’s performance.

## Expectancy formula

Expectancy is the average return for each month, including wins and losses and is calculated as follows:

**Expectancy = (Win % x Average Win Size) – (Loss % x Average Loss Size)**

In different words, it’s the percentage of winning months multiplied by the average monthly profit minus the percentage of losing months multiplied by the average monthly loss.

So in our table, for the 1-month data row, we have a 70% chance of making an average profit of 400 and a 30% chance of losing an average of 200.

The Expectancy = (70% x 400) – (30% x 200) = 220

The 220 number is positive, which shows the strategy – of following this tipster for one month – has a positive Expectancy. We can expect to make money. And we could expect to make 220 points profit (on average).

## Finding the Best Positive Expectancy

Looking at the table for all the different periods, you can see that ** all **the strategies are profit-making. Whether you follow for 1 month or 2 months or 3 or 4.

You could take a one-month subscription to this tipster and you have a 70% chance of making 220 points profit or you could save yourself some money and take a 3-month subscription and expect to make 420 points profit after 3 three months.

But is one strategy any better than the others? Is it better to follow for one month or 3 months?

This is where **Profit Factor** comes in.

## Profit Factor

There’s much less information on Profit Factor but you can read this short article on Profit Factor to get the idea.

Profit Factor is not the subtraction of the Wins from the Losses but the Wins **divided** by the Losses

**Profit Factor = (Win % x Average Win Size) / (Loss % x Average Loss Size)**

This tells us how much better/bigger the “wins” are compared to the “losses”. in other words the relative strength of the strategy.

Here’s our table again.

Consecutive Periods |
Total Periods |
Made Profit |
Made Loss |
%Win Rate |
Avg. Profit |
Avg. Loss |
Expectancy |
Profit Factor |

any 1 month | 30 | 21 | 9 | 70% | 400 | -200 | 220 | 5 |

any 2 months | 29 | 25 | 4 | 85% | 500 | -300 | 380 | 9 |

any 3 months | 28 | 24 | 4 | 85% | 600 | -600 | 420 | 6 |

any 4 months | 27 | 25 | 2 | 95% | 700 | -800 | 625 | 17 |

Looking at the Profit Factor figures, if time wasn’t a concern then committing to following this tipster for 4 months is the best/strongest option (Profit Factor = 17). There’s a 95% chance of winning 700 versus a 5% chance of losing 800. A 95% win chance versus a 5% lose chance is saying it is 19 times more likely you’ll win than lose.

But if you wanted to minimise your time commitment to this tipster while maximising the probability of profits and also the size of those profits then following for 2-months appears to be the optimum choice.

The Profit Factor of committing for 2 months is 9 and that’s better than the 1-month figure and also better than the 3-months figure.

By choosing the two-month option you’re committing to following these tips for half the time (2 months instead of 4). The Profit Factor is halved as well (9 versus 17). So the two options are pretty much equivalent. In other words, two 2-month periods are the equivalent of one 4-month period in terms of profit.

Using this information you can see that if the first month following this tipster was a losing month then there’s a strong possibility of turning that loss into a profit by sticking with them for another month.

And also that doing that is a better option than following them for two further months.

## Real-world Example

If we look at the equivalent set of figures for a real tipster to see firstly if they are worth following and secondly how long we should plan to stick with them if we want to maximise the likelihood of making a profit.

Consecutive Periods |
Total Periods |
Made Profit |
Made Loss |
%Win Rate |
Avg. Profit |
Avg. Loss |
Expectancy |
Profit Factor |

any 1 month | 9 | 3 | 6 | 33% | 921 | -385 | 46 | 1.2 |

any 2 months | 8 | 4 | 4 | 50% | 457 | -740 | -142 | 0.6 |

any 3 months | 7 | 4 | 3 | 57% | 886 | -971 | 87 | 1.2 |

any 4 months | 6 | 3 | 3 | 50% | 811 | -780 | 16 | 1.0 |

any 5 months | 5 | 3 | 2 | 60% | 338 | -847 | -136 | 0.6 |

any 6 months | 4 | 3 | 1 | 75% | 70 | -119 | 23 | 1.8 |

The expectancy is the average return for each month, including wins and losses. And for this tipster, things don’t look great.

Following this tipster for 2 months or 5 months, the likelihood is you’ll make a loss.

Where the Expectancy numbers are positive they are small and where they are negative the numbers are bigger.

The Profit Factor figures for all the time periods never get much above one. That indicates the profits are never that much bigger/stronger than the losses no matter how long you would stick with this tipster. Straight away that’s an indication that this would not be a good tipster to follow.

Looking at the 1-month periods. There’s a 1 chance in 3 (33%) that you’ll make an average 46 points profit in the first month you start following these tips. Those are not great odds.

If you had a losing first month and you stayed with them for another month (the “any 2-months” row) then it’s 50/50 you’ll come out losing 142 points. Do I have any takers for doing that?

But would you persevere for yet a further month (3-months) to have a 57% chance (marginally better than 50/50) of making 87 points profit? I doubt it.

This was Anglo Racing who made it into 12th spot in Tipstrr’s article January’s Best Horse Racing Tipsters.

For me, this shows how little value there is looking at only one month’s results.

## Conclusion

When you join a tipster you do it because you believe he will make a profit – hopefully straightaway in the first month you join.

But what if he doesn’t?

If he doesn’t make a profit in the first month and your sitting on losses, you’re left a whole series of questions like:

- what do I do now, was this losing month just a one-off?
- will he have a profitable month next month?
- is there anything to suggest he WILL have a profitable month next month?
- should I stick with him or cut my losses and move on?
- if I move on who do I move on to? and will I have another losing first month with them?

These Expectancy and Profit Factor figures can help you decide how long you should anticipate following a tipster. It gives you an indication of how likely it is you’ll make a profit over a particular period of time and how much profit that is likely to be.

Armed with these figures, you can start following a tipster knowing for example there’s a 90% chance of coming out with a profit over two months or a 95% chance of coming out with a bigger profit over three months.

This starts to answer some of the questions above before the situation actually arises.

As well as providing guidance on how long to follow a tipster, Profit Factor figures can also help you compare tipsters to decide the best one to follow.

If one tipster has an 80% chance of producing a 100 point profit over two months and another has a 90% chance of producing a 200 point profit over two months then which one to follow becomes an easier decision to make.

I believe Expectancy and Profit Factor will be very useful information for anyone considering following a tipster and I’ll be looking to factor it into future tipster technical assessments.

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