In the article about strike rates, we discussed the importance of the strike rate of the selection system and how to calculate it.
In the article about profitability, we discussed how to use the strike rate, in conjunction with the average odds of the losing/winning bets, to determine whether a system is profitable or not in the long term.
In this article, I want to discuss losing runs, their importance, how their length may be calculated and how this affects the staking strategy.
Losing runs can quickly decimate a betting bank to the point where it is difficult, if not impossible, to recover the losses incurred without an outrageous run of good luck.
Losing runs can occur at any time and without any warning whatsoever.
In my opinion, it is foolhardy to remain ignorant of the existence of losing runs. Anyone who does so is courting with danger.
So, let’s look at how we go about calculating how long the longest losing run of a system is likely to be.
The longest losing run is given by the formula: Log(No. Bets)/- Log(1 - SR - MoE).
Where: Log is the logarithm. No. Bets is the number of bets that we intend to place. SR is the Strike Rate of the selection system (in decimal format). MoE is the Margin of Error associated with the strike rate of the selection system (in decimal format).
Firstly, in order to use the above formula, we need to know the strike rate of the system that we are going to use to generate the selections.
Strike rates are usually presented in percentage terms. However, the above formula requires that it is in decimal format.
To convert a strike rate from a percentage to a decimal format, we simply divide by 100.
For example, if a selection system has a strike rate of 80%, the decimal format of the strike rate is 80/100 = 0.8.
Secondly, we need to determine the Margin of Error (MoE) associated with the selection system. This is fully described in a future article.
Again, as is the case with the strike rate, the MoE must be in decimal format.
For example, if a selection system has a MoE of 2%, the decimal format of the MoE is 2/100 = 0.02.
Notice in the above formula that the MoE is subtracted from, as opposed to added to, the selection system’s strike rate. This is to enable us to cope with the worst case scenario. If we can deal with the worst case scenario, we can deal with anything.
If we were to add the MOE to the selection system’s strike rate, we would only be able to cope with the best case scenario.
Unfortunately, if the worst case scenario occurred, we wouldn’t be in a position to cope since we would lose a significant proportion of our funds
Thirdly, we need to decide upon the number of bets that we are going to place.
In order to illustrate the use of the formula, let’s assume that we plan to place 1,000 bets using a selection system with a strike rate of 71% and a MoE of 1% and that we wish to calculate the longest losing run that we are likely to encounter.
Firstly, we need to convert the strike rate of the system from a percentage to a decimal format.
The strike rate of the system is 71%.
To convert the strike rate to decimal format, we simply divide by 100. This gives us a strike rate of 0.71 in decimal format.
Secondly, we need to convert the MoE of the system from a percentage to a decimal format.
The MoE of the system is 1%.
To convert the MoE to decimal format, we simply divide by 100. This gives us a MoE of 0.01 in decimal format.
Substituting the above information into the formula gives us:
Log (1000)/- Log (1 - 0.71 - 0.01) = Log (1000)/- Log (1 - 0.70) = Log (1000)/ - Log (0.3) = 3/ - (-0.5229) = 3/0.5229 = 5.74 = 6 (rounded to the nearest integer)
So, if we place 1,000 bets and use a selection system with a strike rate of 71% and a MoE of 1%, we can expect to encounter a maximum of 6 consecutive losing bets.
For those who have no wish to engage themselves in the mathematics of losing runs, I have taken the liberty of creating a table which contains the maximum number of consecutive losing bets for selection systems with strike rates between 5% and 95% in steps of 5%.
The MoE for the selection system may be ignored since the strike rates in the table already allow for this.
However, prior to using this table, you must calculate your system’s strike rate and subtract the MoE.
In order to use this table, you should scan down the strike rate column until the entry is encountered that is closest to, but greater than, the strike rate of the selection system.
Then, go to the next lowest strike rate and read the corresponding figure in the Max. Losing Run column to arrive at the maximum length of the losing run that the selection system is likely to encounter.
Notice, in the table, how the maximum losing run decreases as the strike rate of the selection system increases.
To illustrate the use of the above table, let us assume that a selection system has a strike rate of 31.25% and a MoE of 1%.
Subtracting the MoE from the system strike rate gives 31.25% - 1% = 30.25%.
From the above table, we see that the closest strike rate to, but greater than, 30.25% is 35%.
We then need to go to the next lowest strike rate in the table, which is 30%.
Reading across the table, a strike rate of 30% gives us a maximum losing run of 19.
Therefore, if we have a selection system with a strike rate of 31.25% and a MoE of 1%, we can expect to encounter a losing run of 19 bets.
So, we can now calculate the maximum number of consecutive losing bets that we are likely to encounter providing that we know the strike rate of the selection system and its MoE.
Having calculated the maximum number of consecutive losing bets, what use is this to us?
Well, we can use it to calculate what percentage of our betting bank it would be reasonable to expose on a single bet.
For example, if we use a selection system with a strike rate of 75%, we are likely to encounter, at some point, a run of 5 consecutive losing bets.
If we allocate 100%/5 = 20% of betting bank to every bet and we encounter 5 consecutive losing bets, our betting bank will be completely lost and we will not have any funds left with which to recover the losses incurred.
I, therefore, use a formula to determine what percentage of my betting bank to allocate to each bet.
Firstly, using the strike rate of the selection system, I determine the length of the longest losing run that I am likely to encounter.
I then divide the longest losing run into 20%.
The result is the percentage of my betting bank that I allocate to each bet.
If I am using a backing system, then the percentage is applied to the stake.
If I am using a laying system, then the percentage is applied to the liability of the bet.
By using this method, when I encounter the maximum number of losing bets, although I will lose 20% of my betting bank, 80% of my bank will remain intact.
This is more than ample with which to recover the lost funds.
If we again use the above example of a laying selection system with a strike rate of 75%, then we are likely to encounter a maximum losing run of 5 bets.
If we divide 20% by 5, the result is 4%.
I, therefore, allocate 4% of my betting bank to each bet.
So, if I have a betting bank of £1,000, I limit the liability of each bet to 4 x 1,000/100 = 4 x 10 = £40.
Now, when my selection system encounters 5 losing bets in a row, I will only lose 5 x 4% = 20% (= 5 x £40 = £200) of my betting bank and I will still be left with 80% (= £80 x 1,000/100 = £800). This is more than ample to recover the lost funds.
So, we now know how to calculate the maximum losing run that we will encounter if we know the strike rate of the selection system ad the MoE.
If we know the maximum losing run for a selection system, we are able to calculate what percentage of our betting bank we can reasonably allocate to each bet.