Our brains are not used to thinking about probabilities, especially if they are far from 50/50. We have to use some statistics: The binomial function.
The results will surprise you.
Use the Tool
I have prepared a spreadsheet for you to play with the numbers. The probability of being positive or negative after ‘N’ bets depends on the odds ‘O’ and the probability of hitting ‘P’ or the long term yield ‘Y’.
To use the binomial, we need to know the probability of being right. A bettor who bets at odds ‘O’, with a long term yield Y of 0%, has a probability of being right of P=1/O. But what if his yield is not 0%? Then we use the formula: Y=P-O-1 and clearing, P=(1+Y)/O
We already know the probability of a hit. Now we calculate for each possible number of hits, what is the result for a bet size or stake ‘S’: Profit = S-[N wins-(O-1)-N losses].
To calculate the probability of each of the possible numbers of hits (from missing everything, to hitting everything), we use the binomial distribution. P_N wins = B(N wins, P) With this we have everything, let’s see some cases.
For example, the simplest case. A tipster who forecasts at odds 2, 10 bets, and we assume that his long-term yield is 0%. He has a probability of finishing positive of… 37.7%
If I bet randomly on a single bookie, my long-term yield should be equal to the bookie’s margin in negative. Let’s say that bookie’s margin is: M=1/O1+1/O2=1/2+1/1.72=1.0814, a -8.14%. Still, after 10 bets, I will be positive…. 28% of the time!
If, on the other hand, I am a good bettor, with a positive long-term yield of 5% (Ole por mí!), the probability of being positive after 10 bets is “only” 44% of the time, and negative 32% of the time. Hey, but wasn’t he a good bettor? Yes, but 10 bets are very few.
We can change the average odds. If I bet at odds 1.5 with yield 5%, I will be positive 65% of the time. For low odds and the same yield, the number of times you stay positive is higher.
Let’s see a real case.
A WinnerOdds user asked us the probability of being negative after 900 bets.
If the long-term yield of this particular user were 5%, what is the probability of going negative? Surely it would be very low, wouldn’t it? 900 bets!
Well, this is where variance comes into play, and that our brain is not prepared for very high or very low odds. With an average odds of 1.66, the probability of going negative is….. 3.26%!
That is, 1 out of every 1/0.0326=30 times, or 1 out of every 30 5% yield users, will go negative after 900 bets, just because of variance!
It is difficult to assume what is long term.
Or to understand what high or low probabilities are.
It takes a lot of patience.
And think slowly!
You can download the file above to try other numbers and, if you want, share them with us and we will comment on them.