Nick Grey wrote:Soheil listen to Brian. His maths are better than mine.
I still think yours, his and my chance of becoming a GM are very slim.
Actually, Nick, I think "very slim" is overly generous for all three of us.
That previous statistic of roughly 1 in 200 FIDE rated players doesn't tell the whole story because we have additional information and we can use something called Bayes Law or Bayes Theorem to use this additional information to get a more accurate estimate of the likelihood of Soheil becoming a GM. We could do the same for you or more but because we are much older our chances won't be higher than Soheil's.
Bayes Law looks like this:
P(B¦A) = P(A¦B) x P(B) / P(A).
P(B¦A) means the probability of B happening given that we know A is true. P(A) means the probability of A happening, etc.
Now, we know from his FIDE profile that Soheil is 31 or 32 years old and has a highest ever rating of 1830, so the probability we want to calculate is P(B¦A) which is the probability of Soheil becoming a grandmaster given that he is 31 or 32 years old and has a highest ever rating of 1830.
So, we need to calculate the following:
P(A¦B), which is the probability of having had a highest ever rating of 1830 at the age of 31 or 32 and then going on to become a grandmaster
P(A) = the probability of having had a highest ever rating of 1830 at the age of 31 or 32
P(B) = the probability of becoming a grandmaster.
We've previously estimated the chances of becoming a grandmaster as 1/200 which is 0.005
We can estimate the probability of having had a highest ever rating of 1830 at the age of 31 or 32 as being the number of players having had a highest ever rating of 1830 at the age of 31 or 32 divided by the total number of players. If we had all the FIDE rating information in our own database we could get a pretty good figure for this but in the meantime let's estimate about 1/2 or 0.5
So, we have P(A) = 0.5 and P(B) = 0.005 which means that P(B) / P(A) = 0.01 and we've already seen a jump from 1 in 200 to 1 in 100. However now we come to the fly in the ointment. We still have to multiply by P(A¦B) and this is bound to be less than 1.
Does anybody know of a grandmaster who had a highest ever rating of 1830 at the age of 31 or 32? No? Me neither. That gives us an estimate of zero for P(A¦B).
P(A¦B) x P(B) / P(A) = 0 x 0.005 / 0.5 = 0
So, there you have it. The statistical likelihood of Soheil (or you, Nick, or me) becoming a grandmaster is zero.
Still, as Robert Browning said "Ah, but a man's reach should exceed his grasp, or what's a heaven for?"