View Single Post 6 Jun 2019, 02:44 (Ref:3908204)   #12
Schummy
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Join Date: Jul 2001
 Location: Somewhere near 2nd Lagrangian point
Posts: 3,183     Oh, it was an unexpected series of calculations!

I replied a PM to jimclark with my ORG explanation, but here goes an explanation regarding your calculations and ORG.

Variance is the average (mean) of the squared deviations. So, Bottas's would be: 98/6 = 16.33. Variance itself is not directly related to any expectations around the mean, as variance is expressed in squared unit of measurement. Standard deviation I think is what you were referring to, it is the square root of variance. So Bottas's is 16.33^0.5 = 4.04. In gaussian distributions it means Bottas's score has approx 95% of expectations to be between 20-2·4.04 and 20+2·4.04 (i.e. in the interval (11.9,28.1)).

But, under the conditions formerly said, ORG is easiest to calculate (and deduce):

ORG = Gap/sqrt(n), with n= races to go.

In short, it is based in that standard deviation of a sum of n identical uncorrelated random variables is sqrt(n) times the s.d. of one of those variables.

So, ORG(Botas) = 17/15^0.5 = 4.4 (15^0.5 is the square root of 15).

I hope this messy explanation is useful, crmalcolm :-)

PS:

A "funny" consequence of this is one can try to estimate a probability for Bottas overcoming this deficit using past results in the season. For example, in how many possible races Bottas would get more than 4.4 points than Lewis? (knowing the first 6 races). So we would pass from a ORG to a probability.  