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  Formula One. Ratings. Theory Entry   

A Brief Explanation the System for Definition Ratings

       Ratings of pilots, machines and engines calculation independently. The final classifications in the Grand Prix is main criterion of the calculation for execution. Each race is represented as a matrix of pair comparisons. On results of all races the general matrix is filled. The driver (car, engine) worth above in final classification appropriated "victory" for the driver (car, engine), worth below in final classification.
       The simple addition the wins and the loss with different rivals don't impossible to define the force, consequently, to sum up wins and loss it's necessary with provision for the force of the rival.
       For definition of the ratings it's necessary to solve a system of the equations
, (1)
where

i

- quantity the drivers (cars, engines) calculated in the system;

- the rating of i-th drivers (cars, engines);

- sum up weight quantity the wins and the loss of i-th drivers (cars, engines) accordingly.
       Sum up weight quantity the wins and the loss define with help following dependence:
(2)
where

n

- quantity of races in which i-th driver (car, engines) took part;

k

- quantity of participants in race;

- Value of wins and loss i-th the driver (car, engine) in j-th to race with l-th the rival accordingly;
Note: value of wins is appointed two ways. The first (reality) - each higher participant in classification has a wins 1:0 above subordinate. The second (points) - to each participant charges values of wins and loss on system 10, 6, 4, 3, 2, 1, by the others 0, t. e. The winner has a wins above the second participant 10:6 above the third 10:4 etc.

- there is rating of the i-th drivers (cars, engines) in j-th to race.
       For solution the system of the equations are used condition that rating average driver (car, engines) equality one, that is
, (3)
where

n

- quantity the drivers (cars, engines) calculated in the system.




Author: V. Yushkin (Contacts)
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