From the point of view of pure biology the ratio should be 2:1 in favour of the sire.
Mammals inherit genetic characteristics equally from both parents. Thus horse X will inherit 50% of his genetic characteristics from its sire, and 50% from its dam, while the dam will herself have inherited 50% from her own sire (horse X's damsire). The overall influence on horse X's genetics is therefore 50% for the sire and (50% x 50%) = 25% for the damsire - a 2:1 ratio.
I did some analysis in this area a few years ago and found that:
a. the 2:1 ratio works about right in practice
b. sire and damsire records seem to be a markedly better predictor of distance preference than of racing ability
c. if you want to analyse ability, you need to take a horse's gender into account. As a group, fillies achieve lower overall ratings than colts and it's best either to analyse the two gender groups separately or to build in a sex adjustment.