When breeding race horses it is not uncommon for a horse to be bred with a mate that shares a common ancestor. When breeding two horses that share ancestry the Wright's inbreeding coefficient is a calculation that shows the likelihood that an allele possessed by the shared ancestor will be passed on to the foal. The likelihood varies based on the number of generations between the foal and the shared ancestor, both through the sire and the mare.
Count the number of generations between the foal and the ancestor through both the sire and mare. For example, if a foal's father and mother are both descendants of the same sire, with different mares, each would be one generation of separation.
Add the number of generations between the foal through the sire and mare, then add one to the result. In the example, 1 + 1 + 1 would yield a result of 3.
Multiply 1/2 to the power of the number found in the prior step. In the example, 1/2 to the 3rd power is 1/8. An easy way to find the result is to write out 2 x 2 x 2, with the number of twos equal to the number in the prior step, then write 1 over the product.
Add one to the inbreeding coefficient of the shared ancestor. If the shared ancestor in the example had a coefficient of 1/2, the result would be 1 1/2.
Multiply the result of the ancestor's coefficient plus one (step 4) by the result of 1/2 brought to the power of the number of generations (step 3) to find the inbreeding coefficient for the foal. In the example, 1 1/2 would be multiplied by 1/8, yielding a result of 3/16.