Inbreeding is harmful because it produces individuals which are homozygous for deleterious alleles. Each individual has many such alleles, but since each of us has several thousand genes, it is usually unlikely that a random pair of individuals will have a deleterious allele for the same gene. If an individual has at least one good copy of a gene, then in most cases there are no harmful effects. However, inbred individuals are derived from closely related parents, and these parents have a much higher chance of having bad alleles for the same genes, and therefore their children will tend to get two bad copies for many genes, and this will have harmful effects.
Populations that have praticed inbreeding for a long time have abolished many of their harmful alleles, because such alleles are expressed more often, the individuals which express them die or fail to reproduce, and the alleles are removed from the gene pool. On the other hand, by chance, it is possible that alleles with small harmful effects may in fact be fixed in the population, and this reduces the quality of the population.
Thoroughbred horses are both inbred and artificially selected. The genes of champions have a higher chance of passing to the next generation than the genes of average performers or losers. As a result, the quality of the gene pool of thoroughbred horses is very high, because inbreeding and artificial selection has essentially purified it of most harmful mutations.
This comes at a cost: thoroughbred horses have very little genetic variation, that is, they have very few differences from each other. Evolution works by exploiting differences, by favoring some alleles over others. Natural selection leads to evolution only if it has the raw materials of variation to work with.
Therefore, the curve presented in Steve's post is best interpreted as an improvement of the genetic quality of thoroughbreds until 1950 through inbreeding and artificial selection, which reached a plateau; further improvements are no longer possible, because there is very little room in the horse gene pool to create new variants with superior performance.
Why did human performance improve so drastically compared to that of horses? I think that four factors have played a role:
- Better living conditions have greatly increased the fraction of the human population that is healthy enough to compete in sports.
- The human population has grown dramatically, and hence there is a much larger pool of individuals competing at the right tail of the ability distribution.
- The financial rewards of those going into sports have greatly increased, and this has led to many able individuals choosing sports as a career path.
- There have been extreme improvements in sports science in the last decades. Humans can learn easily, and they can improve their technique, experiment with new training regimes and give feedback about what works for them and what does not. Unlike horses, humans use their minds to optimize the performance of their bodies.