Minecraft wiki entry for Horses, associated text: After 3.13 blocks jump, 11 hearts, or 9.71 blocks/second speed, any future breeding will have a higher chance of producing a worse child than a better one. Because the range of horses that are better than a given horse gets narrower as the horse gets better, the likelihood of breeding a horse in that range of better horses also gets linearly narrower as the horse gets better, and as a result, the actual number of breed attempts necessary to likely get a better horse increases exponentially, until a fully perfect horse is unattainable, as shown in the table.