How do you overcome results oriented thinking from a client?
The scenario you described with one horse is basically anecdotal evidence. To objectively evaluate what you're doing, you need to agree with the client to make this an experiment. 


  I understand you don't trust my horse predictions and that's totally
  understandable. It is human nature to worry about the ones that got
  away. Let's handle this objectively and run an experiment. I'll give
  you buy/sell ratings on 50 horses. We then track their performance for
  six months. If on average my ratings outperform a coin flip, we'll
  know we're onto something at a macro level even if a few got away. If
  my models end up being worse than a coinflip, we'll know the model
  needs to be improved or you need to fire me.