To back up what gumtree said-- my great uncle bred, raised and raced thoroughbreds for over 50 years. He was extremely lucky in that his very first horse won the Kentucky Derby. However, that horse had the breeding to win, and he did not breed that horse but bought him as a youngster. And my uncle never won another Derby after that. One stallion won a Breeder's Cup race, and he certainly had his fair share of very good horses over the years, but it just goes to prove how hard it is to produce a Derby-caliber horse.
Again, I'm not trying to dissuade you from getting into breeding TBs, but Helen_S gave you some invaluable bloodline info and others have given you some great advice as well. We only want what is best for you and these particular horses.
You may produce a low level race horse from this breeding. You could have fun racing that at the low end tracks if that is what you want to do. It won't make you rich and you could very well lose money, but if it's a hobby you want and you're going to be a responsible owner and make sure the resulting foal is taken care of after it's racing career is over (which will likely be very early in it's life), go for it.
Not all race horses are created equal.
A horse named Flower Alley ran 14 times in his career. He won $2,533,910, or an average of $180,994 per race. His stud fee is $20,000.
He was bred to a mare named Arch's Gal Edith. That mare only raced one time, but she pocketed $25,000 for that race. Perhaps she got injured? But her single race was against high level competition and she won. Her family (up close) also has blacktype stakes winners all over the place.
Those two horses were bred and they produced I'll Have Another, who won the Kentucky Derby last year. His breeding was "low budget" by Derby standards.
For comparison, Lady on a Run ran 15 times in low end races, averaging less than $700 per start. She won 3 of them against similar quality horses. Her sire averaged about $30k per start and she did not live up to his level of performance.
The stallion you want to breed her to, Slip Me A Mickey raced 7 times and averaged just over $6,300 per start. His sire was a "moderately successful" race horse, but in both horses you have to go back several generations to find a horse that was a super star. You're getting farther and farther away from those talented ancestors.
I'm not saying you shouldn't do it. Go hang out at the low end tracks. See the claiming races - that's where a horse of this breeding would be running. If it's something you're still interested in doing as a way to be a race horse owner, go for it - but you do need to be realistic about what you are producing.
Or invest as part of syndicate to get a better shot at your Derby dream.
The cost of producing a Derby horse start not just with the gamble of breeding (and I agree...nothing in the pedigree and race record of these two and their family indicate a potential to produce a Derby horse)....but don't forget the costs of raising, training and then racing.
I'd geld the stallion. Give him a better life. These horses came to you for a safe place and good life. Enjoy them....NO ONE is saying they are crappy horses by any means.
Good TBs are looking for safe places to land. I just got a mare as a potential broodmare for sport horses....I liked her conformation, she is a lovely mover...and has super SUPER clean legs even after racing in 105 races. Sweet personality and very smart....her pedigree, particularly her dam line has some very strong lines for jumpers. I have little doubt she will produce a nice sport horse for me....and I would never think of breeding her for a race prospect. http://www.pedigreequery.com/kourages+kelly
** Tact is the ability to tell someone to go to hell in such a way that they look forward to the trip. ~Winston Churchill? **