LOUISVILLE, Ky. — The math makes no sense.

You start with about 22,300 foals in 2014. Figure about half of them are colts, so you’re down to 11,000.

Of those, the field gets cut some more at the start of their third year, when you have to pay $600 to nominate your colt – or on rare occasions, filly – to be eligible for the Kentucky Derby. This year there were 418 nominations: 378 colts, 30 geldings, five ridgelings and five fillies.

That puts it at 1.9 percent of the 2014 foals eligible for almost every horse owner’s dream.

Then cut it to a minimum of 18 horses – two of the 20 berths are reserved for the winners of the Hyacinth Stakes in Japan and the UAE Derby in Dubai – and the pool is down to 0.08 percent.

You would have to be a fool to play such odds. Right?

Trainer Doug O’Neill, who has won the Derby twice in the last five years, nominated 21 horses. He’s down to one.

Todd Pletcher, a trainer who has won one Derby, nominated 33 horses. He qualified five but scratched two of them this week.

Trainer John Shirreffs, who has won one Derby, nominated two, and has one in the race and one on the bubble.

And trainer Bob Baffert, who has won four Kentucky Derbies and the Triple Crown, nominated 21 horses with no qualifiers.

“It’s such a huge challenge,” O’Neill said. “The numbers really go against you. What helps us is having guys like (owners) Paul (Reddam) and Kaleem Shah, who are willing to go to auctions and spend money for top prospects. But there are no guarantees.”

O’Neill started with 50 horses, 40 bought at sales. Most of the others were bred by Reddam, O’Neill’s most engaged owner.

“There were six or seven who I thought really had a chance,” O’Neill said.

Reddam bought Dog Gone Lenny for $490,000. The colt has one second in three starts. O’Neill said he just didn’t develop fast enough.

W.C. Racing and Zayat Stables bought Dangerfield for $450,000. In seven starts he has one win, one second and two thirds. He came out of a race sore and O’Neill has him pointed to the second half of the year.

One sure thing is money doesn’t guarantee a winner.

California Chrome, considered a lowly Cal-bred, and I’ll Have Another, bought for $16,000, both won the Kentucky Derby and Preakness. But they also gave hope to the non-big-bucks owners that they don’t have to spend a lot to win racing’s top prize.

“It probably gave most of us in the business the realization that it doesn’t matter if you paid $1 million for a horse,” O’Neill said. “It’s what they have in their heart and their competitive juices that count. If you can keep them injury-free while winning the preps, crazy things happen.”

Shirreffs’ success rate this year will get him into any hall of fame. He has Santa Anita Derby winner Gormley, and Royal Mo is waiting for one horse to scratch to make him eligible.

“I had just five colts,” Shirreffs said. “This was a very good year. Obviously you just have to get really lucky.”