The Breeders’ Cup is a difficult handicapping endeavor. The world’s best horses face off in races that showcase their strengths, often giving each horse a case for victory. That also helps keep favorites from dominating. Post-time favorites have won just 31 percent of Breeders’ Cup races, making the event ripe for playing upsets.

One long shot to consider Saturday is Tacitus (20-1) in the Breeders’ Cup Classic. Tacitus has struggled to find the winner’s circle this year (he’s 1 for 5 with a second- and a third-place finish), but his past two races deserve more scrutiny. The son of Tapit was the victim of a wide trip in October’s Jockey Club Gold Cup at Belmont and was the second-fastest horse after taking into account the actual ground covered (54.8 feet per second). Tacitus was the fastest horse in the Woodward Handicap at Saratoga in September despite finishing second to Global Campaign by 1¾ lengths. That means Tacitus easily could have two Grade I wins in his past two races. He also won July’s Grade II Suburban Handicap by 8¾ lengths.

Trainer Bill Mott has decided Tacitus won’t be on the lead Saturday as he was in the Jockey Club Gold Cup, playing better to his horse’s strengths as a stalker. Jockey Jose Ortiz is also successful with that running style, having won 20 percent of his races in 2020 with horses who stalk the pace rather than press the lead.

Here are three other long shots to consider, with morning line odds as set by Keeneland:

No. 9 Harvey’s Lil Goil (20-1), Filly and Mare Turf

Harvey’s Lil Goil won the Grade I Queen Elizabeth II Challenge Cup Stakes at Keeneland a few weeks ago, giving sire (and Triple Crown winner) American Pharoah his first Grade I winner. Other wins on the filly’s résumé include the Grade III Regret Stakes at Churchill Downs in June and the Busanda Stakes in February.

The latest win at Keeneland also set a new career pace figure (speed to the half-mile marker) for the 3-year-old, indicating her next race should be her best yet.

No. 9 Empire of Gold (30-1), Sprint

This race is light on early speed and heavy on horses who need a faster pace to be successful. Yaupon certainly will be on the lead early, and Frank’s Rockette will be, too. A two-way battle for the lead may be enough to discount both in favor of the next flight of horses, which should include C Z Rocket, Collusion Illusion, Firenze Fire and Empire of Gold.

Empire of Gold has produced the fastest pace figure to the first call (quarter-mile mark) and the second-fastest final speed figure in the field. If he can conserve some of that energy early and use it later in the race, it could make for a lucrative upset.

No. 6 Lady Kate (15-1), Distaff

This race was lacking speed until Lady Kate was given a saddlecloth. She is the lone front-runner in a field of 10, and that could give her an early — and deciding — edge. Adoration went wire-to-wire in 2003 at Santa Anita and paid $83.40. One Dreamer broke from the gate and never looked back in the 1994 Distaff at Churchill Downs and paid $96.20.

Lady Kate’s best effort was two races ago, when she finished second to heavily favored Monomoy Girl in the Grade I La Troienne Stakes at Churchill Downs in September. She also has the pedigree to stay 1⅛ miles. Her sire, Bernardini, was the champion 3-year-old in 2006, and the progeny of her dam’s sire, Street Cry, included Zenyatta, the first female to win the Breeders’ Cup Classic and the first horse to win two Breeders’ Cup races.