Polydream is the morning-line favorite to give trainer Freddie Head and owners Alain and Gerard Wertheimer their fourth win in the Breeders’ Cup Mile on Saturday at Churchill Downs. Kind of.

At odds of 5-1, Polydream is the most tepid of of morning-line choices in a race where eight horses are listed at odds of 10-1 or lower.

An overflow field of 16 was entered Monday in the Mile. Divisidero and Clemmie are on the also-eligible list with 14 permitted into the starting gate. The mile is one lap plus an eighth of a mile around Churchill’s seven-furlong turf course. The grass already was described during racing Sunday as good-to-soft and more than two inches of rain are forecast to fall here midweek. The going will be a concern.

Polydream has two wins and a second from three starts on soft or good-to-soft ground in France, the only country in which she has raced. Head and the Wertheimers famously captured three straight editions of the Mile – the last at Churchill Downs – with the great Goldikova, like Polydream a homebred,

Polydream, who has Maxime Guyon named to ride, drew well in post 5. Stuck on the far outside is Mutashry, who wasn’t originally selected as part of the Mile field and needed a defection to get in. So, too, did Almanaar, who drew post 6. Almanaar, a longshot, is one of two in the race for trainer Chad Brown, who also starts 3-year-old Analyze It, who breaks from post 12 and figures to be prominently placed.

Aidan O’Brien tops Brown with three Mile starters. Three-year-old filly I Can Fly (post 8) is 8-1 on the line after a good second over soft ground Oct. 20 in the Queen Elizabeth II Stakes, a straight-course mile at Ascot. Gustav Klimt (post 13) has struggled to win races but is the mount of Ryan Moore, top dog in O’Brien’s stable of jockeys. Happily drew post 3 and would do well on her established form to crack the top half of the field.

Oscar Performance, the leading North American miler, breaks from post 5 and is 6-1 on the line on the strength of a last-out win in the Woodbine Mile. The draw is good for Oscar Performance, but he ran dismally in a previous race over a wet Churchill course, albeit in the spring.

Next Shares (post 2, 10-1) might have a fondness for softer ground, or so it looked when he upset the Grade 1 Shadwell Turf Mile on Oct. 6 at Keeneland, winning by 3 ½ lengths at odds of 23-1. The Shadwell, like the Woodbine Mile, was a Breeders’ Cup Challenge “Win and You’re In” race linked to the Mile.

One Master, who won the Group 1 Prix de la Foret on Oct. 7 at Longchamp at odds of 47-1, drew post 1 and won’t at all mind soft turf, according to trainer William Haggas, who is running his first Breeders’ Cup horses this weekend.

Expert Eye carries the colors of Khalid Abdullah’s Juddmonte Farms, winner of many Breeder’s Cup races but never the Mile. Expert Eye, who drew post 7 and is 8-1 on the line, will have a solid chance if he can cope with the course condition.

Californians Hunt (post 9, 30-1) and Catapult (post 10, 6-1), are will encounter turf like they’ve never felt beneath them before. Lightning Spear (post 10, 11-1) comes from England but is no fan of boggy courses himself.