DUBAI, United Arab Emirates – Bob Baffert has four older children from a former marriage and a much younger son from his current one. Surely he knows the intricacies of family dynamics running through one’s offspring, and perhaps that’s part of the reason why on Sunday, the morning after Arrogate made everyone’s jaw drop going from last to first in the $10 million Dubai World Cup, Baffert made a point of mentioning a recent former star. “Pharoah is still my boy,” Baffert said in a text message shortly before taking off on a long flight back to California. It was less than two years ago that American Pharoah looked like Baffert’s horse of a lifetime, sweeping through the Triple Crown and crushing a good field at year’s end in the Breeders’ Cup Classic. From November until last August, Baffert was without a superstar – and then Arrogate won the Travers Stakes by 13 1/2 lengths. Arrogate’s name, not American Pharoah’s, is the one on everyone’s mind right now, and after a night of venerating the colt, Baffert didn’t want to forget the more-distant past. Baffert has said repeatedly that Arrogate and American Pharoah are much different sorts of horses, and that goes for the way they conduct their racing business as well as their temperament. Arrogate is not ill-tempered, but American Pharoah was the gentlest and kindest of steeds; a child could have ridden him up and down a shed row. Arrogate is less sociable. He tolerates the humans around him but does not embrace them. A video Baffert shot late Saturday night of Arrogate, post-race, in his stall at the international quarantine barn shows Arrogate hanging his head over the stall door. Someone smooches to the colt and Arrogate tosses his head up and down and puts back his ears. Baffert approaches holding up his mobile device and Arrogate scurries to the back of the stall, craning his head at the window. Equine psychology aside, Arrogate looked anything like a tired horse. After missing the break, bumping hard, spotting the leaders some 15 lengths around the first turn, and then passing 13 horses to win the World Cup by more than two lengths, Arrogate had every right to come back exhausted, but he didn’t. “He wasn’t really tired after the race,” Baffert said. Arrogate earned a 115 Beyer Speed Figure for the Dubai World Cup. Arrogate flies from Dubai to Los Angeles on Wednesday. His year-end goal is to win another Breeders’ Cup Classic, and Baffert and the team from Juddmonte Farms, Arrogate’s owner, will at some point soon get down to plotting a path to it. It seems unlikely that Arrogate will race again before August. Gun Runner, who finished a gallant second, five lengths in front of third-place Neolithic, also came out of the race in good shape, according to assistant trainer Scott Blasi. Gun Runner departs Dubai on Wednesday and will take up residence in trainer Steve Asmussen’s string at Churchill Downs, the rest of his 2017 campaign to be determined. “We’re very proud of him,” Ron Winchell, who co-owns Gun Runner with Three Chimneys Farm, said Sunday. “He ran awesome.” Neolithic was losing ground the last furlong of the 10-furlong World Cup, and might prefer distances up to nine furlongs, but held reasonably well for third to complete an American sweep of the top three placings. Mubtaahij, who came into the race less fit than trainer Mike de Kock had hoped after just one start this winter in Dubai, ran admirably to get fourth, and is likely to make his next start on grass in the Queen Elizabeth II Stakes next month in Hong Kong. Mind Your Biscuits, the impressive three-length winner of the $2 million Golden Shaheen, also appeared to have come out of his race in good order, according to trainer Chad Summers. “I couldn’t be happier with him,” Summers said Sunday. “He drank a quarter-bucket of water last night and was ice cold this morning, and he ate up. We’re on cloud 9.” Mind Your Biscuits, who earned a 101 Beyer for the Golden Shaheen, either will be freshened up or sent to New York to point to the Metropolitan Handicap, Summers said Saturday night. The winner of the UAE Derby, Thunder Snow, was made a late nominee to the Triple Crown last week, and thanks to the 100 qualifying points he earned winning Saturday night has a spot in the Kentucky Derby if his connections want it. The decision about how to handle Thunder Snow, who was given a 94 Beyer Figure for the UAE Derby, is complicated because he is a talented grass horse, too, having won the Group 1 Criterium International last fall in France. Trainer Saeed bin Suroor said after Saturday’s race that Sheikh Mohammed bin Rashid al Maktoum ultimately would decide whether to go for the Derby, and in comments during a post-race television interview, Sheikh Mohammed appeared to open to the door to a trip to Kentucky.