NEW YORK — There’s a lot of rich history behind Ogden Mills ‘‘Dinny’’ Phipps. His great-grandfather, Henry Phipps, made his fortune in the iron and steel business with childhood friend and business partner Andrew Carnegie in the late 1800s. His grandmother, Mrs. Henry Carnegie Phipps, owned Bold Ruler, the sire of 1973 Triple Crown winner Secretariat, the greatest racehorse in history — and a colt the family lost despite winning a coin flip. His father, Ogden Phipps, ran the family’s racing empire that included nine champions, among them Buckpasser, Easy Goer, and the undefeated filly Personal Ensign.His first cousin is Stuart Janney III, whose parents owned the great filly Ruffian. But Dinny Phipps and cousin Stuart may have topped ’em all last week when their 3-year-old colt Orb gave the family its first Kentucky Derby victory. ‘‘It’s terrific, absolutely wonderful,’’ Phipps said as he gears up for this week’s trip to Baltimore to see if Orb can win the Preakness on Saturday and set up a Triple Crown try in the Belmont Stakes three weeks after that.‘‘I’ve received hundreds of e-mails and texts and we are very lucky with what the reaction has been.’’ For a change, it’s been almost all positive. At a time when racing is under intense pressure to come up with uniform medication rules and penalties, it’s refreshing that no dark clouds hang over a renowned stable — or its trainer, Hall of Famer Shug McGaughey — known for patience, priorities, and playing fair. ‘‘The popularity of Orb’s victory has a lot to do with what the Phipps family has meant to racing — a long tradition of service to the industry,’’ said Steven Crist, editor and publisher emeritus of the Daily Racing Form. ‘‘The family has always believed that wealth and privilege also confer responsibility to improve the sport and the welfare of horses.’’ Phipps also is chairman of The Jockey Club, a 119-year-old organization dedicated to improving breeding and racing. Recently, it has taken a lead role in calling for racing commissions to come up with ‘‘common medication rules’’ and dole out stiff penalties to cheaters. That sets Phipps up for plenty of criticism. “I think we can bring people along to get the cheaters out of the game,’’ Phipps said last week at his Manhattan office at Bessemer Trust, the private wealth-management firm where he’s a board member. ‘‘I don’t think there are a lot, but the public perception is there.’’ For all the champions the 72-year-old Phipps has bred and raced over the years, perhaps his most important move was not of the equine kind. In 1985, he was looking for a new trainer and pegged McGaughey as his man. ‘‘We had watched him, saw his fillies run and saw his other horses run, and they looked well taken care of,’’ Phipps said. ‘‘He wasn’t sort of a famous name at that time, but he was up-and-coming, young, and bright, and his horses looked good and he ran a clean stable.’’ Owner and trainer became friends. Champion racehorses followed: 1989 Belmont Stakes winner Easy Goer, Personal Ensign, Inside Information, Rhythm, and Storm Flag Flying, to name a few. McGaughey has been fishing on Phipps’s boat, played golf with him at Augusta National, and has been a dinner guest at his estates in Palm Beach, Fla., and Old Westbury, N.Y. Winning isn’t the only reason their long friendship has flourished. Phipps allows McGaughey to make all the calls when it comes to racing. ‘‘Everything that I do and any success that I’ve had I attribute to this being my ballgame with horses on the racetrack,’’ McGaughey said. ‘‘The Phipps and Janneys don’t question you, they don’t tell you, ‘We want to run in this race, how come the 2-year-olds aren’t running in June?’ They understand. They’re patient with me.’’ Says Phipps: ‘‘He’s somebody who loves to compete. He gets his horses right, and they look well. I have never gone into his barn and seen something I thought was out of place.’’ The Phipps Stable is a breeding business, too, and it’s the backbone of an overall operation totaling about 100 horses, including 20 co-owned with Janney. The stable does not go to sales, like many owners today, to pick out their horses. Instead, they breed their own, and currently have 25 mares at Claiborne Farm in Paris, Ky. ‘‘Our philosophy is that we love our fillies,’’ Phipps said. ‘‘They will all keep producing as long as we treat them well and put the right ones back into stud. We’ve always tried to have trainers that are good filly trainers because to go out in the marketplace today to buy colts and fillies — with a colt you’ve only got 25-30 of them in a crop that do well out of 20,000-25,000. “They are not worth much if they are not in that 25-30. Whereas a filly, if she does decently she is in the position to help you for a long time. We believe the broodmare is the most important quality of the racehorse.’’ Winning the Derby has always been a dream, but never a priority in the Phipps way of thinking. ‘‘Sure, something would have been missing if we didn’t win, but we’ve had such a wonderful career in racing that it really wouldn’t have been something that was glaring missing,’’ Phipps said. ‘‘It does mean a great deal now that we have won it, but we have never tried to force our horses into that race and I just don’t think we need to do that.’’ It’s true there have been some great racing moments for Phipps. He called Personal Ensign’s remarkable, final-stride win over Winning Colors in the 1988 Breeders’ Cup Distaff one of the greatest races he’s ever seen. He ranks Orb’s Derby win right up there, too.