The marathon's odd 385 yards come from a royal box in 1908

The 1908 Olympic marathon in London ran from Windsor Castle to the royal box in the stadium. A late change of entrance cut the stretch inside the stadium to 385 yards.
On July 24, 1908, the Olympic marathon started on the East Lawn of Windsor Castle. King Edward VII had given permission to start inside the private grounds so that the public could not get in the way, and the Princess of Wales drove over with her children to watch.
Until then the Olympic marathon had no fixed length. The races had been about 25 miles, and each depended on its route. For London, the IOC had agreed on about 25 miles. The organizers planned about 26 miles from Windsor to the new White City Stadium, then a full lap of the track, finishing in front of the Royal Box.
Shortly before the Games they found that the runners could not come in through the Royal Entrance. It was raised so the royal party could step down from their carriages, and it did not open onto the track. The runners would use an entrance diagonally across from the Royal Box instead. The finish line stayed where it was, and the race would go around the track the other way, so that more spectators could see the last yards. That left 385 yards to run inside the stadium.
The day was hot. Pietri started slowly and worked his way up through the field. At the 24-mile mark he passed the leader, Charles Hefferon of South Africa. The effort cost him. With just over a mile to go, he began to suffer from exhaustion and dehydration.
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He came into the stadium in front of 75,000 people and turned the wrong way. When the officials redirected him, he fell. They helped him up. He fell four more times, and each time they helped him up again. He crossed the line first, in 2 hours 54 minutes 46 seconds. The last 380 yards had taken him about ten minutes.
Johnny Hayes of the United States finished 32 seconds later. The American team protested at once against the help Pietri had been given. The protest was upheld, Pietri was disqualified, and Hayes got the gold medal. The next day Queen Alexandra gave Pietri a gilded silver cup.
Both men turned professional and raced each other again over 26 miles 385 yards. Pietri won their first rematch, at Madison Square Garden in New York that November. Other marathons took up the London distance too.
In 1921 the sport's international federation fixed the marathon at 42.195 kilometers, which is 26 miles 385 yards. Its minutes reportedly do not say why it chose that figure.