From Wiktionary, the free dictionary
From mid- + stretch.
midstretch (not comparable)
- (sports, often with "in") In the middle of the stretch of a race
2007 August 6, Bill Finley, “Any Given Saturday Outruns His Top Rivals to Win the Haskell”, in New York Times[1]:Ridden by Garrett Gomez, he collared Hard Spun in midstretch and drew away with surprising ease […] .