The oldest study I found on this was with basketball, I believe in the 1950s. The theory was that since the imagination group was able to make perfect shots every time, this accelerated the process.
https://sci-hub.ru/10.1080/10671188.1960.10613109
Clark, L. V. (1960). Effect of Mental Practice on the Development of a Certain Motor Skill. Research Quarterly, 31(4), 560–569.