https://www.strengthandconditioningresearch.com/promotions/quarter-squats-transfer-sprinting/
Cool article.
I'm emailing the author to see if they have video to share - I doubt it... But it would be useful.
The problem with this article and a lot of article is that they don't understand that while joint angles in squats are fixed joint angles in jumps are not. You can't say the joint angle in a quarter squat is more similar to the joint angle in a vertical jump. Kingfish's best vertical jump comes from a joint angle that is identical to a full squat. Mine is between a half and a quarter squat. The vertical jump doesn't have a joint angle - it is a jump not an prescribed exercise with a defined range of motion!
We all do it differently. And unfortunately that difference isn't just dependent on your structure it is dependent on your strength.
Take an extremely weak beginner and make them do a vertical jump or a running double leg jump. (I just trained one). They will do a 1/16 or less squat. So I guess that means for them they should do a 1/16 squat? No way! They are not strong enough to use more than a 1/16 squat - but if we train them and get them strong and stable maybe their best vertical jump comes from a full squat or half squat... We can make guesses based on their structure but we can't be sure...
This is why I think everyone*** should start with full squats. I actually favor half squats over full squats for athletes but I think full squats are a necessary base to build strength and mobility. When your training an athlete who wants to jump you should get him capable of sitting down in a full squat with close to bodyweight. I usually use 135lbs for most guys. Get them able to hit full depth, pause, and drive up with 135. After this is accomplished then train with half squats, quarter squats, etc and test vertical jump. If the athlete performs vertical jumps best with a deep squat then deep squats should not be abandoned - again use structure for clues here. If the athlete doesn't jump with anything near a full squat then they don't necessarily need them - you can keep them as warmup (or do bar overhead full squats - great mobility warmup), but you don't need to progress.
*** Everyone doesn't mean everyone. I make an earnest effort for most people. It might require oly shoes, plates under shoes, a lot of stretching, and it might not be totally full... If the guy is 7' feet tall it might not be worth the effort to build a full bodyweight squat... But within reason I like athletes to get this mobility figured out... How do you know you shouldn't use a deeper squat to get a higher vertical jump if you have zero strength or comfort or range of motion at that angle...
This is my caution with praising partial squats. It allows a shortcut. I feel I have earned the right to do partial squats! I am 5'11 and have really long legs and no torso. I still built up my oly pause squat to 400 and could do 315x15 pause squats. Despite that I could never jump at all out of a full squat and always vertical jumped with a high joint angle... I am confident that I'm not selling myself short by not building my full squat bigger.... But that's not the same as some kid with short legs who jumps 24'' and can't full squat 135 doing ugly pin squats with 405 and claiming that he doesn't full squat because it doesn't translate to his jump. If your vertical is 24'' you don't have a jump.