I think Red is actually in the Purple family…of garlics?
From what i read its anthocyanins that turn garlic purple… and its under certain conditions…what those are i dont know. Maybe more nutrients or more cold or something?
I dont see any red/purple on this pic
https://www.highmowingseeds.com/organic-non-gmo-inchelium-red-garlic.html
Gurneys pic shows them red.
I think big cloves have alot of stored energy which gives the garlic a better chance at growing… however its the nutrients and spacing and lack of competition that makes them grow biggest.
Stuff like compost, leaves, mulch, organics and wood ash and most importantly soft sandy loamy soil grows the biggest garlic… at least from what i have read.