Lets just say that the camel jockeys needed a world superpower
- at war with itself
- at its weakest in 2000 years
- led by a 12 year old boy
- fatigued by 2000 years of non stop war with the Greeks, and Romans, and Byzantines
- an ally that delayed troop deployment
- a kid who waited to long
- an unlucky arrow
and
- a sandstorm from hell in the face of the rallying Persian army
To really defeat the weakest Persian army under the weakest Persian ruler possible and a populace controlled and split by war chieftains (our version of your Jaichands).
The war did not end there. Persians fought on for another 300 years in pockets across the land, as initially only the noblemen converted, till finally the commoners all converted by 1000 AD, crippled by tax and increasingly persecuted by their own, the new Persian converts.
Cheers, Doc