ballast question for hamilton mh pendant

so from my understanding from the previous owner i have a 250w hamilton metal halide pendant with no ballast. with a little research i found what i believe to be the pendant, , so i also see that this same pendant comes in 150, 250, and 400w and the dimensions are the same and everything seems the same other than the ballast itself from what i can see

now the question is, if i were to get a ballast for this would this pendant only function with a 250w mh ballast or can a 150 or 400w be used with the proper bulb?

 

The Ballast needs to be rated for the bulb Wattage as well as the Mogul socket. Make sure they are all compatable.

 

so the socket itself makes a difference as well? thats exactly what i was trying to figure out since the actual pendant is all the same size for that model whether it be 150, 250 or 400 the bulb initially in it was a 250 when i got it so I'll keep an eye out for a ballast for a 250