ZSS's average in my opinion.
Not too different from the average.
Carry: 7 {possibly 8}
Stock Tank: 6
Punisher : 7
DPS: 9
Carry; It's pretty obvious that ZSS is a good team carrier. She's not as subjectable to many combos and locks that characters throw out at the roster on the regular due to her flip jump option, judging she has at least three frames of reaction time. She's extremely decent when it comes to babysitting or assisting due to her mobility on the ground and in the air {not to mention her side+B, both grounded and aerial are decent at assisting her partner}.
Stock Tank; When it comes to stock tanking, ZSS can go both ways. She has good mobility, jumps, options of avoid her opponent with flip jump mind games, but in 2v2s, if both characters are focused on her, she can get wrecked... really, really badly. She's hard to punish, but for the lone fact that she dies so quickly, it's hard to say rather she's a good stock tank or a really bad one.
Punisher; She's a decent punisher. Downsmashing opponents as they attempt to recover back onto the stage, rather they roll onto the stage into a downsmash or attempt to go above the stage and into an up+b. When it comes to partner strategies, if a teammate grabs an opponent while near her, she can space a downsmash and stun her opponent out of the grab without hitting her partner.
DPS; Obvious ratio is obvious. Downsmash -> Downsmash -> Aerial racks up unescapable damage with ease. One downsmash can result in a 30%+ combo with one string of attacks.
Gimmicks; As it's been said ZSS goes well with Ness and Lucas due to the PK Magnet recovery. Game and Watch's bucket fill-up via downsmash. With Snake, stun, C4, Up tilt, kaboom.
One other nice thing about ZSS that works with multiple characters in the roster is her downsmash -> footstool setups. Characters like Pikachu can jab lock an opponent out of it, then ZSS can simply downsmash them again if it comes down to a 2v1. Pretty situational, but it's not hard at all to perform if given the chance.