It could be considered a tank destroyer but not a tank because tanks are mainly meant to support infantry but the Puma is only useful as an AT unit but it would still be a light tank destroyer because its gun would be small for tank destroyers and it has very light armor.
The Pershing is a heavy tank because its gun size and armor are much greater than other American mediums and just because the German military had different standards for what a medium was and what a heavy was doesn't make the Pershing a medium and this fits into the game well because the USF are supposed to have inferior armor in the same categories compared to the Axis.
But Sherman or E8 are not inferior to Pz 4, Jackson is not that inferior to JPIV.
If we take a look at all heavy tanks: Tiger, Elephnat, King Tiger, Sturmtiger, Jadgtiger, IS2, ISU152, Churchills, they have 2 things in common:
- slow speed
- high HP pool
Size of a gun, AoE, cost don't matter becasue we have huge AoE like ISU, or no AoE like Elephant, very expensive tank like King Tiger and way less expensive like Churchill, yet HP pool and speed is something they share.
What about heavy-mediums? Panther, Comet, to some extent Easy Eight and T35-85, but mostly only Panther and Comet:
- high speed
- medium hp pool
- good vs infantry (except Panther)
- armor which matches heavy tanks (Panther & Comet)
So here is thing. Whic group has more in common with Pershing?
Pershing perfetly fits in heavy-medium group like Comet and Panter. It has way more in common with them than with Tiger or IS2. Heavy tank are not made for fast flank, Pershing is, like Panther or Comet.
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@UP What supierior stats Pershing has to Panther? Only AI but apart from that, armor, speed, cost and worse.