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I didn't quite understand... What size are you referring to? Does it take up more cells? Or am I in the wrong section...?
- increased damage
- increased survivability
- decreased initiative
From a practical point of view, it doesn't carry any other information. That is, this is simply how I explained why the summoned phoenix grows in stats and why it grows in this way.
As a side effect of this approach (through physics), there is a limit to the phoenix's development. At its peak (SP 17 expert summoner), the summoned phoenix reaches the strength of approximately 2 dragons. And not unlimited, as in the original, where it could easily take down 10.
A more powerful alternative to the phoenix with very high spell power can be elementals. After all, their strength grows with the number, and there is no such limit.