I think it's important to distinguish the various sets of data. Take character data, for instance:

1. There needs to be a block of constant data for initialization. These are the stats for a level 1 naked character.
2. There is a block of data for the current "naked" character. It is the data from above plus any added boosts from level ups.
3. There is an effective character data. This is number 2 plus any boosts (or penalties) from equipment.
4. Finally, there is a copy of #3 that goes into battle, but can be further modified by spells, status effects, items, etc.


Now let me explain why each one is necessary.
(1) is just the initialization data. It is needed for a base of the character's data. This doesn't have to be stored in memory, but has to be kept separate.
(2) is an accumulation of your stats as a result of level ups. It represents the "current" lowest common denominator. Since the 5 base stats have random chances of increase on each level up, over time, these can vary widely depending on your luck. In short, it cannot be definitely determined from level alone. This is probably what would be copied to a save file.
(3) is needed to indicate the effect of equipment. It is calculated from (2) and the equipment data.
(4) is needed since there are spells (and could easily be items too) that affect attributes. There are spells that lower evasion, for instance.

Each of these transitions (1) to (2), (2) to (3), and (3) to (4) can cause you to hit a cap, either at the top end or the bottom end. [Note, (1) to (2) shouldn't, but it's best to be consistent]. As a result of this necessary clamping, all of these types of data must be kept.

(I chose character data because it's the most complex).