Since champions level, and since experience is gained through combat, it might seem superfluous to detail how many enemies that unit has killed, or how many battles it has survived, but that kind of data really helps me grow attached to some units over others, which enhances immersion and the RPG experience.

When I played X-COM, I would keep a notebook for jotting down what each character--note "character" instead of unit--did in each battle, and I'd detail their entire career, creating a narrative for each of them.  Characters I initially did not care about, like Yuri Petrov, became my favorites because of the amazing things they had accomplished.

The more stats a game compiles for each character, the easier it is to develop those attachments.  Think of baseball, for example, where your star hitter becomes apparent after several games, even though his stats (agility, strength, and so on) may not technically make him the best.  In turn-based strategy, which some describe as playing a spreadsheet, it's important to create those irrational attachments, so that the "optimal" choice may not feel like the best choice to the player.  The player's emotional experience is what's really important.