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i just started again and got focus after fighting ochu in killika and hit it for about 2024 damage with valefors overdrive. then five mins later i used focus a few times agasnt the sin spawn summoned valefor and he did 2900 damage. the only stat change for yuna had been defence increase by 1. so dose focus effect summon strengh?
To the best of my understanding, focus raises the target's magic and magic defense.
What implications that has for you I dunno, but chances are the Sinspawn just had a naturally lower defense than the Lord Ochu... Or Valefor was lucky enough to manage a critical hit...
One of two possibilities could have happened here; either the bonus from Focus passed via Yuna to the Aeon (not 100% sure about that), or the hidden battles bonus occurred.
On the first front Focus effectively increases both your Magic and Magic Defense. Rather than affecting the base stats it adds a bonus during the damage calculations. It stacks up to five times and lasts for the whole of the battle until the target is killed or petrified. On the second front there is a hidden bonus procured on Summons during the game based on the number of battles you have fought, which follows Yuna's sphere grid in terms of gains quite closely. This is to make sure the Summons remain strong throughout the game even if you fail to level-up Yuna.
most of the time i get to that point valefors overdrive dose the same damage to both bosses the only differance in this one is that i used focus in the second boss. it wasnt a critical hit and i used the same overdrive both times.
I don't think any aeon overdrives can critical hit, certainly not either of Valefore's. Maybe Oblivion and/or Delta Attack, but none of the others.
Anyway, Focus doesn't pass to the aeon, so it probably was the battles modifier acting here.
As for exactly how focus works, when casting magic, it's treated as if your Magic stat is 1 higher for each time Focus was used (however, this can only accumulate to a maximum of 5 times). When receiving magic damage, it's reduced by 1/15th for first focus, 2/15th after 2nd focus, and so on, up to 5/15ths on the 5th (after this, it has no further effect).
Note that this works slightly different to Shell and Magic Defence+??% (and it works the same as Magic Break). These two work on magic-type damage, whereas Focus works on attacks that use the magic and magic defence stats. While nearly all attacks with one of these properties also have the other, there are some exceptions. For example, Demi and Gravija do magic-type damage, however the magic and magic defence stats are irrelevant to these. Therefore, while Shell and Magic Defence+??% will effect damage from Demi/Gravija, Focus (and Magic Break) will not. Pretty much the only enemy attack which is the other way around(based on magic stats, but not considered magic-type) is Seymour Omnis's Ultima. You'll notice that while Magic Break(if he's even vunerable to it) and Focus will reduce the damage it deals, while Shell and Magic Defence+??% have no effect on it. (Note that this is NOT a regular property of Ultima. This only happens for Seymour Omnis's Ultima, and when using Ultima Fury... maybe Yu Yevon's Ultima as well, not sure on that one). This kind of property is quite rare for "magic" attacks, it's far more common with physical attacks. (However, your party does have a few magic attacks of this kind - specifically, any overdrive which is based on the magic stat - INCLUDING FURIES)
Focus does not pass from summoner to Aeon, but does Focus or Cheer used by the Aeon itself affect the Aeon's overdrive?
Valefor probably just had its stats improved during the hike from where Ochu is to where the Sinspawn is.