Match History
I know Rod of Ages isn't that very standard on Galio, but if you have a good laning phase and you have the option to buy it, you should.
The regen when leveling up is great to surprise your enemies with in teamfights, and it gives you a good mana pool.
Since Galio does require mana a bit much, buy an Athene's Unholy Grail if you don't go for ROA. Another reason why ROA is good, its the hp.
You have to initiate fights, so that extra HP is helpful too. And well, can't complain about the extra AP either ^^
If you look closely at the enemy team, they barely have any AP (aside from certain skills ofc). Which sucks as Galio, who scales AP on MR.
This is why I also built a ZZ-rot Portal and GA (this is also a reason why ROA works better than Athene's in this match).