I have to say I'm a little confused about the fact that you (imo) don't properly back up some of the claims you make.
1) Saying something is "mathematically better" really doesn't mean much without the numbers to back it up, which is why it seems a little odd to mention that after declaring you haven't done all the math yet :P
Alternatively, you may have left the numbers out since you said at the end of your post that the difference in Magical Power between the two items is 5 instead of 15 and therefore thought doing calculations was unnecessary. Either way, it's important to determine how much gold a difference of 15 Magical Power and 10 Magical Penetration translates to and how that compares to the CDR/Mana from Shoes of Focus.
However, there's one tiny problem when trying to do this: as far as I know, Hi-Rez hasn't actually told us how much every stat in this game is worth. As such, the best way to get an estimate value is to do calculations based on the stats and gold costs of some of the base items, but even that is a nowhere near perfect method. After all, every item in the game has its own "gold efficiency ratio"; some provide exactly as much as you pay for, while others are (slightly) more efficient or inefficient. For example, without even doing any math, it should be clear that using Magic Focus to determine how much 15 Magical Power is roughly worth would lead to a completely different outcome than the more gold-efficient Soul Reliquary, which provides more Magical Power and extra Mana for an overall lower price.
On top of that, some of the other users in this thread have already rightfully pointed out that other factors influence an item's value as well. If your God has such high cooldowns that you'll only be able to use one spell rotation per teamfight, amplifying the damage of that rotation will always prove more efficient than investing in CDR, for example.
For the record, I'm not trying to state that you're wrong in saying that buying Shoes of Focus is mathematically better (in fact, I have no idea whether you are or not), I'm just curious to learn how you reached that conclusion based on the stats alone.
2) While you are right to point out that there's some synergy between Shoes of Focus and Book of Thoth, I feel like I should mention that 3% of the 250 Mana which Shoes of Focus provides is only 7.5 Magical Power. As a result, combining Shoes of the Magi with Book of Thoth should provide 250 less Mana, but still 7.5 more Magical Power. Obviously, there's a decent chance that this synergy makes Shoes of Focus more gold-efficient than Shoes of the Magi overall if it wasn't already (since the gap in Magical Power between the two still becomes smaller with Book of Thoth involved than without it), but I just figured it's worth pointing out.
Also, I feel like some of your numbers are slightly off:
...That should be all I have to say about this for now :P
You're actually right about the second half of my post. I didn't add the value of the base Mana gain of Book of Thoth. Anywho, this post was fairly late, so my math was a complete mess at that point. I'll get to updating it eventually. Thanks for the correction man.
<3
It is 15 ekstra power and 10 ekstra pen for less dosh.
I pretty much only play burst mages (Isis, Ao Kuang etc.) so the early damage is great.
You have like 15 cdr items that do more than just give cdr (winged blade, renewal, breastplate etc) and chronos pendant ofc.
Mana is in my opinion a useless stat, come lategame the 250 mana wont matter at all, get meditation Kappa
Focus is good for healers though, and Janus, Nox and other gods that have big useful abilities that you want to be able to spam.
It is 15 ekstra power and 10 ekstra pen for less dosh.
I pretty much only play burst mages (Isis, Ao Kuang etc.) so the early damage is great.
You have like 15 cdr items that do more than just give cdr (winged blade, renewal, breastplate etc) and chronos pendant ofc.
Mana is in my opinion a useless stat, come lategame the 250 mana wont matter at all, get meditation Kappa
Focus is good for healers though, and Janus, Nox and other gods that have big useful abilities that you want to be able to spam.
uhm maybe I'm interpreting (or reading wrong whatever) dosh but it costs more then focus.
Also I'm still for the pool over regen part (still for kkk focus with passive an toth make him only stronger)
Shoes of Focus of course. I haven't touched Shoes of the Magi ever since they've removed the mana from it, it's more expensive and it only provides me 15 more MP and 10 pen, which I can easily get out from spear of the magi later on, most likely 3rd/4th item.
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