Ionian Boots of Lucidity are a good choice if the enemy team doesn't build Magic resistance. I find that in many matches where you're the only mage, the enemy team doesn't build magic resistance, and therefore the faster ability cool down is more useful.

@jokersprank : Thanks for your comment. As you said, There is still much to do on that guide.
I didn't modified it for years and many details has changed. It takes times to correct everything and I'm doing this slowly. =)

Concerning the runes, I agree about CDR quint. It is interesting especially the Scaling CDR quint. 15% CDR at level 18 is huge. I was calculating those days the better way to reach the 45% CDR cap and still maximize the damage output. I'll take it in account in my math formula. Thanks ! =D

About the Marks of MPen, this is not exactly true. I'll explain, Mpen is really much more interesting starting from some amount of AP. That amount of AP depends on few facters which are : enemy's magic resist, your own AP and MPen and MR reduction. Of course, as flat MPen is applied last, it is the least effective stat for damage dealing.

According to the damage formula (math based on 5th rank of   Orb of Deception), on a standard match up, i.e. a champion with 30 base MR, the efficiency of flat MPen will be visible starting from 182 AP if you stay at 7.83 Mpen (marks only). Admitting you buy Sorcerer's Shoes, you gain 15 flat MPen, meaning you have 22.83 flat MPen, in that case, your MPen will be effective starting at 76 AP.
If you have an MR tanky champions with 54.6 base MR like Mordekaiser, the efficiency of MPen vs AP will be visible with 7.83 Mpen (marks only) at 374 AP. If you have bought Sorcerer's Shoes, 254 AP.
Of course, MR reduction and % MR reduction or % Mpen reduce greatly the AP cap for the MPen efficiency. On champions with 54.6 MR, with 20 MR reduction (from Abyssal Mask), the efficiency of 22.83 flat MPen is visible starting from 108 AP.

Concerning Masteries, I agree that Secret Stash may be of any use in some situations but when you are facing an assassin like LeBlanc, it's useless. The damages assassins champions are dealing are too important to be healed by few potions. Late game, a good LeBlanc will be able to quickly kill any Ahri if in range. A potion never helps in such match up.
the most commonly useful mastery here was Assassin , that's why it was my first choice.

For the summoner spell, I forgot to remove Garrison. Thanks for the information. I fixed that. =D

About my MPen efficiency section, my plan is to calculate the best build in order to maximize all the stats in a standard situation. I planned to have a sort of diagram of choice depending on the situation. But it's the hardest part of my guide as it will include a tremendous number of variables. I'll try to work on this quickly.

To finish, thank you very much for your comment, it helped me a lot ! =D

I didn't know there was such an old Ahri guide. Will look later over it!

Edit:

Runes

Will it always do 5% more damage? I would have to make the math on Greater Mark of Magic Penetration.
I think Greater Quintessence of Health is totally outdated. The new weird quint is CDR. Additionally, you shouldn't always compare the AP version with your choice. There are different primary marks you could compare with (link for more information).

Masteries

First thing I want to notice is that Assassin is not the only choice. The range of the mastery is like 700 range and in the mid game you already start to group for dragon or ganks. Ganks happen quite often in the mid lane. I think a better reasoning would be that Assassin increases your chance of winning the lane, hence, snowball out of control. Furthermore, Secret Stash is never bad. Sometimes you are against someone who is stronger than you in lane, e.g. Zed or LeBlanc and there you need the increased duration of pots.

Summoner Spells

Don't recommend stuff that isn't in the game anymore since I assume you mean to play on SR.

Magic Penetration

I think this somebody meant the usefullness of flat magic penetration vs %-magic penetration. I think you should rather make the math when you should buy Sorcerer's Shoes, Void Staff or Abyssal Mask. Additionally, the difference between Piercing Thoughts and Precision.

Conclusion

Much work is left.

+1 deserve a better ranking

Nice build but i prefer to buy both RoA and rylai. I'm so tanky with that. <3

@Edelweiss
Merci =p

gg pour ton guide.

@Goetite & @Hakuoro

Thanks =D

You should have bought Rylai's directly after Hextech revolver.

nice guide,good job!

explain ?