More on Ezreal and CDR (and also Ryze somewhat)

In my earlier blog about CDR, I told you that 40% CDR translated to 2/3 more spells. But it gets better. Ezreal's Q Mystic Shot reduces all his cooldowns by 1 second whenever it hits. Which makes it interact very favorably with CDR. Lets look at numbers, supported by my Blue Ezreal spreadsheet from that earlier blog.

At 0% CDR, You get 0.33Qs per second, assuming you hit. Add 20% CDR, and you 0.45Qs per second. That's a 36% increase in Qs. At 40%, you get 0.71Qs per second. That's more than twice as many Qs compared to 0%. CDR. (Now consider how important CDR must be on Ryze, where all his spells interact with all his cooldowns.)
So the curve is really steep on this one. The last 5% CDR gives you almost 3.75 times more Qs per second than the first 5%. So when people started going BT instead of Spirit of the Elder Lizard, I was somewhat concerned.

Q/min along the X axis, CDR along the Y axis

In fact, if you compare a build of CDR boots, Manamune and BT at level 16 with the same build except Brutalizer instead of BT, with the average armor of a level 16 champion plus masteries and seals, despite the BT build costing 45% (1863g) more than the Brutalizer build, the build with Brutalizer is more cost efficient by 12%. And remember, that's ignoring that it stacks Ezreal's passive faster and lowers cooldown on his E for mobility.
And one might inquire as to what happens if your target has more armor than that. But you'd need atrocious amounts of armor to make the BT build more cost effective. About 60000 armor in fact. And if your target has even less armor than in the example above, the Brutalizer build just pulls further ahead.

But what about later down the line, after Last Whisper and Iceborn Gauntlet? Well, even there the Brutalizer build pulls ahead by 8% cost efficiency, again with the same uncalculated benefits of more CDR.

I showed you the effect of CDR on Ezreal's Q, but I'd also like to show you its effect on his E.
At 0% CDR, the CD of E is 11 seconds and you can get in 3 Qs, for ~8 seconds between Es.
At 20% CDR, the CD of E is 8.8 seconds, and you can get in 3Qs, for ~6 seconds between Es.
At 40% CDR, the CD of E is 6.6 seconds, and you can get in 3Qs, for ~4 seconds between Es.
Air time and Q hitting while there's less than 1 full second CD accounts for the squiggly line. 20% is closer to 5.5ish seconds and 40% is pretty close to 4 seconds.
The effect on his R is the same. The CD assuming constant Q spam is 44 seconds at 20% CDR, and 28 seconds at 40% CDR.
 

E/min along the X axis, CDR along the Y axis

So why aren't the pros building their Blue Ezreal with Brutalizer these days? Either they want the lifesteal and ult damage from BT, or their managers aren't paying enough attention to my blog. And given how squishy and mobile Blue Ezreal is, I assert that it is the latter that is the case.