the beginning of a thought: shyvanna hextech revolver math
vs 
Normally I imagine you wouldn't want to build either one on shyv but they did add an ap ratio to her W a while back and they did change 
In the case of
its more of a strong AD item that actually costs 150g more than
. I doubt you'd want to build one on shyv but I like to think we've all thought of trying it just once to see how that straight damage melts somebody who is stuck for whatever reason. But
seems to give more burst damage and deals magic damage. This makes it both situationally useful and better against people running
or maybe
in some ways. It also doesn't get trolled by
W or things like this if there is anything else like this or that has a similar effect. Like this guy
or this other one 
A probably incorrect build I have in mind is fervor +
into

assuming this is even a good idea for any reason probably the superior option would be to build into
but this may still be fairly troll.
But this is all just a thought I figured I'd bounce around and see what happens
W deals Damage Per Second: 20 / 32 / 45 / 57 / 70 (+ 20% bonus AD) (+ 10% AP) per second for 3 seconds and Damage Per Attack: 5 / 8 / 11.25 / 14.25 / 17.5 (+ 5% bonus AD) (+ 2.5% AP) per autoattack
it also gives a speed boost etcetc
but I wonder what happens if you only get two autos in but you get the full duration of the flame at two autoattacks
each autoattack increases the effect by 1 second so it will be 2 extra seconds making it a 5 second DoT
Total damage for the flame itself will be
100 / 160 / 225 / 285 / 350 + (1.0 bonus AD) + (0.5AP)
attack speed is already accounted for more or less. There are a few currently minor factors that may become more important in the real world scenario but for now lets just add the two autoattacks under the assumption you run full attack speed reds and quints
That will be 10/16/22.5/28.5/35 + (0.1bonus AD) + ( .05AP) in total
all in all it comes out to a total of
110 / 172 / 247.5 / 313.5 / 385 + (1.1 bonus AD) + (0.55AP)
Or in other words 2 auto attacks increase the damage of W by 10% and another two will be another 10% or put another way, each autoattack increases damage by 5% + extra for her base damage of course.
_For reference her autoattack is 60.712 (+ 3.4) and twin bite deals Bonus Physical Damage: 40 / 55 / 70 / 85 / 100% AD and triggers onhit abilities twice, note that it gives 4 stacks of fervor. _
Just for reference again here's the damage on flame breath Magic Damage: 60 / 100 / 140 / 180 / 220 (+ 60% AP) and 2.5 maximum hp per auto, 5% when hit with twinbite I believe. All of this is magic damage
Q and W will be our "points" factor or points in an ability
Twinbite is definitely gonna happen so for
without landing E we get
110 / 172 / 247.5 / 313.5 / 385 + (1.1 bonus AD) + (0.55AP) + Bonus Physical Damage: 40 / 55 / 70 / 85 / 100% AD
110 + 70W + bonusAD*(0.4+0.15Q) + 0.5AP
0 AP
bonus AD = 40 from
so
110 + 70W + 40 *(0.4+0.15Q) + 0.5 *0
110 + 70W + 16 +6Q
126 + 70W + 6Q
Where Q is your points in shyv's Q and W is points in W
and for
without landing E we get
110 / 172 / 247.5 / 313.5 / 385 + (1.1 bonus AD) + (0.55AP) + Bonus Physical Damage: 40 / 55 / 70 / 85 / 100% AD
110 + 70W + bonusAD*(0.4+0.15Q) + 0.5AP
0 Bonus AD
bonus AP = 40 from
so
110 + 70W + 0 *(0.4+0.15Q) + 0.5 *40
130 + 70W
And the almost-end result of this is
= 126 + 70W + 6Q
= 130 + 70W
Assuming you max W first the two are very similar in damage but then consider the fact that
is also able to deal 75 bonus damage giving us vs the damage of 2 autoattacks. The base damage will negate itself no matter what assuming both actually level at about the same speed. But
will give us +80 damage
= 126 + 70W + 6Q + 80
= 130 + 70W + 75
or
= 206 + 70W + 6Q
= 205 + 70W
I'm sure I messed something up but everything I likely made a mistake on is stuff that negates itself in the comparison.
then add E and ignore the bonus damage since it negates anyways and we get an extra 60 / 100 / 140 / 180 / 220 (+ 60% AP) damage. We'll use E to represent the damage so for
it'll be 60 + 40E + .6* 40ap or 144 + 40E giving us
= 326 + 70W + 6Q
= 409 + 70W + 40E
so in the more braindead scenario where you don't use the
onhit passive or the extra damage on E you get
= 206 + 70W + 6Q
= 205 + 70W
and if you can land a skillshot and somehow manage not to fuck up the use of your
onhit passive that only works on champions you get
= 326 + 70W + 6Q
= 409 + 70W + 40E
to this i'd also like to add that shyv's ult has a .7 AP ratio and no AD ratio and gives her W a bonus effect which basically lets her use it from a longer range i.e. it is the one more likely to see actual use out of W and Q in quite a few ways whatever that may mean for these purposes