Some math about Twin bite or Flame breath

[quote=Oillamp]So it came that I bought Shyvana, thus having spent a lot of time reading guides to see what other players build. What I noticed and struck me was that nearly everybody leveled Q before E. However, there was never really an explanation why this priority was set. Therefor, I'm gonna use math to prove that, pure damage wise, leveling E before Q is stronger. I first thought leveling E would benefit more from a better attack speed, so I wrote down two functions with x as a variable, representing the attack speed, and t (=time) as a parameter. My goal was to find the attack speed limit from where leveling E first is stronger. I am gonna assume everybody levels W first, so that the pain of choice happens at level 8. The basic attack damage at level 8 is 81,7, and with the second assumption that the only attack damage bonus we normally have at level 8 is wriggle's lantern, we end up with 104.7 attack damage. Now to the functions : Q(x) is the function that represents the damage Q and E do when having Q at rank 2 at level 8, E(x) when having E at rank 2. In general, the function will look like this : f = [(number of hits in time t) + (number of Qs in time t)*2]*15%*E-damage*(percentage of time the E debuff is on the target) + (flat damage of E hit in time t) + (flat damage of Q in time t) Back to our functions Q(x) and E(x) : E(x)= [ (x*t) + (t/10)*2 + x*0.5/10*t ]*15/100*125*4/11 + t/11*125 + (t/10 + x*0.5/10*t)*1.8*104.7 Q(x)= [ (x*t) + (t/9)*2 + x*0.5/9*t ]*15/100*80*4/12 + t/12*80 + (t/9 + x*0.5/9*t)*1.85*104.7 After simplification : E(x)= t*(16.5821*x + 31.5733) Q(x)= t*(14.9831*x+29.0772) Then after resolving the inequation E(x)>Q(x) I find the solution : x > -1.56. This means that as long as your attack speed is greater than -1.56, having E at rank 2 at level 8 instead of Q provides a better damage output. This, of course, under the assumption you hit all of your E's. To make clear how much of a difference it does, I'm gonna write down how much E(x) and Q(x) are after 10 seconds and with an attack speed of 0.747 (which is Shyvana's basic attack speed at level 8) : Q(x)= 402.601 E(x)= 439.601 So after 10 seconds, in the case E is at rank 2 you have done 37 more damage. Again, under the assumption you hit all your E's. The pure damage, of course is not the only reason why you'd want to level Q before E or E before Q, as leveling Q before E has a better synergy with Wriggle's Lantern and other on-hit effects (even your own W). However, keep in mind that this 46.01 damage after 10 seconds becomes greater if you keep leveling up E before Q. So, all in all, E benefits more from attack speed but Q applies onhit effects. The difference, however, is not that big, so pick what you like :).[/quote]

[quote=pasha]Well, leveling E gets you an ap scaling skill shot nuke that gets reduced cd and more damage as you level it, the armor reduction does not increase. Leveling q gets you lower cd and better ad scaling, it also lets you charge the ulti faster. I prefer going w>q>e.[/quote]

[quote=Darcurse]Bluntly said, its a hassle to go through all that right now, so Ill ask you directly: Did you add sth else or crosscalculated, applying Twin Bite on Flame Breath and vice versa? If I stick to your numbers, and only add a Wriggle's as influence point: Calculated both separately for 10sec/0.747AS: Bonus dmg TB: 104.7*85%*2 = 177.99 ~ 178 Bonus dmg FB: 125 + 5(!)*104.7*15% + 5(!)*125*15% = 125 + 78.525 + 93.75 = 297.275 ~ 297.3 (!)= With AS of 0.747, 5 autohits in 4 secs debuff time. (Edit: Totally forgot the attack reset on TB. With that you can easily fit in an extra hit nearly equating FB and TB) But youre right: Adding AD preference/Trinity(onhit)/Dragon form/etc to the mix makes its a matter of opinion.[/quote]

[quote=Oillamp]@Darcurse : I calculated the damage you'd do without autoattacks or W, basically, as those are not influenced by what you leveled first. If I see it right, you only calculated the damage in 10 seconds without really going into detail. What I mean is that when leveling Q, the cooldown is reduced by 1 thus even increasing the damage you do with your E-debuff. All of Shyvana's spells have a too great synergy to be calculated that easily, I'm afraid :).[/quote]

[quote=Darcurse]Thats why i asked, since only (what I did) calculating seperate dmg for both, isnt going to cut it. But, correct me if im wrong: I also didnt intend to add some autohit dmg, the only thing i added was the extra dmg from skills you'd gain by autoattacking. These 5 autohits are those you can set off while the targets debuffed. And ofc the extra autoattack while using TB counting as "extra" dmg since you gained it using TB. Dunno if I got you wrong there: "I calculated the damage you'd do without autoattacks or W, basically, as those are not influenced by what you leveled first" You did, didnt you? You added the 15% extra dmg from FB, at least. Dunno about the 15% ArP right now, though. Edit: Just found the difference between our calcs, I guess: Indeed, you didnt calculated 15% ArP from FB as its bonus dmg and also didnt add the extra autohit youd gain using TB. Edit2: ACK damnit, just found out where my brain totally went off track xDDD Ofc FB is wrong (way too high) thx to me confusing 15% ArP with 15% dmg. And ofc youre right then, this part cant really be calculated either. Also, you can easily creat a calc to indicate the dmg of FB rank2/TB rank2 in synergy with another, while the non choosen one is rank1, ofc. But speaking about adding dragon form youre right, too unpredictable to calculate.[/quote]