Notes

Runes
7.83 pen, 14.85 AP

4 abilities. base damage at R5. AP ratio. Required AP to double damage
Q- 255. 65% ratio. 392.30 AP
W- 210. 35% ratio. 600 AP
*E- 140. 30% ratio. 466.67 AP
**R- 400/600. 73.3%/110%. 545.70 AP/545.45 AP***

Lichbane-80.25. 50% ratio. 160.5 AP
Auto- 160. 50% ratio. 320 AP

Q

*E damage is simplified to 1 mine, for convenience.
** Second set of numbers is for damage in the center
*** even with differing numbers ratio stays the same so only one calculation needs to be done

Calculations will be done for Q and R, and lichbane and auto to save time since they are the majority of Ziggs' burst

================Rcap vs Void Staff===================
Total AP/pen before rab cap or void staff
374.85AP / 37.83 pen

RoA > Sorc's > Liandries > Luden's > Rcap > Lich Bane
100ap, 15 pen, 80ap +15 pen, 100, 120 +30% total ap, 80ap
Total AP: 668.0475
Total Pen: 37.83 pen

Damage increase
Q- 1.38
R- 1.31
Lichbane- 1.54
E.auto - 1.42

RoA > Sorc's > Liandries > Luden's > Lich Bane > Void Staff
100ap, 15 pen, 80ap +15 pen, 100, 80ap, 80ap +35% pen
Total AP: 454.85 AP
Total Pen: 37.83 pen + 35% mr pen

Benefit needed to match Rab Cap
Q. 1.2497
R. 1.2053

Lich Bane 1.33
Auto 1.27

MR needed to reach benefit
Q. 82.70 MR
R. 53.93 MR

Lich Bane- 151.41 MR
Auto- 96.194

**********
Percentage of damage from total burst Q, R, Lich bane + passive Auto. full build minus rab cap or void staff assuming R damage is the lower value.
Total damage from burst 1788.51
Q- 27.9%
R- 37.8%
Lich bane- 15.0%
Auto-19.3%

Extra conclusions.

Yes lich bane and Auto require higher MR for void staff to be better, BUT looking at the damage from your burst, only 34.3% requires this boost.

If you were against a team of all squishy mages/adc's with no MR then this would be insignificant bc the other 65.7% from the Q and R would also benefit the rab cap over the void staff. However, this is never the case. you will have MR builders and you wont be dealing with only adc's and mages. so the 65.7% of your damage will benefit from building void staff over rab cap.

this number (65.7%) increases if you land the bomb on them and get the bonus damage for them being in the center area. making the more significant portion of your burst, even more significant

so against people who build light MR, your majority damage 65.7% benefits with void staff over rab cap

against people who build heavy MR (tanks and bruisers), your majority damage and most likely the extra third benefits with void staff over rab cap

against squishies with NO MR, the whole kit benefits from rab cap over void staff.



*************
Conclusions-
Mages traditionally bring Ap glyphs (12.06) MR
Squishy Mages generally have base 38.5 MR at max lvl
so Squishy mages at lvl 18 have 50.56 MR ignoring any MR they might have gotten.

However, mages do buy MR. Merc treads (25 MR), banshee's veil (60 MR), athene's unholy grail (30 MR) are viable options and have showed up on mages in professional leagues and lower tier ranked games.

ADC's also generally follow the same glyphs and tend to have the same base MR at max lvl.

They also have viable MR items. Maw of malmortius (45 MR), Mercurial Scimitar (35 MR)

So for just those 2 enemies, yes, rab cap outclasses void staff. However this is ONLY if they fail to purchase an MR item, and even without it. your R is only 3.37 MR short of breaking even with an item that is MUCH cheaper, and allows you to grab an elixir giving you an even further power spike (50 AP) that would shift the balance back in the favor of Void Staff *Note: I was tired and didnt feel like doing the calculation. And as a reminder, this was only with basic MR, with viable MR items, void staff > rab cap in damage efficiency and gold efficiency.

With bruisers and Tanks. Void staff is much better than Rabadons death cap since enemies will have built MR and will have MR totals higher than the aforementioned numbers

Assassins generally sit on 53.4MR without runes, yup right above the MR needed for Void staff to benefit more than Rab Cap for your ultimate. So with runes, and viable items like Maw, Banshee's, Edge of night they easily pass the required amounts

=====================================================
RoA > Sorc's > Liandries > Luden's > Rcap > Void Staff
100ap, 15 pen, 80ap +15 pen, 100, 120 +30% total ap, 80ap +35% pen