Changes to CDR: Doing the Math

Here is where you can find the writing as a properly formatted document. Its kind of ugly on the boards

Changing CDR in League Premise Currently, there are numerous issues in the game revolving around damage and volatility right now. One of the many reasons is the current way CDR works. It stacks additively, and caps at 40%. Its very easy to come by, and its very important, especially to the mages in the game who are squeezing maximum effect out of it. CDR sits at a weird and precarious place. Its needed for mid laners to carry late game, as well as things like enchanter supports (Janna) who scale well. However, its also very important for tanks, who rely on it to get more CC off, to cast more of their durability steroids, and to have more threat both for and against dives. A straight nerf to CDR doesn’t work well, because then it would simply shift the problem into those using flat stats, and it becomes unrealistic to play a proper scaling ability based carry or tank. Trying to find the needle point precision to balance these two things out with eachother has been Riot’s approach for the last few years, and anytime they get it right, its shattered by the next changes to other stats, gold income, or resource costs. The game is in need of a much better option, which is built with flexibility in mind. Hopefully, this will make it that close counts in more than just horseshoes and hand grenades. Solution Change CDR to a multiplicative stat like Tenacity. Very simple, I know, but here are the list of benefits 1. Total damage in the game goes down, as people who don’t stack tons of CDR will never get to benefit from the loss of the cap. 2. Blunts the gold efficiency curve between CDR and AP over time, so that AP is the more valuable damage stat into late game, without requiring much consideration in early game. This provide a very clear and distinct choice between player who want to itemize for utility and who want damage. 3. Current problem mages like Swain will no longer get to double dip on their safety afforded from utility, CC, and Sustain while also being able to gain carry lord damage. 4. Riot gets an additional balance lever for tanks and mage carries with shifting the ratio between how much CDR total there is, and how large the chunks are that it comes in. Having chunkier CDR means that it can be obtained easier early, vs how much is in the game total changing how well and how fast they scale. The Math So, the rest of this is me using what is currently the top build on Heimer according to Champion.gg with the intention being to demonstrate how much of his damage is secretly coming from his CDR and base damage. Trust me, its more than you think. The Swain build I will be talking about is the Luuden > Sorcs > Zhonyas > Morello > Void > Deathcap The Skill Order being R > Q > W > E From first item, finished around level 7 ish, so four levels in Q, Heimer’s turrets do 15 Damage base, plus 30 more from AP, the beam does 100 Base with 55 Damage from AP. His W does 60 base form first rocket, plus 45 from AP scaling with 12 base, and 12 from AP on each additional point of damage. It also procs the Beam on all nearby turrets, so taking all the ideals for just nice easy consistent math, its 3 times those earlier numbers. His E does 60 Base, and 60 From AP. Plus, it procs the beam attacks. So add all those again. At this point, Heimers full rotation does 815 Magic damage base, and 450 Damage from his Bonus AP. For his upfront burst rotation. For his ideal DPS it works out to be approximately 79.4 From base and 60.5 From his AP. Most of this is assuming you just stand in his turrets. Without standing in his turrets, but still in beam poke range, the values shift to 71.0 from base and 43.45 from AP. Heres a nice little table for it

Base AP Ratio 815 450 0.644 79.4 60.5 0.567 71.0 43.45 0.620

Following the vein of these DPS values, the CDR from Luddens contributes a 10% increase in total DPS. Heimer gains about 10.4 DPS from this, to accomplish the same thing with his AP, he would require 23.9 more AP, or about 519 Gold, a little more than an Amp Tome, however, 10% CDR only costs 266 gold. Essentially, Heimer has squeezed an additional 253 gold from thin air in raw damage. Please keep in mind, that this is without accounting for one very large an important detail: You can’t do damage while you’re dead. Even If Heimer only manages to get off one extra stun grenade in a 2v2, and only lives the extra 2 seconds that it stuns for, he still adds 280 damage to his lifetime. And thats being lazy with using the DPS numbers, in actuality its much much more, because it reprocs the beams. This is also without considering it frees heimer up to fish for more stuns, and to generally be more aggressive because he can rely on its cooldown more frequently. This is also no accounting for his being able to use his ult, because its a bit to complicated to do the math on cleanly Now, lets repeat all this math on third item Zhonyas, I’m skipping sorc shoes, cause its same math just different levels in the abilities For this we’ll say Heimer is level 12.

Base AP Ratio 1104 845.25 .5664 130.8 119.25 .5230 120.5 89.25 .5744

These are all base values before any CDR, after the additional CDR from Zhonyas, we see another 10% increase in DPS. This is an additional 25.01 DPS added to heimer, to accomplish this same increase in damage from AP, heimer would need to about 36.7 more AP, or roughly 798 gold. Though he only paid 266 gold for this stat increase. Essentially, heimer invented 532 from thin air. Over time, this egregious amount of stats secretly coming from heimer’s CDR increases more and more. At level 12 with Zhonyas and Luudens, Heimerdinger has around 300.06 DPS, with only 119.25 of that coming from his AP. That means 60.25% of all damage dealt by Heimerdinger is coming from base values, and CDR. Its all hidden in their, somewhere you can’t touch. It also means when Heimer must make the choice between more damage, and more defense, the choice favors defense 3 to 5. Essentially, Heimer gets to live longer, and survive more due to his CDR, movement speed, and Zhonyas active, but because of how high his base values are, and that it behave additively, he also gains more damage from these items. More than he would get if he built full damage and just left himself flapping in the wind. Worse Than You Think I have done Hiemer here, because hes a great example. And cause hes easy. But, go do the math on Karma, Morgana, Zoe. Suddenly you notice a pattern emerging. Numerous champions with massive amounts of utility, set, and pressure in the form of poke and CC also fall into this same category of really high base stats that let them double dip on CDR damage. Then look at the jungle, look at red smite. Whats this? The single most complained about thing of all time ever, what is it? Its something that allows people to double dip on both damage and utility/safety. Noticing a trend here anyone?

The Solution The solution is to drive a wedge between three categories. • People who have lots of Utility, and really don’t want to waste money on damage. • People who very little utility, do tons of damage, and need to scale big time with AP • People with a mix of utility and damage, and are currently double dipping. Category one is tank, changing CDR to be multiplicative and removing the cap is awesome for them, because it means they get more CDR and get to spend more time landing abilities and have better scaling options late, especially for ones with some durability steroid like a shield, damage reduction, or resist stat gains. Category two is AP Stackers. Things like Veigar, also assassins like Katarina, Diana, and Elise and poke champions lie Xerath, Velkoz, and Zoe. Changes to CDR will both mean playing against them is more interactive as each ability is more important, and there are fewer abilities. You in fact could dodge it all, and they may be encouraged to take risk to hit shots. This added layer of making each shot more valuable can mean those champions can be brought to a healthier and more interactive place as a clear pro con emerges from them. As well as assassins who can more diverse items, but defeating their rotation, interrupting it, or surviving it is more rewarding to the player on the receiving end. Essentially, the game has been raised. Category three is tricky, they’re the AP Carries, the ones doing DPS, clearing waves, and winning teamfights. These champions want to use CDR and AP, because of their legitimate scaling use. These are Azir, Cass, Ryze and so forth.

Champions like Heimer, like Swain, like Morgana need to be kept from using CDR stacking as a viable way to gain damage, but this needs to not come at the detriment of other mages and tanks. The shift to multiplicative would make it possible for mage items to properly form this distinction, and to separate those seeking utility from those seeking damage, even allowing those with the right champions to decide after loading in which path they intend to pursue. Going Forward and Applying The Fixes Having CDR as a multiplicative stat is great, for all the good that it does to enforce the barriers between itemization types and paths, but it does not however do this on its own. Currently things are messed up due to the old approach of handling CDR. Items need to be shifted around to enforce this new paradigm, and progress mage itemization towards a more healthy and intuitive system. Some examples of this are things like Luudens, which should lose their CDR. Its already perfect for poke champions, and its not great for DPS champions who dont get much use over the course of their draw out preference of fight when compared to Liandrys. It may even be appropriate to change its build path depending if the mana sustain and movement speed are also a little too much defense on an item that is engouraged on champions that already gain safety from utility or range. CDR should be added to something like Liandry or Rabadons. Its important to incorporate it into the build of a proper carry, and its kind of annoying trying to grab it without also spending money on defensive stats. These items high AP values shouldn't be built often by no DPS champions, because their passives consume a large amount of their gold efficiency. AP should be stripped from defensive items like Rylais, Roa, Zhonyas, and the like. They offer way to much safety, and have all kinds of neat things like sustain and CDR on them that make getting to double dip on some damage is ridiculous. If you want to buy those items and be unkillable, you should do no damage like the tank you are