How to balance champions:
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power curve and "net power curve" equality - my overall power on a game averaged out if played to full build should match that of yours... but my peaks and troughs might be at different times. I might not reach my peak power if you manage to end the game early and I'm on a scaling champ, but had I gotten there, our average of power throughout the game would be equal.
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mobility, durability, damage (burst & sustained). Similar to power curves having early, mid and late game values that differ; these 3 tenets of a champ can come in different combinations. But they SHOULD always be balanced such that a champ is not superior in one or more while being equal in the other(s) to another champ. Ex: if sion were to have the mobility and damage of a yasuo or vayne, yet he retained his durability we would have problems.
This has been lost sight of by champ designers and the balance team for quite awhile now. Thus you have some champs with far too much of all 3 (damage, mobility, durability) and/or champs that have too much power throughout the game or too little. Or... their power curve is simply too skewed. That last bit was evidenced by crit adc's in spring split solo carrying and deciding the game basically no matter how well other roles and champs played - better adc or more fed adc won game. Period.
Building on that example... this summer we saw a patch or so where crit adc's weren't viable. This wasn't simply because their power curve was too weak, but rather because of that bit I mentioned about it being too skewed. They had massive power advantage at full build to make up for their massive weakness in laning phase... but their laning phase weakness was too great and exploitable to ever reach late game. And thus they were unviable. But if the "net power curve" of crit adc's at the time was balanced/comparable to that of the swain's and yasuo's etc. that crowded them out for a time... then a simple buff wouldn't fix the problem. It would only make champs playing against crit adc's unviable. Hence to buff their early game, something had to be done to weaken their late game to a comparable degree. We saw this attempted at least when adjustments were made to make crit adc's viable again.
Example of point 2. Lucian vs traditional midlaner. Quinn, vayne, kai'sa top. Jhin outruns hecarim with hecarim using his e for extra movespeed. Etc. If you are going to make a champ so insanely mobile and have great dps or burst (or both), then it needs to pay for that by lacking durability. It gets caught? It gets 1-shot. Flip side... you create a mobile and durable tank... he better not have a ton of burst or dps. We had this be a problem with tank ekko quite awhile back now as an example. There are others I could name, but that one should be known by just about everyone and was a high profile case, so I think it serves as a good illustration of the point.
Things are not being properly considered and balanced in many situations. This leads to a small pool of champs being much stronger than others not due to their kit matching up well vs another's or anything that should acceptably give one champ the edge. This leads to people taking awkward builds for some champs because the only way they are playable is to go overkill on damage so you can 1-shot an adc for example. Rather than create a world where a melee can catch an adc, re-catch them if necessary... and potentially cut them down over time, the melee is forced to spec into untraditional builds to try to 1-shot adc because they don't stand a chance to re-catch the adc if their first combo fails to kill. This leaves the melee generally overly squishy and flash-dependent for teamfighting... leading to the melee feeling frustrated. While the adc is left frustrated because there's not much counterplay to being 1-shot. Fixing mobility creep of adc's due to crit items giving far too much mobility to them and due to their base movespeed creeping closer to that of melees (who traditionally had movespeed advantage FOR A REASON) gives both sides more incentive to build reasonably and a chance to outplay the other rather than 1-shot or be 1-shot (for both parties).