I still wish on-hits would still occur during a dodge. Some champions are very reliant on those, not to mention, 10% dodge is still giving semi-rare occasions of 3 dodges in a row.
Dodge itself is very unrewarding for those who don't hit. Jax being of course the biggest issue since he turns AD and AP into health, he then builds dodge, which counters the AD side of the enemy damage and his Ulti turns that dodge into MR. Meaning he has lots of health that's hard to burst down because of the defenses he has, meanwhile he can deal a lot of damage. People are wary to make this stronger.
Dodge enables a champion to mitigate no damage, that some champions are balanced off of. Take Tristana for a semi-weak ranged carry. Her base AD is weaker than Sona's. This means that instead of a few hits for a certain amount of damage, she has to rely on more hits for a more evened out damage. If she misses 2 out of 10 hits, from the enemy having say 20% dodge (not an exact science, but saying that it did happen). Then you take Ashe, who crits her first hit, hits say 4 more times, at the same 20%, she misses 1/5 hits. The next shot of both champs can then be taken into account. Who's more inclined to hit and who's more likely to kill any said champ?
Overall, the Ashe with 300 AD only has to hit say 5 times and crit once to kill a said target. (Again it's not an exact science, but this example is based of numbers.) Now give Tristana half that AD and she's at 150. At 150, lets say she needs to hit the enemy 10 times and crit twice. If the enemy is to dodge 2/5 of all the hits taken, who's more likely to kill the enemy? The answer is Ashe, because the mathmatical probability is greater that ashe's crit will miss compared to 1 of Tristana's hits will miss. Tristana would have more chances to miss overall.
Again, this isn't an exact science, however, when you slice it thin enough, you'll see recurring moments where certain champs are countered a bit too hard by that dodge. With less dodge, it's less likely it will be abused as much, however it doesn't stop Ashe from beating Tristana in the above instance.
Dodge itself is designed to avoid the damage entirely. Crit increases damage. Crit being the modifier, much like Lich's Bane, Sheen or Trinity Blade proc, except all the time without that trigger. Dodge negates all damage, no matter how much AD you build (spells being the exception). 900 AD and 10 AD both deal no damage if the person dodges (ridiculous damage example albeit).
This means that if you can negate all damage, it doesn't matter how much damage the enemy should deal, it means it's negated at rates even faster than a Banshee's Veil. Take Banshee's Veil as an awkward comparison. Banshee's Veil blocks 1 spell every 45 seconds, but once it's down, you know it's down. Now take Dodge, it's always up. It can proc sporadically and make all the difference to an Ashe with a Jax on her face (though he does that to everyone, so maybe take someone similar instead).
Dodge itself is countered by 1 item. Crit is really countered by primarily Thornmail, but also countered by Armor in general. (I still like my idea of on-hit being able to proc, like Wit's End still dealing 42 damage, but dodge still negating the auto-attack. However, that's just silly and would be harder to balance I think, maybe.)
Now the problem with Dodge is that it doesn't lead to fun for either side. There is a difference between "You skillfully dodged that missile, good play!" and "Hey look, you didn't even have to work to dodge that." The person who didn't hit isn't having fun for obvious reasons, "30% of my damage was just negated, not reduced." and the person who dodged might have fun at the time, but overall in the end, they haven't put out as much effort to get where they are, leading to feeling less good about themselves. (Well, really people don't think that, they think "Hey, I won, again! This is easy.") However, the lack of effort put into it simply is too rewarding.
EDIT: And I meant to end on "Which is why Riot needs to find that point where dodge is fun for both sides without being too rewarding for what little effort goes into it." however therein lies a problem, because it's very difficult to say what's fun for both sides. Nimbleness was yet another reward to something that took no effort. One could negate damage and move faster because of it. Two rewards for something that uses no effort. You build it and you've got it.
I think one point that hasn't been brought up enough is that dodge essentially creates an environment where AP and AD carries do not scale comparatively. Because Dodge only effects physical attacks, you cannot dodge most abilities. This creates a scenario where AD carries do not have as much an incentive to be played if there is a lot of Dodge items. If I could get to say 50% dodge, and I was facing a Tryndamere or Ashe, they would not be able to hit me often. So I would have less incentive to play them over some other champions that still offer good physical damage but are more caster related, such as Urgot.
Meanwhile your inability to dodge Brand, Anivia, or other characters attacks makes it so there is not a comparative defensive statistic for them. You can say you have magic resist still, but on that note you had armor before. So you would have Armor + dodge for physical damage and only MR for ability power, providing more incentive to play AP carries.
There is also something that people haven't notated from statistics called Standard Deviation. Or on average how far away from your expected long term average you can expect to be within reason. The more random factors you have, the more you can expect to deviate. As a developer I believe you have to make a decision on how much deviation from random probabilities is acceptable and still be fun. Consider the following situations
(Note: For the math in the following section it was assumed your normal attacks do 100 damage and crits do 200 damage)
If you have 15% chance to crit, you can expect to do about 115 damage per hit long run. You expect to deviate from your 115 damage though, about 35.7. So it wouldn't be unreasonable for you to average 115+35.7 damage for a fight, or about 150 damage. Likewise it wouldn't be that unreasonable for you to never crit averaging 100 damage for the fight.
Assuming you cannot Critically strike, with 15% dodge you average about 85 damage a strike, and still 35.7 variation. This isn't too unreasonable.
Let's assume you can do both Critically Strike and your opponent can dodge at 15% ratios, the math gets a little trickier, but in essence you can expect to do 97.75 damage per swing, but now you can expect your damage to vary about 52.63.
That's just at 15%. Let's assume now they are significant numbers. Let's say 50% Critical Strike and 25% dodge. Now you average 112.5 damage per swing long term, but can expect to vary on an individual fight by 78.05.
There are 2 things to note with this. The more kinds of random chances and the higher those chances will occur, the more variation we can expect from fight to fight. There is a 65% chance to be within 1 standard deviation of our expected average. That means that 65% of the time with our last scenario we will do on average 34.45 damage - 190.55 Damage for an individual fight. While long term we expect to get the average value, on a fight to fight basis 65% of the time, you could be anywhere.
The second thing to note is Dodge scales better than Crit. Dodge you just dodge. You avoid all damage. Dodge actually reduces Crit chance because of this. Why? I swing 100 times. At 25 percent dodge, I will hit 75% of those, so 75 hits. Now we have a 33% chance to critically strike. So out of those 75 hits 25 will be Critical Strikes. Now I just said I swung 100 times, but I only got 25 Critical strikes... Essentially dodging removed 8% of my critical strike chance.
TLDR: Dodge does not create unpredictability in and of itself... Dodge + Crit creates a massive amount of unpredictability as well as other "random" events that can occur. Dodge scales better than critical strike does.
In essence I agree with riot on one thing - too much randomness in the game makes fighting feel more like gambling than skill to skill match ups. For you gamblers out there, you may actually love the idea of the extra variation. But think about this, if you were riot and half your player base wanted some unpredictability because of the gambler excitement mentality and others wanted it to be purely skill based, wouldn't a compromise be necessary? Too much randomness and you excommunicate 50% of your player base. Not enough, and you excommunicate another 50%. So I think you are left with the decision of what random events are the most fun and the easiest to balance around. I think they chose correctly with Critical Strikes being the better of the two.
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