How is 200% damage, to 125% or 150% = the same?
Because it's every attack, whereas random crit does not activate every attack. This lets the expected damage be exactly the same. I'll prove this mathematically below.
You won't be building 100%, this crit build though would work to well on certain adc's
You don't need to. You won't need to build any more crit than you do right now. Why do you think they would need to?
Here, let me do some math and show you what I mean. Say that you have 20% crit chance and 100 AD with the random crit. If you attacked 10 times, you would expect to hit for 100 damage 8 times, and 200 damage twice. That would be 1,200 damage. There could be variance, but a core principle of variance is that it will favor increases and decreases at the same rate, meaning that the amount of times we'll get more damage than 1,200 should be exactly the same as the number
Now, say that we had 20% crit chance and 100 AD and attacked 10 times with a derandomized system. We would attack 10 times for (100 * 1.2 = 120) damage. 10 * 120 = 1,200 damage. That's the same number we had before. Same expected damage, and like I said before, variance does not systematically benefit or harm this number.
Just for kicks, let's prove that it works with IE too.. Say that we had IE and its crit bonus damage in the past equation. On live, our two crits would hit for 250 damage, so we'd do _**1,300 damage. **_With my system, every autoattack would hit for (100 * (20% * 1.5 = 30% = 1.30)), and 130 * 10 = 1,300 damage. See, exactly the same expected damage.
This will work with any numbers. Seriously, any numbers you choose, you'll get the exact same DPS. This means that you don't need any more crit than you would currently need. Whether you build 0%, 50% or 100%, you'll get the same expected dps before as you will now.
So, once again, I ask where, where do you see damage differences? Numbers, real situations and/or math would help a TON here.