There is nothing wrong with using the PRD counter for the chance to fail to proc instead of using it for the chance to proc. It does leave open the possibility of failing to proc many times in a row, much like the current system leaves open the possibility of successfully proccing many times in a row for low probability events. You can decide whether you like that or not.

(2/2) So as an example, if you Duel for 5.5 seconds (t = 5.5) and are being attacked by the target 3 times per second (f = 3), then the EIAS is 170 / 5.5 + 30.6 * 3/(1 + 0.144 * 3) = 95. Note that this assumes several things. Most importantly, it assumes the fight lasts at least long enough to get the first proc (i.e. at least 1/(.18 f) seconds). If it does not, then the effective IAS is just 170*(.18 f) = 30.6 f. This is the same equation we would use for any duration of time if there were no cooldown. It also assumes incoming attacks are periodic. In other words, if I get attacked once per second, that means I get hit every second on the dot with no attacks in-between. Real attacks tend to come in at random intervals, so the true value should be somewhat less than this. In the limit as the frequency of attacks approaches infinity (in other words, LC is getting attacked every microsecond), this approaches 170/t + 212.5. That 170/t term represents the first proc which in this case will happen almost immediately, while the 212.5 = 1.7/0.8 represents the maximum possible rate of procs over the long term (i.e. proccing immediately every time MoC cools down).

(1/2) Well for level 4 MoC, LC has an 18% chance to proc when attacked. That means on average, she will proc once every 1/0.18 = 5.56 attacks. If she is being attacked with frequency f (in attacks/sec), then on average it will take 1/(.18 f) seconds before a proc if the ability is not on cooldown. If it has just been put on cooldown, then it will take 1/(.18 f) + 0.8 seconds on average. Over long time scales we can neglect the first proc, but realistically that is rarely the case. Therefore we need to know how long we are talking about. For a fight lasting t seconds, on average she will proc the first hit after the first 1/(.18 f) seconds and once ever 1/(.18 f) + 0.8 seconds for the remainder, meaning the total number of procs will be 1 + t/[1/(.18 f) + 0.8] as a first order approximation. That should be good enough for most cases. If you want to equate this to an increase in attack speed, then as you said, you can equate 1 proc per 1.7 seconds to 100 IAS. For a time t with p procs, you have EIAS = 100 * p * 1.7/t. Plugging in the above formula, we get EIAS = 100 * (1 + t/[1/(.18 f) + 0.8]) * 1.7/t. Simplifying gives EIAS = 170/t + 30.6 f/(1 + 0.144 f).

No, that is only relevant for abilities based on Orb of Slow or Orb of Lightning (basically two names for the same ability) with the helper ability on cooldown (or otherwise unavailable). So it matters for Spirit Bear's Entangle but that's about it, as I think that's the only ability in DotA based on Orb of Slow which has both a cooldown and a probability that isn't 0 or 1. In the case that Spirit Bear is attacking with Entangle on cooldown, in that situation and only in that situation could it make any difference. Specifically, if by chance he rolls a low enough random real to proc Entangle, but can't actually use it because it's on cooldown, then a boolean is set to 1 that guarantees the next hit will proc Entangle if it is available. You won't know that this has occurred though, and usually it won't, and if you issue any orders to the bear at all (except perhaps a redundant attack order), the boolean will reset to 0. It's basically a useless bug, since the bear's long attack backswing makes it costly to attempt to exploit, and most of the time it won't even work. And no, this does not apply to Dota 2.

That's a quality of life change tbh. I always thought it worked that way and just now found out that it didn't disjoint projectiles.

You don't generally want attack speed and damage to be equal. You do want to balance them, but exactly where that balance lies depends on a huge number of factors. Attack speed is nice for attack modifiers like Bash, whereas damage is better against fixed reductions like Stout Shield. Attack speed is less useful when chasing an enemy, where the number of attacks you land depends more on movement than attack speed. Damage benefits Moment of Courage too. If you have high damage but low attack speed, you can use the time you have between attacks to do other things like move and cast spells, while if you have high attack speed but low damage, you have to practically stand still and attack to get full value. And that's before we consider the costs. Maxing Press the Attack and casting it on yourself is one way to get attack speed, but at the cost of other skills. You can buy attack speed items, but few items give pure attack speed, instead giving a wide range of bonuses, and the same is true of damage items. It's complicated. I can't tell you what to buy in general. I will say that for the most part, you tend to get more attack speed than damage per gold (with the notable exception of Divine Rapier), but it's usually not as good. Either way, if you feel like you have way more damage than attack speed or vice-versa, you will probably want to buy some of the other. That's about the best advice I can give.

For your second question, no direct comparison is possible due to numerous complicating factors. For one, treads give stats, any stats, which opens up lots of possible questions (do you need the mana? do you need the HP? do you need the attack speed? do you need the armor?). For another, phase boots give movement speed and phasing, and you can't easily determine a value for that. Phase Boots are also slightly cheaper than Power Treads. On top of that, LC has both an attack speed steroid and a steady increase in damage, so which of the two is preferable will depend not only on all those other factors and on the rest of your inventory as usual, but also on your current level of Press the Attack, how much you are actually able to use it, and how much Duel damage you have. But that's even before you worry about Moment of Courage. In Dota 2, Moment of Courage essentially gives you extra free attacks independent of attack speed, similar to Geminate Attack, making damage substantially more cost-effective than attack speed. I think Moment of Courage more than Press the Attack is the reason stacking damage is usually more effective than attack speed on LC. Additionally, in DotA 1, MoC works just by maxing LC's attack speed briefly. If she already has a lot of attack speed, that buff is less useful, and if she has a lot of damage, it is more useful. (In Dota 2 that shouldn't be an issue, since MoC always just gives one extra attack free.)

For your first question, what do you mean by "average increase"? Increase in what? And why are you comparing evasion to critical strike? Anyway, strictly from the perspective of probability stacking, they use the same formula but obviously with different values. Butterfly gives a 35% chance to evade, so two butterflies give a 1-(1-0.35)(1-0.35) = 57.75% chance to evade. Buriza-do Kyanon gives a 25% chance to crit, so two burizas give a 1-(1-0.25)(1-0.25) = 43.75% chance to crit. Assuming no attack modifiers, this should yield a 0.4375 * 1.4 = 61.25% increase in DPS. However, in Dota 2, Daedalus currently has a 30% chance to crit for 2.2x, so two daedaluses give a 1-(1-0.3)(1-0.3) = 51% chance to proc for a 0.51 * 1.2 = 61.2% increase in DPS. Or if you are talking about taking two identical heroes, giving one hero two butterflies and the other two daedaluses and letting them fight, you have to remember that each butterfly also gives 30 agility which adds 4.2 armor, or 8.4 armor for two.

As it's more of a debate whether you should go Phase or PT, it should stay in GS. Advanced Mechanics is purely for questions regarding certain hero mechanics which do not necessarily include strategy. P.S. I only have mod powers in Dota Chat, Suggestions and Video Games. So for your thread to be moved, you'll need to contact a mod which moderates that section or a global mod, since they have control over the whole forum. ;)

Yo, well, I have no idea about 2-3k mmr range, but my thread was purely about that 4k players are having more enjoyable games than 5ks.

uhh not sure what you want me to agree on... it was a dick move by valve that set the bar really low for future streams