Plantissue wrote:That maths isn't right. You've either swopped the probabilities for 30% dodge with the 70% dodge somewhere and/or applied 1/(P) when you shouldn't have.
How did you get [ 24% attacks so it blocks/dodges 44% attacks ]and [56% attacks so it blocks/dodges 76%] ?
There's no error there. You can see this because "blocks/dodges 44%" is the same statement as your "56% attacks get through" and "blocks/dodges 76%" is the same statement as your "24% attacks get through". You've both arrived at exactly the same probability of being hit in each case, so in fact your arithmetic agrees so far.
VeryAngryFelid has performed a calculation that goes: suppose we block before dodging[1]. Let B be the proportion of attacks that are blocked and D the proportion that would be dodged if unblocked (either because no shield, or not blocked). B of the total attacks will be blocked - what proportion of the total attacks will be dodged? (1-B) of them could possibly be dodged because they weren't blocked, and of those, D of the total will actually be dodged, so the proportion of the total that will be dodged is (1-B)*D. Then add that to the B proportion that were blocked and we have B+(1-B)*D = B+(D-BD) = B+D-BD as the chance of a successful block or dodge.
There's nothing wrong with this calculation except that it is needlessly complex compared to the one you have done, which is to multiply (1-B), the chance of not blocking, by (1-D), the chance of not dodging. But (1-B)*(1-D) = 1-B-D+BD = 1-(B+D-BD). This is of course the inverse of the probability that VAF's method calculates, so in fact both methods necessarily give the same answer.
Improvement to survivability (or effective HP or whatever measuremnt you use) shouldn't change depending on dodge. If you don't believe me, try working out your maths again with 99% dodge rate and 1% dodge rate, and you will see that your mathematical method doesn't make any sense.
In fact VAF's method continues to give exactly the same probability of a hit as yours does, as illustrated above. They would say the 99th character blocks 20% attacks and dodges 0.8*0.99=79.2% attacks so it blocks/dodges 99.2% attacks. You would say 0.8 * 0.01 = 0.008 so it fails to dodge/block 0.8% of attacks. These are still the same answer.
The confusion arises because you have then calculated the change in defense in different ways. You have calculated the percentage reduction in the chance of getting hit. VAF has calculated the percentage improvement in the chance of not being hit. These are different things, not simply the inverse of each other, so it is unremarkable that yours stays the same for any value of D but VAF's changes.
Who has the most useful metric? In my view that can be seen from the 99% dodge case. As the chance of dodging tends to 100%, your metric continues to give the same value, "25% increase in survival", or rather "20% reduction in incoming damage". VAF's metric tends towards "no improvement in chance of avoiding attack". However, it's plainly obvious that a hypothetical character that did dodge 100% of attacks would get no defensive benefit from a shield whatsoever, and that the 99% dodger is getting almost no benefit, which suggests to me your metric is not a useful one - put another way, for a given number of current hitpoints, I care a lot more about a 20% reduction in incoming damage from a shield if my expected undodged incoming damage this turn is 50 than 5.
[1] which we do, but while this matters for reflection, riposte, OODs zooming past you, the odds of blocking multiple attacks, etc, it doesn't matter here, so VAF's calculation would be correct either way.
Ascension reports with too many words since 2016.
Saturday, 21st July 2018, 15:22 
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