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Message: <blockquote data-quote="Elric" data-source="post: 4693625" data-attributes="member: 1139">I'd go a little further.  I don't think 2c is a valid calculation either.  As you can see, in 2c,d,e the chance that Shield works is completely unrelated to its +4 bonus.  2c and d are hard to get a realistic calculation for, because it means specifying player knowledge of the monster's distribution of attack bonuses/what save they're attacking, versus the actual numbers.  Scenario 2e is much easier.Here's how to do a valid calculation for 2e.  Let's take the simplest scenario possible: all attacks are identical in their chance to hit (hitting at least 25% of the time) and damage, with a set number n of attacks per encounter (all this information is known to the player).  We're only considering "attacks" something that targets Reflex and AC here, and expected damage prevented (==number of attacks blocked here) is the metric for effectiveness.  When I run a comparison with Second Chance, assuming that all attacks are equal is definitely in Shield's favor.  Shield's chance to be effective per attack is p= 0.2, since it's a +4 bonus.  Then the chance that Shield is effective is 1- (1-p)^n, and p=0.2, so this is 1-0.8^n.  When you use Shield, you also get the benefit until the end of your next turn.  So this means that Shield stops more than one expected attack if you’re targeted by additional attacks.  Let’s assume conservatively that you’ll get targeted by 0.25 additional attacks while the Shield power lasts; at a 0.2 chance to block each, that means each time you use Shield you’re blocking 1+0.2*0.25= 1.05 attacks.  This gives us an expected number of attacks blocked by Shield equal to 1.05*[1- (1-p)^n].  Plug in for a few different values of n:n      Number of attacks blocked1    0.21002    0.37803    0.51244    0.61995    0.70596    0.7747The more attacks there are, the better Shield gets, because the more likely it is to block an attack.  Likewise, if Shield gave higher than a +4 bonus it would also be more valuable under this metric.  Second Chance: Optimal use of Second Chance, even assuming all attacks were identical, involves solving a dynamic programming problem to determine whether you should reserve it for a critical or should simply use it on any hit.  Optimal strategy in this simple example would presumably be "if there will be k or more attacks against me left after this attack, only use Second Chance against a critical hit; otherwise use it against any hit."  From this you can determine the optimal k relatively easily.  If you assume a crit is equivalent to 1.5 regular hits, and the chance to hit is 0.5 (0.45 of that non-crit, 0.05 of that a critical hit) you get optimal k=4.  That is, if there will be 4 or more attacks against you after the current attack, only use Second Chance against a critical hit; if there will be fewer than 4 attacks against you after the current attack, use Second Chance against any hit (side note: assuming that the player knows exactly how many attacks there will be against him helps to use Second Chance more effectively, but as long as the player has a pretty good idea of the number of attacks he’ll face, this shouldn’t change much).Doing some further calculations, the “regular hit equivalents” blocked by Second Chance here are a function of the number of attacks as follows:    # attacks    Regular-hit equivalents blocked1    0.28502    0.42753    0.49884    0.53445    0.55646    0.59347    0.62018    0.64159    0.659910    0.676511    0.691812    0.7061Note that the number of “attacks” facing a character with Shield and Second Chance is going to be different because Shield only applies to AC/Ref, and because as a racial power, Second Chance can be used by non-wizard classes who will tend to be attacked more in combat.  Let’s ignore the second factor and assume we’re only comparing them for the same wizard character.  Then we can use the “75% of attacks target AC/Reflex” assumption, which means we should pick the number for Second Chance to be 4/3 of that for Shield.  For easy comparison, let’s call a number of attacks 3 (Shield) vs. 4 (Second Chance) the low case and 6 vs. 8 the high case.  Low attacks case:Shield: 0.5124 blockedSecond Chance: 0.5344 blockedHigh attacks caseShield: 0.7747 blockedSecond Chance: 0.6415 blockedIn conclusion, from this simple calculation it should be clear that Shield and Second Chance are comparable unless these assumptions are dramatically different from actual practice.  The attacks are identical assumption is the biggest simplification I’ve made, and that certainly helps Shield (though I was conservative on the number of additional attacks that Shield would apply to), but its lead in the “high case” is still under 20%.</blockquote>

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