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Do wizards suck? / multiple attacks
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<blockquote data-quote="Goumindong" data-source="post: 4721156" data-attributes="member: 70874"><p>No, its not. You're looking at the marginal percentage chance that it goes off and not its marginal value. You're also ignoring the diminishing marginal returns on increased hit points and the the diminishing marginal returns on actions. You're also ignoring the opportunity cost of blocking an attack</p><p></p><p>Why does diminishing marginal returns on actions and hit points increase the returns on protection? Well, your expected value for loss depends on both the chance you get hit, the damage you take, and actions you lose. So as the damage you take gets higher and the actions you lose get more costly, its more important to block those attacks.</p><p></p><p>Now, the cost of blocking an attack is the chance that you can block another. So initially, with a low value you get a chance to block an attack you pretty much have to take it, the cost of not doing so is low(you might not be able to use it again), but the gain is relatively high.</p><p></p><p>However, as your percentage chance of blocking anything increases, those opportunity costs increase for all attacks that are of low value, since you can get hit by something of high value instead and as your percentage chance of that happening increases the cost increases. But remember what opportunity cost is, its what we're giving up. Since the value of blocking any one attack is static then our other options must be increasing in value.</p><p></p><p>And since we know that there is a decreasing marginal return on hit points and action(that is to say that attacks that take away more hit points or actions have an increasing marginal cost to us for every hit point and action they take away) we know that we're essentially increasing our marginal utility of our total expected payout faster than we're increases our marginal utility based on the question of "will i be able to use this". Because the question is rightly "will i be able to use this to block an attack that damages me greatly". I.E. since the vast majority of attacks do not impose a high cost, the ability to choose lets you choose the highest cost to block. The chance to block any single attack with a +1 gives you a linear increases in the payout of blocking that attack. The increasing chance to use that on a higher value attack means you must be increasing your payout in an increasingly marginal fashion.</p><p></p><p>Ergo its marginal utility is increasing. </p><p></p><p>Its for this reason that the wand bonus also has an increasing marginal return, because the question is not "do i get more of a chance to use this" or "do i get to to increase my return on any specific attack" but "do i get to hit with my best attack when i need to, and do i increase that probability?"</p><p></p><p>And again, that is not what we care about. We care about how long, on average, any enemy will be held. I.E. we don't necessarily care that the +1 doesn't help us on a roll of a 4, but we do care when they start rolling above 10. The marginal utility rightly then becomes for the first +1 1/10 and for the second 1/9 and for the third 1/8.</p><p></p><p>Now, there is a limiting factor in that total lockdown is unnecessary since you're only going to be fighting for so many rounds(though this increases as time goes on), however this factor is not rubbed up against until you're looking at the huge marginal utility gains brought on by having +9 or more wisdom. A number which precludes a strong value in constitution, making an argument about its marginal utility at those values pointless for our discussion. Before that, the increases in utility are overhwelmingly marginally positive.</p><p></p><p>Status effects on enemies you're attacking aren't all that valueable. If you were attacking the monster you would be laying down your encounter and at-will effects making him weaker. The idea of a status effect is to remove an enemy from the fight so that you don't have to deal with him. At epic levels you're going to be dealing with 10-15 round fights. Anything you do to increase your average hold over that is a big deal. </p><p></p><p>Optimal play strategy has the wizard landing a save ends that hampers on an enemy and then ignoring it while they kill everything else. Marginal returns on the time itself are only slightly dimished(since the enemy is not dealing damage there is no increasing marginal cost imposted as combat extends and your hit points and surges get lower[these things being marginally more valuable the less you have]) compared to the massive increase in time that higher values represent[its possible that marginal returns are initially negative though i find it unlikely, but the margin on the margin is overwhelmingly positive]</p><p></p><p>Wand is an immediate interrupt. You apply it after the roll like the staff, you just don't apply it after the damage roll.</p><p></p><p>Granted that doesn't matter as much because the difference between "after the damage roll" and "before the damage roll" are very small when you're launching the power. You have an expected return for the power and know the total you rolled. You get a pretty even expected increase with the same opportunity cost caveat that allows you to increase your expected return above that by not using it on a power that you don't "need" to hit. </p><p></p><p>Ironically if you rule that the ability cannot be used after you know whether or not it hits, the marginal utility increases dramatically, because for every + you add, not only do you increase linearly the chance you turn a miss into a hit, but you also decrease the uncertainty that exists from the question of "will this bonus on this attack hit the enemy" and "do i need to use this bonus to hit the enemy". Both of these will increase your expected return.</p><p></p><p>That is increasing marginal return.</p><p></p><p>A little of both, remember, thunderwave ends up as a ranged 2 blast 4. This means not only do you have a decent amount of range and better area on each blast, but your ability to hit enemies around cover is increased. With a thunderwave your ability to place a blast extends 4 squares beyond the point where you can place it. The ability to place a scorching burst is much lower.</p><p></p><p>E.G. A wizard with thunderwave can land a blast at T while being in the position W by placing the origin square at O even if there is a wall at -</p><p></p><p>[code]</p><p></p><p>TTTT</p><p>TTTT</p><p>TTTT</p><p>TTTT</p><p>----0</p><p> W[/code]In many situations this extends the wizards ability to hit enemies just as much as a scorching burst can when terrain is very open.</p><p></p><p>Fake Edit: I am sorry if the latter replies are not as in depth, i just lost the majority of them to a browser screw up</p><p></p><p>Combat round time increases increasing the liklihood that people will be using their at will. The presence of a strong push at will increases the versatility of the player to choose effects on his encounters that do not overlap, this gives him more tactical control of the situation.</p><p></p><p>2 Feats. One of the three i listed is unnecessary. And Ray of Frost certainly doesn't with distance advantage and other abilities</p><p></p><p>You're not making it more powerful. You're increasing the power of non-optimal builds. Its the same thing as saying "great weapon fighters are at a disadvantage compared to sword and board fighters and should get an increase somewhere"</p><p></p><p>The other option is to nerf the option for wisdom based wizards or to add effects to other at wills that scale with their respective secondary stats (effects that are as strong as the push on thunderwave)</p><p></p><p>They do. They increase their ability to lock down enemies with save ends. In just the same way, staff wizards get a beneficial impact from pumping constitution. They get an increase in the ability to block an incoming attack once per round. Why should one of them get an increasing marginal return on an at will while the other doesn't. [Push strength is an increasing marginal return]</p><p></p><p>Sweet, did not know that, power just got a lot better for me.</p><p></p><p>The retrain it for a utility that you can use.</p><p></p><p>The opportunity cost of choosing a wisdom based wizard is increased when you give the other options the ability to have that strong control mechanism.</p><p></p><p>The opportunity cost of choosing a staff wizard or wand wizard is static when you give them the ability to have that strong control mechanism. Their opportunity cost is unchanged, their benefit is increased.</p><p></p><p>Depends on what else is happening. Push 4 allows you to more easily clump and position enemies where you want. I would say the situations where push 4 is better than push 2 is about equal to where it doesn't much matter. Especially since other players can impart status effects of their own.</p><p></p><p>E.G. suppose you've got a rogue, fighter, or whatever knocking enemies down, And you've got some difficult terrain floating around. Well if you push 2 the melee enemy can stand up and charge, if you push 4, he needs a move of 8 to do so. Suppose that you've got an enemy on the back rank of your rogue like so</p><p></p><p>F=Fighter, W= Wizard, E=Enemy, R=Rogue</p><p>[code]</p><p> </p><p> F </p><p> E </p><p> R </p><p> E</p><p>W </p><p>[/code]If you only have a push 2 you can prevent the flank on the rogue, but you can't stop the enemy from shifting again and striking the rogue. If you have a push 4, you can push the enemy to a position where he has to shift twice or provoke an OA for movement from the fighter.</p><p></p><p>The further away you are the more this matters. Also, the more push you have the more likely you can trigger agile opportunist(another thoroughly ridiculous feat) for the fighter.(though you have to hit the fighter with the wave for this to work)</p><p></p><p>This is just one of the many likely combinations that you're likely to face where a push 2 is insufficient compared to a push 4.</p></blockquote><p></p>
[QUOTE="Goumindong, post: 4721156, member: 70874"] No, its not. You're looking at the marginal percentage chance that it goes off and not its marginal value. You're also ignoring the diminishing marginal returns on increased hit points and the the diminishing marginal returns on actions. You're also ignoring the opportunity cost of blocking an attack Why does diminishing marginal returns on actions and hit points increase the returns on protection? Well, your expected value for loss depends on both the chance you get hit, the damage you take, and actions you lose. So as the damage you take gets higher and the actions you lose get more costly, its more important to block those attacks. Now, the cost of blocking an attack is the chance that you can block another. So initially, with a low value you get a chance to block an attack you pretty much have to take it, the cost of not doing so is low(you might not be able to use it again), but the gain is relatively high. However, as your percentage chance of blocking anything increases, those opportunity costs increase for all attacks that are of low value, since you can get hit by something of high value instead and as your percentage chance of that happening increases the cost increases. But remember what opportunity cost is, its what we're giving up. Since the value of blocking any one attack is static then our other options must be increasing in value. And since we know that there is a decreasing marginal return on hit points and action(that is to say that attacks that take away more hit points or actions have an increasing marginal cost to us for every hit point and action they take away) we know that we're essentially increasing our marginal utility of our total expected payout faster than we're increases our marginal utility based on the question of "will i be able to use this". Because the question is rightly "will i be able to use this to block an attack that damages me greatly". I.E. since the vast majority of attacks do not impose a high cost, the ability to choose lets you choose the highest cost to block. The chance to block any single attack with a +1 gives you a linear increases in the payout of blocking that attack. The increasing chance to use that on a higher value attack means you must be increasing your payout in an increasingly marginal fashion. Ergo its marginal utility is increasing. Its for this reason that the wand bonus also has an increasing marginal return, because the question is not "do i get more of a chance to use this" or "do i get to to increase my return on any specific attack" but "do i get to hit with my best attack when i need to, and do i increase that probability?" And again, that is not what we care about. We care about how long, on average, any enemy will be held. I.E. we don't necessarily care that the +1 doesn't help us on a roll of a 4, but we do care when they start rolling above 10. The marginal utility rightly then becomes for the first +1 1/10 and for the second 1/9 and for the third 1/8. Now, there is a limiting factor in that total lockdown is unnecessary since you're only going to be fighting for so many rounds(though this increases as time goes on), however this factor is not rubbed up against until you're looking at the huge marginal utility gains brought on by having +9 or more wisdom. A number which precludes a strong value in constitution, making an argument about its marginal utility at those values pointless for our discussion. Before that, the increases in utility are overhwelmingly marginally positive. Status effects on enemies you're attacking aren't all that valueable. If you were attacking the monster you would be laying down your encounter and at-will effects making him weaker. The idea of a status effect is to remove an enemy from the fight so that you don't have to deal with him. At epic levels you're going to be dealing with 10-15 round fights. Anything you do to increase your average hold over that is a big deal. Optimal play strategy has the wizard landing a save ends that hampers on an enemy and then ignoring it while they kill everything else. Marginal returns on the time itself are only slightly dimished(since the enemy is not dealing damage there is no increasing marginal cost imposted as combat extends and your hit points and surges get lower[these things being marginally more valuable the less you have]) compared to the massive increase in time that higher values represent[its possible that marginal returns are initially negative though i find it unlikely, but the margin on the margin is overwhelmingly positive] Wand is an immediate interrupt. You apply it after the roll like the staff, you just don't apply it after the damage roll. Granted that doesn't matter as much because the difference between "after the damage roll" and "before the damage roll" are very small when you're launching the power. You have an expected return for the power and know the total you rolled. You get a pretty even expected increase with the same opportunity cost caveat that allows you to increase your expected return above that by not using it on a power that you don't "need" to hit. Ironically if you rule that the ability cannot be used after you know whether or not it hits, the marginal utility increases dramatically, because for every + you add, not only do you increase linearly the chance you turn a miss into a hit, but you also decrease the uncertainty that exists from the question of "will this bonus on this attack hit the enemy" and "do i need to use this bonus to hit the enemy". Both of these will increase your expected return. That is increasing marginal return. A little of both, remember, thunderwave ends up as a ranged 2 blast 4. This means not only do you have a decent amount of range and better area on each blast, but your ability to hit enemies around cover is increased. With a thunderwave your ability to place a blast extends 4 squares beyond the point where you can place it. The ability to place a scorching burst is much lower. E.G. A wizard with thunderwave can land a blast at T while being in the position W by placing the origin square at O even if there is a wall at - [code] TTTT TTTT TTTT TTTT ----0 W[/code]In many situations this extends the wizards ability to hit enemies just as much as a scorching burst can when terrain is very open. Fake Edit: I am sorry if the latter replies are not as in depth, i just lost the majority of them to a browser screw up Combat round time increases increasing the liklihood that people will be using their at will. The presence of a strong push at will increases the versatility of the player to choose effects on his encounters that do not overlap, this gives him more tactical control of the situation. 2 Feats. One of the three i listed is unnecessary. And Ray of Frost certainly doesn't with distance advantage and other abilities You're not making it more powerful. You're increasing the power of non-optimal builds. Its the same thing as saying "great weapon fighters are at a disadvantage compared to sword and board fighters and should get an increase somewhere" The other option is to nerf the option for wisdom based wizards or to add effects to other at wills that scale with their respective secondary stats (effects that are as strong as the push on thunderwave) They do. They increase their ability to lock down enemies with save ends. In just the same way, staff wizards get a beneficial impact from pumping constitution. They get an increase in the ability to block an incoming attack once per round. Why should one of them get an increasing marginal return on an at will while the other doesn't. [Push strength is an increasing marginal return] Sweet, did not know that, power just got a lot better for me. The retrain it for a utility that you can use. The opportunity cost of choosing a wisdom based wizard is increased when you give the other options the ability to have that strong control mechanism. The opportunity cost of choosing a staff wizard or wand wizard is static when you give them the ability to have that strong control mechanism. Their opportunity cost is unchanged, their benefit is increased. Depends on what else is happening. Push 4 allows you to more easily clump and position enemies where you want. I would say the situations where push 4 is better than push 2 is about equal to where it doesn't much matter. Especially since other players can impart status effects of their own. E.G. suppose you've got a rogue, fighter, or whatever knocking enemies down, And you've got some difficult terrain floating around. Well if you push 2 the melee enemy can stand up and charge, if you push 4, he needs a move of 8 to do so. Suppose that you've got an enemy on the back rank of your rogue like so F=Fighter, W= Wizard, E=Enemy, R=Rogue [code] F E R E W [/code]If you only have a push 2 you can prevent the flank on the rogue, but you can't stop the enemy from shifting again and striking the rogue. If you have a push 4, you can push the enemy to a position where he has to shift twice or provoke an OA for movement from the fighter. The further away you are the more this matters. Also, the more push you have the more likely you can trigger agile opportunist(another thoroughly ridiculous feat) for the fighter.(though you have to hit the fighter with the wave for this to work) This is just one of the many likely combinations that you're likely to face where a push 2 is insufficient compared to a push 4. [/QUOTE]
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