I don't want to get too much on Blizzard's back for their "bring the player, not the class" mantra. It has been quite successful in a number of ways. People who don't think it is successful need to take a look at raid composition at the end of BC, where you needed a shaman in every group and multiple shadow priests just to get things going, and where rogues did the most damage but needed so many other classes to enable them to do the most damage that there often simply wasn't space for them. It was a real mess.
Raid buffs are still a very tricky situation in 10-player raids. You want to try to make sure you have them, but having them all is pretty impossible. Blizzard has indicated that in 10-player raids they expect you will have some but not all raid buffs. And that's fine, of course. Raid buffs tend to give a little more than a 2% bonus to overall raid damage, and most of them apply multiplicatively. So they assume you have all 17 raid buffs for 25-player and some less number for 10-player when they set the health of the bosses.
Of course all raid buffs are not made equal, so I took one of my raids and did a little analysis. First, I know the percentage of the total damage each person did, so from there I figured out what portion of each person's damage was physical and what was magic (as well as what part was a "magic strike" which deals magic damage but hits and crits as a swing not a spell). I figured out what portion of each person's damage could benefit from haste rating and an approximate value for how much benefit to damage each person gets from crit. All of this allowed me to compile the following table:
While some buffs are barely a 1% bonus and others manage to get over 3%, the 13% spell damage buff is well over 8% bonus to overall raid damage. This is not a caster stacked raid either. The raid in question had 9 different dpsers swap in and out through the night. The number 1, 2 and 3 damage spots were a rogue, a hunter, and a shadow priest. But almost 17% of the rogue's damage is affected by +13% magic damage, it would be more for mutilate spec, I believe. Almost 50% of the hunter's damage and 40% of the death knight's damage was magic. The paladin was half and half as well. Basically 13% spell damage gives 13% damage to half your raid and half that to the other half, so it's more than twice as good as the next best buff.
And then there is the way it is handed out. Balance druids put it up on the main target you are attacking only. Any warlock can put it up, but they use a GCD to do so for each target and have to take a personal damage loss by not using other curses. Unholy death knights put it up on all enemies you are facing by doing their normal damage rotation. So if there are multiple adds being burned down, only one spec of one class provides a buff that is over twice as good as any other buff.
One of the most mind-boggling things about all of this is that there used to be a 10% spell crit debuff that mages put on the enemies and Blizzard toned it down to 5% because they thought it was too powerful. The 5% magic crit debuff on the enemy is worth around 1.75% damage, so doubling that would bring it to 3.5%, which is better than the next best buff, but still less than half of +13% spell damage. If instead of halving it they had doubled it, it would still not be as much of a problem as 13% spell damage. What's more, while it is limited to a number of classes and specs, all those classes and specs apply it in a relatively equal manner by putting it on targets only with single target spells.
They argued that because crit gives lots of other benefits, it was more important to drop the crit debuff than the bonus damage debuff, but in reality 1% spell crit is worth less raid damage than 1% magic damage. This is in large part because the 1% magic damage affects many things (like rogue poisons and explosive shot) that 1% spell crit does not. It is also because if things are only critting for double and you have 40% crit already, then 1% crit only increases your damage by .7%. Things crit for more than double in many cases, but also people have a lot more than 40% crit in many cases. Plus, not everything can crit, but everything does damage. Crits may proc buffs or other effects, but most of those work either as just bonus damage (ignite) which effectively increase your crit multiplier, or they have high uptime with existing crit values and upping crit by 5% might change uptime from 90% to 91%.
But 13% spell damage isn't even the biggest problem on the buff/debuff scene. I used an Anub'arak log to estimate the percentage damage value bonus of mortal strike on that fight for phase three.
The mortal strike debuff can be applied by a pretty wide range of classes and specs, since you can get it from any hunter, any rogue and two specs of warriors. But in the hard phase of the toughest encounter from the last tier of content, in order to make up for the healing it removed from the boss you would have had to do 20% more damage. Assuming you couldn't do 20% more damage, that would not mean the fight would go on a little longer. It would mean you'd have to kill another wave of adds that you would otherwise have just ignored while you finished him off. Of course in that time you are killing adds he is healing, which will give him time to summon another wave of adds. In fact, when we were fighting Anub in mostly 226 and 232 gear and we forgot to bring an MS effect to a fight we literally weren't doing any damage to him. The amount of damage we did to him between add summons was completely healed back by the time the adds were dead. We could not win without this debuff, even if he had no enrage timer we just weren't making progress.
Last night we were working on Lich King and talking about what we would do if we didn't have paladins to hammer of justice the Val'kyrs. Availability of long stuns is not something that I normally try to plan raids around, but this section of the fight would be hugely more difficult without paladins.
And I posted just recently about paladins and Valithria Dreamwalker. The challenge that fight presents without a holy paladin is astronomical compared to how hard it is with one. While I can forgive this one as a one time thing - especially since Beacon of Light is a problem in so many different ways - it is another example where the difficulty of a fight hinges hugely upon raid composition.1
Because raid buffs are still very powerful, Blizzard's "Bring the player, not the class" is only half honest. They do want you to think about raid buffs and bring a mix of people. It is not their intention that any raid will be good enough. You still need tanks, healers and damage dealers, after all. Runescrolls and drums are making previously necessary classes even more skipable.
But when a single debuff makes the difference between winning and losing - not because you had a 1% wipe - because the fight is just designed so that you can't win without it, things have swung back way to far into "Bring the class no matter who is playing it" territory. We would have a better chance against Anub with a hunter who went afk with one of those little birds tapping his aimed shot button than we would with a serious high dps class in that spot if we had no other source of healing reduction. Enemy heals are absolutely huge (they have to be to make them worth using) so that debuff is overpowered any time it is at all useful. We should not be so dependent on a single ability.
I think that healing reduction debuffs should just go away completely. Find a different way to make classes competitive in PvP and reduce healing on PvE enemies to account for the fact that it is gone. Or if the PvP problem can't be solved then just make bosses who heal immune to it. At the very least make the 10-player version immune. As lame as that is, requiring that debuff is even more lame.
1. Fun Fact: A group of 10 ilvl 245 geared holy paladins would beat the Dreamwalker encounter before the first blazing skeleton.
An endless list of nit-picking complaints inflated to make it seem like I can't stand something that I obviously love.
Monday, February 22, 2010
Tuesday, February 16, 2010
Overhealing
Note: I talked to a shaman after posting this and realized where I had gone wrong with the shaman numbers; part of it was ignoring earthliving weapon and another part was just a lot of bad information about coefficients. The maximal shaman case presented here is much lower than it ought to be, and the single target case with earth shield should be higher as well, with proportionally higher mana efficiency since the output should be higher with no increase in cost. I generally think that shamans are the most reasonable class in terms of their throughput and mana efficiency, and do not tend to extremes. Also it is very important to realize that when AoE healing shaman get much closer to their ideal scenario much more often than other classes, but that's sort of what this post is about.
Valithria Dreamwalker brings up a great opportunity to talk about something that is totally insane about this game, and that is the unbelievable imbalance between the amount of healing that the different classes can put out. I composed healing profiles of each class using my own base stats. Bear in mind this means that all classes other than discipline priests suffer somewhat because they would have better itemization for their own healing spells, but ultimately we end up with near the same spell power and the other stuff matters somewhat but is a bit of a wash.
This is what happens when different classes direct the maximum healing they can an Valithria, in a stand-and-"nuke" fashion, before portal multipliers:
That is pretty substantially imbalanced. Paladins do a good 50% more than discipline priests. Of course, discipline priests are basically custom-screwed for this task by having a lot of their best healing being dependent on shields, which do nothing for Valithria. But the few oddball facts about Valithria don't really swing the balance. When you look at the same numbers, but this time applied to a person who is actually getting hit and taking damage (shields and trigger on damage effects matter), it doesn't look all that different:
This is assuming proper glyphing and talent spec for the task at hand. The main difference between this chart and the last one is that discipline priests move up above holy priests. Now lets look at the chart of the maximal healing scenario, the case where the enemies do damage in a profile perfectly suited to you and you do no overhealing:
Wow.
We are faced with some simple facts:
Valithria Dreamwalker brings up a great opportunity to talk about something that is totally insane about this game, and that is the unbelievable imbalance between the amount of healing that the different classes can put out. I composed healing profiles of each class using my own base stats. Bear in mind this means that all classes other than discipline priests suffer somewhat because they would have better itemization for their own healing spells, but ultimately we end up with near the same spell power and the other stuff matters somewhat but is a bit of a wash.
This is what happens when different classes direct the maximum healing they can an Valithria, in a stand-and-"nuke" fashion, before portal multipliers:
That is pretty substantially imbalanced. Paladins do a good 50% more than discipline priests. Of course, discipline priests are basically custom-screwed for this task by having a lot of their best healing being dependent on shields, which do nothing for Valithria. But the few oddball facts about Valithria don't really swing the balance. When you look at the same numbers, but this time applied to a person who is actually getting hit and taking damage (shields and trigger on damage effects matter), it doesn't look all that different:
This is assuming proper glyphing and talent spec for the task at hand. The main difference between this chart and the last one is that discipline priests move up above holy priests. Now lets look at the chart of the maximal healing scenario, the case where the enemies do damage in a profile perfectly suited to you and you do no overhealing:
Wow.
We are faced with some simple facts:
- Paladins can heal for at least 10%, or as much as 50%, more than the next best healer and can more than double other healers even when circumstances are equally optimal for both
- Druid mana efficiency is so high that if tree of life did not reduce the mana cost of their spells, they would still be the most mana efficient healer, leading second place by a noticable margin and close to doubling the mana efficiency of the worst healers
- Shamans appear to be heinously bad at AoE healing; I'm going to have to check with a shaman friend of mine to verify this, because it's hard for me to believe it's actually as bad as the information I have makes it look
The answer is overhealing! Overhealing is basically responsible for healer balance. The fact that bosses can kill your tank in a couple seconds means that everyone overheals a bunch in order to make sure everyone is topped up all the time. Druids preempt damage by throwing HoTs all over, Paladins cast Holy Light on people who can only use two thirds of the hit points when their beacon target is at full.
On a recent night of lich king attempts, my healing per second while active was 3330 while a druid in the guild healed for 3218 per second while active. A pretty minor difference, well within the margin of critical hit caused error and the discipline priest actually came out ahead, so those numbers don't immediately seem to bolster my case. My overhealing was 26.6%, so my raw healing output per second was 4536. The druid's overhealing was 70.9%. Go look at some logs, that is not atypical for druids at all. That means his raw healing was 11058, about 2.4 times mine.
Right now, paladins and druids have overhealing numbers that are really through the roof. There is simply no way to avoid them. And most of the time, that's fine. They are as good at healing when more than half their healing is wasted as priests are when none of their healing is wasted. But of course not every fight limits healing with player max health like this, and the more damage that goes out, the more the imbalance starts to show itself. There are quite a few fights that I feel as a discipline priest I am simply a liability because of my inability to deal out the healing numbers required. Anub'arak comes to mind.
I'm not saying that discipline priests are underpowered, because I still think priests are some of the best healers. The fact is that Power Word: Shield, with's it's instant speed, usefully large size, pre-healing power, and ability to play well with other heals is such a powerful tool that discipline priests are very meaningful in most situations. And, of course, in the vast majority of fights the strongest healers do just overheal their power away, leaving them close to par with their weaker compatriots.
But with the coming of Cataclysm, Blizzard has indicated that there will be a shift to a slower, more thoughtful healing game. A game where you have to try to choose the right tool for the job and where overhealing is something to worry about because you could run yourself out of mana spamming your biggest heals. In a game like that, these differences are going to be extremely pronounced. When the tank is in danger of dying in 5 seconds instead of 2, healers will be able to opt to play the game where the tank is in danger of dying within 3.5 seconds by just leaving the tank at 70% of their health. Compared to what we are doing now this will seem downright relaxed. At that point, noone will have to worry about overhealing at all and that druid raider in my guild will simply be 2.4 times as good as me.
Obviously there will be some pretty substantial changes between now and cataclysm, and I think they will rework some of these things. But I really don't think they are going to turn all this over before the expansion releases. Druids complained at the end of BC that they didn't have Flash Heal, then blizzard gave them Flash Heal and druids simply didn't cast it. Then the druid Flash Heal was made somewhere in the neighborhood of 50% better than the priest Flash Heal, for 20% less mana, and most druids still scoff at it, while priests spam Flash Heal all day long. Remember when Wild Growth was released on the beta? It was a better single target heal than holy light. We are going to have to wait for a lot of iteration before there is any semblance of balance, and sometimes iteration just pushes more and more in the direction of imbalance.
With 5 seconds instead of 2 to die, the difference between big heals and little heals, HoTs and shields, instants and channels will really start to wash out. The difference between their power and cost is going to have to even out a lot as well. Without priests getting a really substantial boost relative to the other classes paladins are just going to be casting Flash of Lights as big as our Flash Heals for half the mana and doubling their effect with Beacon of Light while druids leave HoTs on the tank that outheal our maximum single-target healing. Ten man raids will simply be choosing between bringing a druid and a paladin to the boss, or a shaman and two priests. At least shadow is doing competitive dps.
Friday, February 12, 2010
Grace
At some point Blizzard let us in on a design goal of theirs, which is to have talents be worth about 1% each. 1% more damage, more healing, more whatever. Of course there would be exceptions. It would be pretty boring if every talent were the same. But that is the baseline: more than 1% means a good talent, less than 1% is a weaker talent. Often you need to take weaker talents on the way up to the good ones.
Now discipline priests, I feel, are particularly bad when it comes to having good and bad talents, or I suppose just when it comes to having bad talents. Discipline Talents do not improve overall throughput as much as perhaps they should. Or it might be that discipline talents are about where they want things to be and most other trees are overpowered (the average talent a discipline priest takes increases effect by just over 1%, the good ones being balanced by very bad ones).
Generally, I'd rather not be taking a talent that has less than half a percent effect on my output. Those seem like very weak talents that I should be looking for something else to put in place of. Unfortunately, that is not really an option. A lot of talents such as Improved Inner Fire are just stepping stones with no other options available (18 spell power per point!). But when it comes to the top of the discipline tree, there are lots of good options, and I shouldn't be left scooping up the filler.
And that's where Grace comes in. According to the stats provided by www.quickarmory.com 94% of discipline priests take this talent and 82% take both points in it. This puts it on about even representation with Divine Aegis.
My spreadsheet works with my actual casts. I wrote a crude log parser (I call it crude because it's an excel macro) to get data from my combat logs and that data feeds into the spreadsheet to give me my own actual healing per second, mana use, and how that would be affected by changing stats and talents, so I know how good these talents are relative to one another. Divine Aegis increases healing done (counting absorbs as healing) by about 2.7% per point, so it is a very strong talent indeed. That second point of Grace is worth a whopping 0.3%.
That's right, it is total garbage.
In order to understand how bad Grace is, you have to know a bit about how Grace works. Take a moment to read the description of it's effect and I'll go on. So the second point of grace gives you a 100% chance to stack the effect, while the first point gives you only a 50% chance to stack the effect.
Imagine I focus most of my heals on a single target. That target will have Grace stacked up on them a lot of the time. Regardless of whether I have one or two points, I'm pretty likely to maintain a three stack. After all, if I am focusing heals on someone, 15 seconds is a very long time to hit with enough heals that the chance it doesn't renew becomes awfully small. But what if I throw a Penance or Flash Heal at another target who needs it? If a lose my stack, it will take longer to rebuild with only 1 point than it will with 2. On the other hand, with only one point, there is only a 50% chance I lose it from my main target in the first place. If it doesn't get applied to the target of my heal, it doesn't drop from the target of my previous heal.
In addition to all the real things going on, my parser puts a "Fake Grace 1" and "Fake Grace 2" buff on people I heal. The numbers represent the number of points. So whenever I cast one of specified spells I put Fake Grace 2 on the target, increment the stack if they already have it, and remove the stack from anyone else. I also flip a coin to see whether I do the same with Fake Grace 1. Doing this allows me to get results for the average number of Grace stacks that I would have on my targets for each spell.
As you can see, the difference is not that great. For some spells it works out to be a lot more than others. It isn't surprising that Greater Heal ended up with the same stacks for 1 and 2 points because I only have 2 GH casts in the logs I am using for this and so a couple of coin flips would make it come out the same. As you can see, the difference in average number of stacks is not double when you put that second point in, in many cases it is increased by about half or less. Every stack is a 3% throughput on that spell. So for Penance, which goes from 0.77 to 1.19 stacks, that second point is about a 1.26% increase in the effect. For Flash Heal, whose average goes from 0.32 to 0.47 stacks, that's a 0.45% increase in effect.
Of course the first point in Grace is not that overwhelming either, the reality of that point's effect on my healing is about a 0.56% increase. Almost double the effect of the second point, but still a pretty bad talent. The thing is, the first point can be a 9% increase in healing when you need it most. If one person is taking really massive damage and you are chaining heals on them then Grace does what it is supposed to, and does it about as well whether you made the half or full investment in it. There is a situation in which the first point of Grace really performs. The second point of Grace, however, performs quite randomly. It is not particularly better in the situation that it is designed to work for, and when throwing heals around the raid they are almost the same.
What is so sad about all of this is that I have two points in Grace. When it comes to spending those last few talents points I'm just scraping the bottom of the barrel so badly that a 0.3% increase in my overall healing, doled out at random, is better than my other options1. Discipline priest throughput is really, really weak compared to other healers and I wish that this talent was doing what it looks like it was meant to do, but for now there is nothing I can do but take it anyway.
1. Spell Warding is the next best thing I could take from a raid healing perspective. Reducing the amount of magic damage I take by 2% is about 86% as good as that second point of Grace is for improving the total health of the raid.
Now discipline priests, I feel, are particularly bad when it comes to having good and bad talents, or I suppose just when it comes to having bad talents. Discipline Talents do not improve overall throughput as much as perhaps they should. Or it might be that discipline talents are about where they want things to be and most other trees are overpowered (the average talent a discipline priest takes increases effect by just over 1%, the good ones being balanced by very bad ones).
Generally, I'd rather not be taking a talent that has less than half a percent effect on my output. Those seem like very weak talents that I should be looking for something else to put in place of. Unfortunately, that is not really an option. A lot of talents such as Improved Inner Fire are just stepping stones with no other options available (18 spell power per point!). But when it comes to the top of the discipline tree, there are lots of good options, and I shouldn't be left scooping up the filler.
And that's where Grace comes in. According to the stats provided by www.quickarmory.com 94% of discipline priests take this talent and 82% take both points in it. This puts it on about even representation with Divine Aegis.
My spreadsheet works with my actual casts. I wrote a crude log parser (I call it crude because it's an excel macro) to get data from my combat logs and that data feeds into the spreadsheet to give me my own actual healing per second, mana use, and how that would be affected by changing stats and talents, so I know how good these talents are relative to one another. Divine Aegis increases healing done (counting absorbs as healing) by about 2.7% per point, so it is a very strong talent indeed. That second point of Grace is worth a whopping 0.3%.
That's right, it is total garbage.
In order to understand how bad Grace is, you have to know a bit about how Grace works. Take a moment to read the description of it's effect and I'll go on. So the second point of grace gives you a 100% chance to stack the effect, while the first point gives you only a 50% chance to stack the effect.
Imagine I focus most of my heals on a single target. That target will have Grace stacked up on them a lot of the time. Regardless of whether I have one or two points, I'm pretty likely to maintain a three stack. After all, if I am focusing heals on someone, 15 seconds is a very long time to hit with enough heals that the chance it doesn't renew becomes awfully small. But what if I throw a Penance or Flash Heal at another target who needs it? If a lose my stack, it will take longer to rebuild with only 1 point than it will with 2. On the other hand, with only one point, there is only a 50% chance I lose it from my main target in the first place. If it doesn't get applied to the target of my heal, it doesn't drop from the target of my previous heal.
In addition to all the real things going on, my parser puts a "Fake Grace 1" and "Fake Grace 2" buff on people I heal. The numbers represent the number of points. So whenever I cast one of specified spells I put Fake Grace 2 on the target, increment the stack if they already have it, and remove the stack from anyone else. I also flip a coin to see whether I do the same with Fake Grace 1. Doing this allows me to get results for the average number of Grace stacks that I would have on my targets for each spell.
As you can see, the difference is not that great. For some spells it works out to be a lot more than others. It isn't surprising that Greater Heal ended up with the same stacks for 1 and 2 points because I only have 2 GH casts in the logs I am using for this and so a couple of coin flips would make it come out the same. As you can see, the difference in average number of stacks is not double when you put that second point in, in many cases it is increased by about half or less. Every stack is a 3% throughput on that spell. So for Penance, which goes from 0.77 to 1.19 stacks, that second point is about a 1.26% increase in the effect. For Flash Heal, whose average goes from 0.32 to 0.47 stacks, that's a 0.45% increase in effect.
Of course the first point in Grace is not that overwhelming either, the reality of that point's effect on my healing is about a 0.56% increase. Almost double the effect of the second point, but still a pretty bad talent. The thing is, the first point can be a 9% increase in healing when you need it most. If one person is taking really massive damage and you are chaining heals on them then Grace does what it is supposed to, and does it about as well whether you made the half or full investment in it. There is a situation in which the first point of Grace really performs. The second point of Grace, however, performs quite randomly. It is not particularly better in the situation that it is designed to work for, and when throwing heals around the raid they are almost the same.
What is so sad about all of this is that I have two points in Grace. When it comes to spending those last few talents points I'm just scraping the bottom of the barrel so badly that a 0.3% increase in my overall healing, doled out at random, is better than my other options1. Discipline priest throughput is really, really weak compared to other healers and I wish that this talent was doing what it looks like it was meant to do, but for now there is nothing I can do but take it anyway.
1. Spell Warding is the next best thing I could take from a raid healing perspective. Reducing the amount of magic damage I take by 2% is about 86% as good as that second point of Grace is for improving the total health of the raid.
Monday, February 8, 2010
Gotta Catch 'em All
I'm not normally one to complain that Blizzard can't do math1, because I generally feel that they can do math pretty well. There are some hilarious slips, like in the beta when Wild Growth was a better single-target heal than Holy Light, but generally these things happen before their math teams gets a hold of things and never make it live. Sure, things are off what they should be, but compared to pretty much every other game, computer or otherwise, that has ever been made, WoW is pretty remarkably well balanced.
But I am not here to talk about how Blizzard gets things right, and there is one particular area where they seem consistently incapable of doing the math required to understand how long certain things will take.
The new Love is in the Air redesign corrects a lot of the boredom and frustration of the old event and updates the achievements associated with it. Probably the most infamous achievement that has been updated is the Be Mine! achievement. This year you have to eat all eight different candies and you can trade them around to other people, so it's a matter of making candies and then trading until you get the complete set. Last year the achievement was to make each candy from a candy bag. And the candy bags, of course, were rewarded at random from giving out cards to people... and they were bind on pickup. "No problem," I'm sure someone thought. You see, you only need 8 different candies and each bag has 10 charges. What's more, if you are aggressive about giving out love tokens you'll probably get two bags before the holiday is over.
This is the math I'm talking about. How many charges of candy bags does it actually take to get this done? Well, the first charge you use definitely gives you a candy you don't have, since you don't have any of them. The second time you use one there is a seven-in-eight chance you get a new candy. Once you have two candies there is a 6/8 chance, and so on. That means the average number of attempts to generate all the candies is 8/8 (first candy) + 8/7 (second candy) + 8/6 (third candy) + ... + 8 (last candy). Stated otherwise this is 8 * (1 + 1/2 + 1/3 + ... + 1/8). In general, any time you want to collect N different objects that appear with uniform probability it will take you, on average, N * sum(1/1, 1/2, ..., 1/N) attempts.
That series we are summing, the reciprocals of the natural numbers, is called the Harmonic Series. Summing this series and multiplying by N gives us the average we are looking for, and so it is kind of amazing that Blizzard seems incapable of figuring out the impact of this series on the game. Perhaps they can be forgiven as there is no closed form algebraic expression for the sum of the first N terms of the Harmonic Series2, but it's really not that hard to do it by hand for numbers like 8 and we do have computers to do these things for us when the number gets into the double digits.
Notice that the average is a little over 20. That means on average you needed three entire bags of candy, because having all but one of the candies when you finished your second bag did you no good at all. This led Blizzard to change the achievement to give it to you when you had made 6 different candies. And it's good that they did that, but couldn't someone have noticed that the achievement was inordinately cumbersome by doing some simple math ahead of time?
Of course all of this is just averages, and averages tell only a small part of the story. Another question we could ask is: if I have to collect a number of things, what are the chances I am done after a certain number of attempts? Here is the answer:
That is the likelihood you will be done after a number of attempts given trying to collect 6, 8, 10 and 20 things. I've marked the multiples of 10 attempts at 8 items so you could see the results relevant to the task at hand. You see, if you got two bags of candy there was about a 53% chance you were going to be finished. If you got three bags, 86%. Now don't be so happy about 86%. That means that if you were trying really hard to get this achievement done, being very dedicated to giving out those tokens and getting those presents, about 1 in 7 times you would have failed anyway because those bags just wouldn't give you that last candy. A very frustrating situation. Sure, the fourth bag brings it up to 96.27%, but that still leaves over 1 in 30 people without, and getting four bags required not only a lot of dedication but a *lot* of luck too.
I graphed how many attempts it would take for numbers other than eight so you could see how this thing gets out of hand. With eight items to collect you cross the 50% chance of being done mark at 20 attempts. With ten you need 27 attempts. That means a 25% increase in items to be collected resulted in a 35% increase in attempts to get to 50% chance of getting them (and a similar increase in the number of attempts to get to a 95% chance of finishing). With 20 items to collect the 50% mark is crossed at 67 items collected. So multiplying the number of items to collect by 2.5 multiplies the number of attempts by 3.35. Collection time expands more than linearly with items to collect.
So how does this apply to what ought to be the most infamous achievement of all, A Mask for All Occasions? Each time you open a treat bag you have about a 1 in 4 chance of getting a mask. Each time you complete one of the dailies you have a 1 in 10 chance of getting a mask. There are 20 different masks to collect. How long is this going to take?
Well, when you trick or treat you don't necessarily get a treat bag. Let's say you get one about three in four times (I think it might be less than this, but this seems like a decent estimate). Based on that, I calculated the average number of 2 week periods it would take to complete this achievement based on three different standards:
Typical participation - Complete the daily every day and Trick or Treat three times a day
Aggressive participation - Complete the daily and Trick or Treat eight times a day
Insane participation - Complete the daily and Trick or Treat 24 times a day
Here is the graph:
So, if you are insane enough to trick or treat on the hour every hour for two weeks you have a whopping 44.9% chance to complete the achievement in a year. Less than 50%. If you are quite aggressive about it (for people go to work, go to school and don't set alarms to wake them in the middle of the night but try really hard) then you have a less than 50% chance of being done in three years, but a pretty good chance of being done in four, and about a 93% chance of being done in five years. That means of all people who put every waking non-occupied hour into this for five years, about 1 in 14 of them won't be done. If you trick or treat a few times a day forget about it. You don't cross the 50% chance threshold for eight years, and after five years your chances have barely cracked one in ten.
This achievement is worth 10 points! The achievement Veteran Nanny which requires completing an easy series of quests that take about an hour once a year for three years is worth 50 points in recognition of the dedication it requires. A typical person who is interested in this achievement but doesn't have the ability to take two weeks leave from work and life every year near hallowe'en will never get this.
Achievements are not examined with a fine-toothed math comb to weed out outliers like this, but this is seriously egregious, and pretty much outdoes everything else in the game. Someone needs to check the math on the gotta catch 'em all feats in this game and fix up the odds.
1. Ignore the fact that this blog is here mostly so I can complain that Blizzard can't do math
2. To understand what this means, consider the sum of 1 + 2 + 3 + ... + N. That is always equal to N * (N + 1) / 2. There being no closed form algebraic expression of the Harmonic Series means that there is no neat way to write it like there is a neat way to write the sum of the natural numbers. In fact, in involves using a function called the Psi function which is the natural logarithm of the derivative of the Gamma function, which is an expansion of the concept of factorials to the real numbers (Gamma of n where n is a natural number is the same as n!). The idea that blizzard could be forgiven not being able to do this math on this account was, naturally, sarcasm.
But I am not here to talk about how Blizzard gets things right, and there is one particular area where they seem consistently incapable of doing the math required to understand how long certain things will take.
The new Love is in the Air redesign corrects a lot of the boredom and frustration of the old event and updates the achievements associated with it. Probably the most infamous achievement that has been updated is the Be Mine! achievement. This year you have to eat all eight different candies and you can trade them around to other people, so it's a matter of making candies and then trading until you get the complete set. Last year the achievement was to make each candy from a candy bag. And the candy bags, of course, were rewarded at random from giving out cards to people... and they were bind on pickup. "No problem," I'm sure someone thought. You see, you only need 8 different candies and each bag has 10 charges. What's more, if you are aggressive about giving out love tokens you'll probably get two bags before the holiday is over.
This is the math I'm talking about. How many charges of candy bags does it actually take to get this done? Well, the first charge you use definitely gives you a candy you don't have, since you don't have any of them. The second time you use one there is a seven-in-eight chance you get a new candy. Once you have two candies there is a 6/8 chance, and so on. That means the average number of attempts to generate all the candies is 8/8 (first candy) + 8/7 (second candy) + 8/6 (third candy) + ... + 8 (last candy). Stated otherwise this is 8 * (1 + 1/2 + 1/3 + ... + 1/8). In general, any time you want to collect N different objects that appear with uniform probability it will take you, on average, N * sum(1/1, 1/2, ..., 1/N) attempts.
That series we are summing, the reciprocals of the natural numbers, is called the Harmonic Series. Summing this series and multiplying by N gives us the average we are looking for, and so it is kind of amazing that Blizzard seems incapable of figuring out the impact of this series on the game. Perhaps they can be forgiven as there is no closed form algebraic expression for the sum of the first N terms of the Harmonic Series2, but it's really not that hard to do it by hand for numbers like 8 and we do have computers to do these things for us when the number gets into the double digits.
Notice that the average is a little over 20. That means on average you needed three entire bags of candy, because having all but one of the candies when you finished your second bag did you no good at all. This led Blizzard to change the achievement to give it to you when you had made 6 different candies. And it's good that they did that, but couldn't someone have noticed that the achievement was inordinately cumbersome by doing some simple math ahead of time?
Of course all of this is just averages, and averages tell only a small part of the story. Another question we could ask is: if I have to collect a number of things, what are the chances I am done after a certain number of attempts? Here is the answer:
That is the likelihood you will be done after a number of attempts given trying to collect 6, 8, 10 and 20 things. I've marked the multiples of 10 attempts at 8 items so you could see the results relevant to the task at hand. You see, if you got two bags of candy there was about a 53% chance you were going to be finished. If you got three bags, 86%. Now don't be so happy about 86%. That means that if you were trying really hard to get this achievement done, being very dedicated to giving out those tokens and getting those presents, about 1 in 7 times you would have failed anyway because those bags just wouldn't give you that last candy. A very frustrating situation. Sure, the fourth bag brings it up to 96.27%, but that still leaves over 1 in 30 people without, and getting four bags required not only a lot of dedication but a *lot* of luck too.
I graphed how many attempts it would take for numbers other than eight so you could see how this thing gets out of hand. With eight items to collect you cross the 50% chance of being done mark at 20 attempts. With ten you need 27 attempts. That means a 25% increase in items to be collected resulted in a 35% increase in attempts to get to 50% chance of getting them (and a similar increase in the number of attempts to get to a 95% chance of finishing). With 20 items to collect the 50% mark is crossed at 67 items collected. So multiplying the number of items to collect by 2.5 multiplies the number of attempts by 3.35. Collection time expands more than linearly with items to collect.
So how does this apply to what ought to be the most infamous achievement of all, A Mask for All Occasions? Each time you open a treat bag you have about a 1 in 4 chance of getting a mask. Each time you complete one of the dailies you have a 1 in 10 chance of getting a mask. There are 20 different masks to collect. How long is this going to take?
Well, when you trick or treat you don't necessarily get a treat bag. Let's say you get one about three in four times (I think it might be less than this, but this seems like a decent estimate). Based on that, I calculated the average number of 2 week periods it would take to complete this achievement based on three different standards:
Typical participation - Complete the daily every day and Trick or Treat three times a day
Aggressive participation - Complete the daily and Trick or Treat eight times a day
Insane participation - Complete the daily and Trick or Treat 24 times a day
Here is the graph:
So, if you are insane enough to trick or treat on the hour every hour for two weeks you have a whopping 44.9% chance to complete the achievement in a year. Less than 50%. If you are quite aggressive about it (for people go to work, go to school and don't set alarms to wake them in the middle of the night but try really hard) then you have a less than 50% chance of being done in three years, but a pretty good chance of being done in four, and about a 93% chance of being done in five years. That means of all people who put every waking non-occupied hour into this for five years, about 1 in 14 of them won't be done. If you trick or treat a few times a day forget about it. You don't cross the 50% chance threshold for eight years, and after five years your chances have barely cracked one in ten.
This achievement is worth 10 points! The achievement Veteran Nanny which requires completing an easy series of quests that take about an hour once a year for three years is worth 50 points in recognition of the dedication it requires. A typical person who is interested in this achievement but doesn't have the ability to take two weeks leave from work and life every year near hallowe'en will never get this.
Achievements are not examined with a fine-toothed math comb to weed out outliers like this, but this is seriously egregious, and pretty much outdoes everything else in the game. Someone needs to check the math on the gotta catch 'em all feats in this game and fix up the odds.
1. Ignore the fact that this blog is here mostly so I can complain that Blizzard can't do math
2. To understand what this means, consider the sum of 1 + 2 + 3 + ... + N. That is always equal to N * (N + 1) / 2. There being no closed form algebraic expression of the Harmonic Series means that there is no neat way to write it like there is a neat way to write the sum of the natural numbers. In fact, in involves using a function called the Psi function which is the natural logarithm of the derivative of the Gamma function, which is an expansion of the concept of factorials to the real numbers (Gamma of n where n is a natural number is the same as n!). The idea that blizzard could be forgiven not being able to do this math on this account was, naturally, sarcasm.
Monday, February 1, 2010
1 to 100
I'm on my way to It's Over Nine Thousand! and though I'm pretty much in striking distance and I expect I'll get it over the next few weeks thanks to soon-to-be-released ICC achievements. If I did 25-player raids this would have been pretty easy and I'd have it now from a few original Glory of the Raider achievements alone. But with a relatively small number of 25-player achievements under my belt (such as Dwarfageddon which can be two-boxed easily enough) I am down to scraping the bottom of the barrel and waiting for wings to open to get these last few points.
I have a lot more 10-player raiding achievement points than a typical player who focused on raiding, and my guild's top 10 spot on the GuildOx 10-player strict achievement rankings confirms this, but nine thousand is still an awful lot, and you don't get it strictly by doing PvE.
I'm not much of a PvPer normally, but I've done a lot of it to get achievement points. I made myself a big list of things that seemed reasonable to shoot for to separate them from things that don't seem reasonable at all (Ironman is pretty tough to get as a priest) from the perspective that I'm not going to trouble my guildmates by trying to convince them to run BGs in big teams devoted to pointing me up. Among the achievements in reach are the achievements for getting 100 wins in various BGs. The fact is, if you play a BG over and over and over you will eventually get 100 wins regardless of whether you can put together a high-caliber team to go in with. My win-loss record tends to remain pretty close to 50%, so it takes about 200 games to get the wins.
200 games, of course, is an awful lot. AB games take about 16-20 minutes. WSG takes anywhere from 6 to 27 minutes. SotA is usually shorter, but still over 10 minutes for most games. That places the time commitment to get 100 wins around the 50 hour mark plus or minus depending on the BG. And that's only counting time in the BG, not queue time.
I have no objection to achievements that take 50 hours. And I don't mind that they are only worth 10 points. I think trying to set the worth of achievements based on how long they take or how hard they are to achieve would be mostly silly, and giving 10 points for very easy and very hard achievements alike is a pretty good system. On the other hand, comparing BG wins to quests completed, money looted, emblems looted, levels attained, or any of a number of other things that you take a long time acquiring sort of makes the lack of steps in BG wins really stand out. I get an achievement for 50 quests, 100 quests, 250 quests, 500 quests, 1000, 2000 and 3000 quests completed. That is seven achievements. For battleground wins, I get an achievement for winning the first time, then I get another if I win 100 times.
So I go in, have no idea what I'm doing, play around, get lucky, and a little box pops on the screen to congratulate me (Hooray!). Then I spend 49 hours playing replaying and mastering the battleground (for whatever little effect that has on my team's ability to win) and I am greeted by nothing. No "Way to go!" or "At a' boy" for me, just a cold slog through a myriad of flags and corpses.
Now as I mentioned, I am pretty much going to get my achievement points over 9000 on the back of the raiding achievements for ICC at this point, so I have no need to beg for achievement points. This isn't about earning points. This is about the idea of achievement. 100 wins is a damn lot, and its an appropriate number, if you ask me, for the pinnacle of battleground wins, though putting in a higher and more ludicrous number wouldn't hurt (100 wins is a lot less than 3000 quests). But there should be stepping stones along the way. 10 wins, 25 wins, 50 wins. The point of this is not to hand out achievement points like candy, and it wouldn't be doing that, the point is that achievements are little congratulations for the things you do. They let your guild know what you are doing with your time when they pop up and mark milestones along your path. I completed every Strand of the Ancients achievement, aside from the 100 wins, in about 10 games. There are no milestones or landmarks along the way now, just another 168 gates to break down (in multiples of four or it doesn't count).
It's pretty obvious from a number of angles that there wasn't a great deal of thought put into what should be an achievement and what shouldn't be. There was clearly one team that made up the PvP achievements and another team that made up raiding achievements, and they didn't discuss methodology much. Achievements do not require balancing the way other aspects of the game do, but there are a few glaring problems that could be corrected. I think achievements have been very well received and are now an important part of the game, and I hope they fix the very haphazard nature of them when they are forced to reexamine them for Cataclysm.
I have a lot more 10-player raiding achievement points than a typical player who focused on raiding, and my guild's top 10 spot on the GuildOx 10-player strict achievement rankings confirms this, but nine thousand is still an awful lot, and you don't get it strictly by doing PvE.
I'm not much of a PvPer normally, but I've done a lot of it to get achievement points. I made myself a big list of things that seemed reasonable to shoot for to separate them from things that don't seem reasonable at all (Ironman is pretty tough to get as a priest) from the perspective that I'm not going to trouble my guildmates by trying to convince them to run BGs in big teams devoted to pointing me up. Among the achievements in reach are the achievements for getting 100 wins in various BGs. The fact is, if you play a BG over and over and over you will eventually get 100 wins regardless of whether you can put together a high-caliber team to go in with. My win-loss record tends to remain pretty close to 50%, so it takes about 200 games to get the wins.
200 games, of course, is an awful lot. AB games take about 16-20 minutes. WSG takes anywhere from 6 to 27 minutes. SotA is usually shorter, but still over 10 minutes for most games. That places the time commitment to get 100 wins around the 50 hour mark plus or minus depending on the BG. And that's only counting time in the BG, not queue time.
I have no objection to achievements that take 50 hours. And I don't mind that they are only worth 10 points. I think trying to set the worth of achievements based on how long they take or how hard they are to achieve would be mostly silly, and giving 10 points for very easy and very hard achievements alike is a pretty good system. On the other hand, comparing BG wins to quests completed, money looted, emblems looted, levels attained, or any of a number of other things that you take a long time acquiring sort of makes the lack of steps in BG wins really stand out. I get an achievement for 50 quests, 100 quests, 250 quests, 500 quests, 1000, 2000 and 3000 quests completed. That is seven achievements. For battleground wins, I get an achievement for winning the first time, then I get another if I win 100 times.
So I go in, have no idea what I'm doing, play around, get lucky, and a little box pops on the screen to congratulate me (Hooray!). Then I spend 49 hours playing replaying and mastering the battleground (for whatever little effect that has on my team's ability to win) and I am greeted by nothing. No "Way to go!" or "At a' boy" for me, just a cold slog through a myriad of flags and corpses.
Now as I mentioned, I am pretty much going to get my achievement points over 9000 on the back of the raiding achievements for ICC at this point, so I have no need to beg for achievement points. This isn't about earning points. This is about the idea of achievement. 100 wins is a damn lot, and its an appropriate number, if you ask me, for the pinnacle of battleground wins, though putting in a higher and more ludicrous number wouldn't hurt (100 wins is a lot less than 3000 quests). But there should be stepping stones along the way. 10 wins, 25 wins, 50 wins. The point of this is not to hand out achievement points like candy, and it wouldn't be doing that, the point is that achievements are little congratulations for the things you do. They let your guild know what you are doing with your time when they pop up and mark milestones along your path. I completed every Strand of the Ancients achievement, aside from the 100 wins, in about 10 games. There are no milestones or landmarks along the way now, just another 168 gates to break down (in multiples of four or it doesn't count).
It's pretty obvious from a number of angles that there wasn't a great deal of thought put into what should be an achievement and what shouldn't be. There was clearly one team that made up the PvP achievements and another team that made up raiding achievements, and they didn't discuss methodology much. Achievements do not require balancing the way other aspects of the game do, but there are a few glaring problems that could be corrected. I think achievements have been very well received and are now an important part of the game, and I hope they fix the very haphazard nature of them when they are forced to reexamine them for Cataclysm.
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