Not Dumbledore’s Army

Today we take up the DA modifier, or written in full, the Double Attack modifier. Double Attack Percentage ranges from 0 to 100%. Double attacks are not called out in the logs as such, so it is difficult to gather data on them as such. In a run of 267 melee atttacks versus basilisks in Bonemire, I had one attack that might have been a double attack. Given that my Double Attack percentage is 1%, this is a reasonable outcome, in fact, there’s a 7% chance that I would get no double attacks whatsoever in a run of 267 autoattacks.

So, I’m going to assume the following things about double attacks:

  • Double attack chance is rolled on an attack that hits. Misses are ignored.
  • If the double attack chance succeeds, it means a second attack has hit, no “to-hit” roll applies.
  • Damage for the second hit is calculated normally, subject to DPS mod, STR, critical hits, and so on.
  • Second hits will not trigger procs.
  • Only autoattack hits are affected.

Ok, I’ve made a few charts showing tradeoffs between DA and Attack Speed (haste). The first thing to notice is that X% DA has the same effect on DPS as X% haste, assuming that the other modifier is zero. Put another way, swapping your DA and attack speed modifier will leave your DPS unchanged.

The second thing to notice is that the same 50 points of modifier gives the largest gain when spread equally between haste and DA. Which gives us an important rule of thumb: increases in the smaller modifier are worth more, even if you figure in diminishing returns.

The next table considers a character with 70% haste and 5% double attack. This isn’t too unreasonable for someone who has the haste cloak and is grouped with an illusionist or troubador. We then look at the effect of adding between one and five points to either haste or DA.

We see that adding to DA increases output DPS by more than adding the same amount to haste in this situation. And that’s not accounting for the fact that haste is on diminishing returns. I used the percentage figures in the chart, but at that level of haste, one point of Attack Speed is going to be worth less than 1% haste, perhaps only .75%.

There’s nothing special about the nature of haste or DA that makes this so, if someone had 70% DA and 5% haste, then adding to haste would have the larger effect. In fact, we could substitute in Melee crit chance and the effects would be similar. The big problem with modeling Melee Critical is that the magnitude of its effect on DPS depends on the damage spread of the weapon used, because of the critical damage minimum value. Melee Critical chance affects combat arts, too. So we’ll leave the tradeoffs for another day.

Melee Crit Chance

Recently, I wrote about the Attack Speed (haste) modifier, and how the math of it worked, and it’s implications. This time, I want to explore the Melee Critical modifier.

This modifier is on a diminishing returns curve exactly like the Attack Speed modifier. The nominal value is translated to a percentage, which represents the probability of a normal hit being a critical hit. So, what does a critical hit do for you?

To explore this, I took a sample of 66 normal hits and 66 critical hits from a night my bruiser spent in Chelsith with a group. My bruiser was using the Bo of Flowing Blood, from Unrest. My critical hit chance was NOT 50 percent, by the way, but I’ve stacked up the data this way because I want to visualize the relationship between a normal hit and a critical hit.

You can look at the data if you want to. The data points are sorted by size, so we can see the trends. They occured consecutively in the dataset, but not in this order.

The first thing of note is that the critical hits have a definite minimum value. That’s the flat part of the red curve on the left. In this dataset, that value is 604. The average damage, in this dataset, of a normal hit was 376 hit points, while the average damage of a critical was 703, which is nearly double.

Let’s try to cancel out the effect of the floor. We’ll do this by taking the average of those critical hits bigger than 604, and the average of the normal hits corresponding to them (underneath them in the graph). The average of the critical hits in this subset is 788, while the average of the corresponding normal hits is 501. Others have claimed that the raw critical hit ratio is 3 to 2, this is pretty close to what we see in the upper half of the data, where the minimum damage value is not in effect.

So how is the mininmum crit damage determined? The claim is that is is the maximum weapon damage, plus one. No criticals can do more damage than that.

However, in our dataset, there are 6 normal hits larger than 604. This is a very odd tail to this curve, with a much steeper slope. There are 3 points on the critical curve with a similar slope.

It appears that there is a special kind of “normal” hit, that exceeds the normal maximum damage. This is in agreement with raiders expressed experience with certain raid mobs, which sometimes do very large hits which aren’t logged as critical hits.

I’m willing to support the notion that melee crits have the following model. For all normal hits, roll damage, including a small chance of a “super normal” hit. Then roll the chance that the hit is a critical. If it is a critical hit, multiply the damage by 1.5. If the result is less than the maximum damage for the weapon, increase it to the weapon maximum damage, perhaps plus one or two points.

So, the bigger the damage spread, the more a critical hit will help your damage. In this dataset a critical nearly doubled the amount of damage. At a minimum, a critical will improve your damage by a factor of 1.5.

Ok, what about combat arts, are they affected by “melee crit chance”? I made the following chart of all outgoing damage for the same instance crawl, plotting the percentage of hits that were criticals.

Here’s the entire dataset for that chart.

Most of these ratios look pretty good. Savage Bruising is a DOT, only the first tick of a DOT can critical, so that accounts for it’s lower ratio. Engulf is very low, and Master’s Strike is low as well. My guess is that these skills are treated differently. Engulf does fire damage, that might well be treated as a spell. Master’s Strike does slashing damage, but since we are calculating the ratio of crits to melee hits, any difference in crushing skill versus slashing skill should be factored out. But it appears to critical at a rate different from the other combat arts.

Melee Critical chance does not affect ranged attacks, whether autoattack or combat arts. For those kinds of attacks, Ranged Critical chance works exactly like Melee Critical chance works for melee attacks.

Ok, bottom line time. Melee crit chance affects both autoattack damage and combat arts, at least most of them. But not ranged or spell attacks. Which makes it extremely valuable to classes that do mostly melee damage. Conservatively, figure that a +1 to Melee Critical is going to be worth a 1.5 to 2 percent increase to your overall dps. That is, if you are averaging 500 dps right now, then a +1 will be worth 8-10 extra dps.

Melee and Haste.

I have a bruiser alt, and I’ve been doing some research trying to figure out how to get his DPS up. One of the best articles I’ve read on the subject is this thread on EQ2Flames. I’m going to make a series of posts on the subject, to see if I can’t sort this all out. I’m going to assume you know nothing to start with, but that’s probably because of my math background. State the assumptions up front, and all that.

So, this time around, I’m going to talk about Attack Speed, or haste, as it is commonly called. How does this work?

Your Attack Speed rating is a number that goes from 0 to 200. These are not percentages. They are on the “diminishing returns curve” that is widely used in EQ2, so that an increase of 10 points from 10 to 20 will be worth a lot more than an increase from 110 to 120. If you open your persona window you will find that if you hover the cursor over the Attack Speed rating, it will translate that into a percentage for you, the diminishing returns is figured into that percentage.

Ok, now remember how a percentage is equivalent to a decimal fraction? You know, 15% is equivalent to 0.15? Ok. The Attack Speed Percentage is used to alter the speed of the weapon that you are using, via the following formula:

Actual Attack Speed = (Nominal Attack Speed)/(1 + Attack Speed Percentage)

Given a weapon with a delay of 4.0 sec, 15 percent haste (which you might get with an Attack Speed Modifier of 13 or 14) lowers the delay of that weapon to 4.0/1.15 = 3.48. This translates to a 15 percent increase in the DPS from autoattack. Combat Arts and Spells are not affected. But we all knew that, right?

So far so good. But there’s some twists. First of all, weapons cannot have a delay faster that 1 second. Period. And I don’t care if it says they do somewhere on your screen, it doesn’t happen in the game. Self-buffed, this isn’t going to come up that much, but once you get into a group or a raid with one of the attack-speed buffing classes (Illusionist, Troubador, and Monk are the most notable), it will really start to get noticeable.

When you dual wield weapons, each weapon’s delay is multiplied by 1.33. So a weapon delay of 4.0 becomes 5.33. So you can’t just add together the dps ratings of two weapons and compare it to a two-handed weapon. You have to divide the rating by 1.33, or, if you’re like me, multiply by 3/4 (that’s 1/1.33, by the way).

Ok, now here’s the really interesting, (or annoying, perhaps) part. Weapon speed does not affect the proc rate of something that is rated as X times per minute. No, it doesn’t. No, really, it doesn’t. The probability of proccing is jiggered so that a weapon with a delay of 4.0s is four times more likely to proc per swing than a weapon with a delay of 1.0s So, assuming you are swinging the whole time, you should get the same number of procs in a minute of auto-attacking.

However, boosts to haste DO affect proc rate. The proc probability is figured on the weapons base delay, not its hasted delay. So when you are hasted, your poisons and items will proc more. Good stuff. I don’t know how dual wielding affects proc rate.

The final thing, and it’s important, is to note that only one item will be permitted to give you a boost to attack speed modifier, along with one adornment. That isn’t quite true. If an item gives “+1 Attack Speed” in the same color and font as say “+ 20 STR” or “+757 Poison” then that modifier will stack with other items, but such items are very rare.

The basic haste items available in the game are the Tier 8 Mastercrafted cloak, the Pristine Clandestine Swiftcloth Cloak, with a boost of 26 to Attack Speed. Get it. Mantrap roots aren’t that expensive. There is also the smoldering spry buckle, a Legendary T8 belt adornment that adds +3.0 attack speed. It’s also available in lower tiers at +2.0 and +1.0. It isn’t fabled, so it’s not going to be outrageously expensive to buy the components. Until you get something better to drop, I think it’s going to be well worth it to get these items.

Ok, let’s review. Attack Speed translates to Attack Speed Percentage, which affects the delay of weapons. Weapon delay can’t be smaller than 1.0s. Proc rate is affected by haste, but not by weapon delay. This gives a fast, light weapon no significant advantage over a slower, harder hitting one, as long as the ratings are the same.

In fact, the faster weapons are at a distinct disadvantage to the slow ones. I’ll have to wait to get into some of the other reasons for other posts, but the advantage that slow weapons have is real, and significant.

Geeks Rule the World

I read this interview at TenTonHammer with Monty Sharma, a representative of Vivox, the company who will be providing voice chat to EQ2 and other SOE games. And it made me realize that, once again, geeks rule the world.

Monty says, in talking about the “voice fonts” that he was demoing,

“We’re actually creating the physiological modeling where we’re mimicking the resonance of a larger chest cavity to create the deeper voice,” Monty said. “We’re tipping the pitch to turn men into women or little children. I can make my 10 year old son sound like his 16 year old cousin. There are couple companies that are ready to start using this technology, specifically Wizards of the Coast with their newest edition of Dungeons and Dragons. The dungeon master can speak in different fonts for different characters, and all the players can adopt voices that are more applicable for their characters. I got my start with Dungeons and Dragons, so this is fairly important to me.

He goes on to say

“It’s that sort of feeling that you got when you first started playing D&D,” Monty continued. “Instead of sounding like a bunch of weak-voiced thirteen year olds, now we can make gamers really sound like their character counterparts.”

John Rogers made a great point at an old post of his about the San Diego Comics Convention:

I noticed multiple news camera crews, and each time it was the same. 124,000 people at the Con, give or take. But if you turn on your news coverage you won’t see the giggling, happy five year-olds with their parents, having the “together family time” we’re always whinging on about. You won’t see the young woman who wrote and drew a comic about her time as a soldier in Israel. You won’t see the scrum of young Marines I spotted as they compared Magic the Gathering cards. You won’t meet the junior high teachers who are using my comic in their predominantly Hispanic classrooms to spark discussion about racial representation in the media. You won’t see the indie film-makers, the kid who shot this 25 minutes in a week and left every industry pro who stumbled across him slack-jawed.

A thousand stories, tens of thousands of familes … yet the newshacks couldn’t wait to hustle up the dozen or so real freaks in costumes, the literally .001% that gave them what they wanted. Not even the kids in the Harry Potter outfits, or the Japanese anime kids, or even the clever unfolding Transformer rigs — no, they found every empty-eyed overweight forty-five year old Flash or flab-rolled part-time stripper Catwoman and latched on tight for the creepy interview.

John also points out that four million people play World of Warcraft online. A smaller number play EQ2, maybe a million? SOE doesn’t tell us. There’s some overlap. That’s more people playing these games than work on farms or ranches, which number the USDA places at 2 million.

I’m not knocking them, I knew them growing up. But the notion that they are normative, and the 3 million of us working in Computer and Mathematical fields are not is a bit suspect. We’re both “normative”.

Integrated Voice Chat in Eq2

SOE and Vivox recently announced that they would be partnering to allow in-game integrated voice chat in all of Sony Online Entertainment’s games.

Need standard chat for groups and raids? Check. Don’t want to tie up your own bandwidth? Roger that. Want your voice to sound completely different? Done. Late for your raid but want to take part in the group setup by cell phone? Can do. Dream of having in-game voicemail? There ya go. Playing a non-SOE game but want to use this service, free of charge? Aye.

These powerful community building features and tools are coming to SOE games at no additional cost to players and go far beyond basic real-time chat with the usual headset and microphone setup that is commonly used today.

This could be really interesting. Audio will apparently be spatialized, so if you have the permissions turned on, you will simply hear people who are nearby when they talk over the channel. And they will get louder when closer, and sound like they are ahead, behind you, around a corner, whatever.

Not only that, but Vivox is supplying “voice fonts” which will make your voice sound different, male to female, and ranging in size from Fae to Barbarian. Apparently, there will be a fixed set of voice fonts available at first, and EQ2 will be among the first MMORPGs to provide this as part of the service.

One comment that puzzles me is the “don’t tie up your own bandwidth” business. Of course, you’re going to use your own bandwidth. How else will the voices get into your house? Apparently Vivox will host the voice servers, and processing, spatialization, and routing will be handled there, and then the voice signal will be sent down to your client in an easy-to-decode compressed format. So it won’t use that much CPU or memory or bandwidth.

There’s another comment that’s interesting. “Playing a non-SOE game but want to use this service, free of charge? Aye.” I’m guessing that only holds if you subscribe to an SOE game, and/or use the Station Launcher. So, if we decide to go play WoW for an afternoon, we can still use the Vivox chat to talk to each other.

Apparently, the service will be enhanced with all manner of “presence” features. Text messaging, connection to the normal phone system, etc. That’s not really what I’m about, but I think some users will like it.

A big hat tip to Joshua at The Joshua Tree, who will be working on making this happen from the SOE technical side.

Raging Cybermaniac

So, with all the hacking that’s going around, what can be done to prevent it happening to you.

One of the vulnerabilities I mentioned are keyloggers. A keylogger records your keystrokes and sends it to the thieves. In principle, they can also monitor your internet traffic and pick out data of interest, as long as it’s not encrypted. Keyloggers most often get into your system via the web, either through a trojan horse, a download of something you wanted, that was, shall we say, more than what you wanted, or via a hidden download that some innocent-seeming email or website perpetrated.

The other possibility is that you chose a very poor, easily guessed password for your Station account, or your email account. (See here how email hacking can allow EQ2 hacking.)

Anyway, here are some of my security policies. I have avoided a lot of trouble with these.

  • I use AdAware fairly consistently. A version of this can be downloaded for free.
  • I don’t have an anti-virus. I hate how everything grinds to a halt when they run.
  • Firewalls are good. Most newer versions of Windows have one. Use it.
  • I never, ever, EVER use Outlook for anything except to download the Firefox browser. This is probably an overreaction. If you keep Outlook up to date, and push the security settings up high, it probably will be ok. But I don’t use it. Firefox comes with high security by default.
  • There’s a corollary to the last point. Minimize your use of the in-game browser. Go only to trusted sites, like eq2i, or Allakhazam which seem pretty safe.
  • I keep my software up-to-date. Firefox has an auto-update function. I use it. Many exploits go through holes that have been fixed, but not updated.
  • I think hard about who/what site I’m going to trust. I don’t trust plat-sellers, though a plat selling site might not be to blame. I don’t trust porn sites, they range from honorable to horribly sleazy, and it’s hard to tell the difference, er, up front. I don’t trust sites that offer “cracked” software, or bot programs and “illegal” enhancements. Anything that seems too good to be true, probably is.
  • Any window that manages, despite Firefox’s best efforts, to pop up gets removed by clicking the little “x” in the corner. No other action, repeat, NO OTHER ACTION, is taken with such a window.
  • I do trust sites like eq2inteface, eq2maps, and ACT. These are so widely used, and have a long track record of actually doing what they promise to do.
  • I think most of my readers make pretty good decisions about who to trust in real life. Start extending that to cyberspace.
  • If I get an email from someone I don’t know, I delete it without opening it. If it’s from someone I know, but has a very odd title, and an unknown attachment, I am cautious. I might confirm with my friend what it is before opening it. I use web-based email, which isn’t bullet-proof, but harder to hack than Outlook.
  • I watch out for “phishing” emails, which will send me links to websites that “look” just like a legitimate site, but have a numbered url instead of the normal url. Sony will never, never send me a link to something that requires me to put in my account name and password. The word “Sony” in the last sentence is a link. Hover your cursor over it, you should see, in the bottom line of your browser, the url that the link will send you to. Instead of saying “http://sony.com” or “http://station.sony.com” or something like that, it says “http://192.168.1.255/station.sony.com”. Beware of urls that begin with numbers like that, it’s a sure sign of a faked website. Especially if there’s stuff afterward that’s associated with the legitmate site. The stuff that comes right after “http://” is what counts. Phishing is one way bad guys can get your account information.

Sony has one problem with their website which I wish they would fix. They have a security flaw which allows a certain kind of exploit known as cross-site scripting (xss) to occur. Here is a link to a page at The Station. Here is the same link, with an alert I added, just by changing the way I link to it. That something more could be anything I chose it to be, and it might be able to install spyware on your system, even as you are visiting an entirely legitimate site. Sony needs to fix this vulnerability.

Are you scared silly yet? Well, I don’t want you to curl up in a ball in the corner, but I do want you to take action to make yourself more secure. Because we should be talking about how tough that nasty named boss was, not how nasty the hackers were to you.

Plat-Stealing Hacks

There seems to have been an outbreak of account hacking recently in EQ2. Here’s a typical story, told to me by Chuman, a leader of the guild Lineage on Butcherblock. A good friend and former guildie.

“Our friend was on Vent with us when he gets booted out of the game for no apparent reason. No suspicions yet, since that happens sometimes. Soon the other players see him logging back in. There’s just one problem: our friend says on Vent that he can’t log back in, the game won’t let him. Yet there he is.

Meanwhile, the in-game (hacked) toon says nothing and immediately starts casting Call of the Overlord. Being clued in, we asked our friend, “hey, where’s your bind point?” The hacked toon is followed. It arrives in Freeport and heads for the nearest bank. Fortunately, the toon is then immediately deguilded. However, it goes to a vendor, and armor begins disappearing. Finally, with a wave to the watcher, the toon logs out.

This happened after-hours for SOE Customer Service. When all is said and done, the account password, which had been changed, had been restored. Perhaps, after investigation, the account assets will be restored.”

The most noteworthy thing about this account, which I’ve seen more or less mirrored in several other similar stories, is the fact that it begins while someone is online. This strikes me as both difficult to do, and an odd strategy. Why not do the theft in the middle of the night?

Ok, let’s review some basics. Lots of account damage is done by someone who was trusted, and who violated that trust. Friends, lovers, spouses, and exes. We’ve all heard the story of the jealous boyfriend who deleted all the toons. That’s not what this is. It’s theft. Organized theft. Get in, get as much as you can, then get out, and on to the next victim.

I can think of two ways in which you might bump someone off their account. First, if you can find out their IP address, you can send a denial-of-service (DOS) attack their way. Basically, this means sending so much data at your computer that the real data from and to SOE’s servers can’t make it through, and the result is linkdeath.

The second way involves hacking into your email. If you have a web-based email account, such as Yahoo mail, Gmail, or Hotmail, and your password to it can be captured, or easily guessed, then all the bad guys need to do is go to the Station website and tell them you’ve forgotten your password. Sony will then send you an email with a link that will reset your password, and force-logout anyone who happens to be online.

I think it is plausible that email adresses and toon names might have been gathered by plat sellers. And I can imagine that those who have been hacked might not be up-front about their purchase of plat from said sites.

Another major suspect, beyond email hacking, is some form of keylogging software, maliciously downloaded via some website. This Yahoo article mentions Lord of the Rings online. LotR can’t be the only game of interest to thieves.

I’m planning another post where I talk about security measures. In the meantime, use common sense.

Ultra Drama on Eq2flames.com

Well, a guy takes a few days away from the keyboard, and what happens? Only the biggest flurry of drama ever on Eq2flames.

It’s come out that some game developers, employees of SOE, play the game in their spare time. In fact, some of them belong to raiding guilds. In fact, some of them belong to one of the top raiding guilds in the game, Ne Plus Ultra.

That, in and of itself, isn’t what’s got people so riled up. What’s really grinding teeth is the evidence presented that some of these employees are handing out game information to their guild. So far, to support this claim, I’ve seen screenshots from guild forums, and an alleged email, giving quite extensive details on how the upcoming encounter with Trakanon, in Trakanon’s Lair, accessed through Veeshan’s Peak, will work.

It is claimed that free transfers were given to players who just happened to end up on the Guk server as members of Ne Plus Ultra.

There are some other charges which I find to be unfounded slander, and so I won’t repeat them here. All the above charges at least have some evidence in their favor, though screenshots and repostings bear something less than absolute authority.

In addition, there has been an escalation of tension between the administrators/regulars of eq2flames and SOE community relations. Real life names, email addresses and character names of EQ2 developers were published, or “outed”. Rumors of other abusive behavior by game devs in game were published.

In retaliation, SOE’s Community Relations Department sent LFG, the administrator of Eq2flames a letter stating that they no longer want him to participate in their Influencers Program. I gather that this is a program for reviewers, etc., Sort of an online press program through which members get, under NDA, early access to new material and announcements, as well as more contact with game developers and plans.

LFG has posted that he has not, nor will ever, publish any information given to him under NDA.

Were the developer’s names, emails, and character names under NDA? I don’t know, and furthermore, it wasn’t LFG that published them, but another regular named Snark, but, as administrator, LFG does have the power to remove them.

There’s an old saying that it’s much easier to start a war than to stop it. That feels like what’s going on now. Charges, countercharges, hurt feelings, lashing back, the situation is in an escalating spiral. Eventually it will stop, and there will be fallout everywhere.

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I started reading Eq2Flames a couple of months ago. It has two notable differences from the official SOE boards. First, posts are not censored for coarse language. Second, posts are not censored for material that reflects negatively on SOE business policies or developers. Site rules do prohibit incitement to or threats of violence, incitement to violation of the terms of service, or existing laws. Posting of material that is in violation of NDA’s is prohibited too.

However, posters are otherwised encouraged to express their feelings in as colorful or dramatic way as possible, and this is often viewed as entertainment, a la Jerry Springer. I am, in spite of the red hair, not in the habit of being overly dramatic, so it came as a bit of a shock. But I soon grew to like it, for reasons that are a little hard to explain.

We need to talk to each other, to say how we really feel. To stand in the full force of the hurricane of emotion, I guess. For every poster saying how fucked up something or other is, there are others who will mock them for their drama, and tell them exactly how they are being stupid. And perhaps more. As a student of humanoid nature, as all illusionists are, this sort of electronic primal scream holds some strange fascination. Just as I’m sure the shattering of Luclin did for those upon Norrath.

There is good information in the forums, valuable information. And, in the past, certain developers would post there. That will happen no more, it seems. And that’s a shame.

Though to tell the truth, Eq2flames might be better off for having no official ties to SOE. As part of the Influencers program as well as running a site where people feel free to criticize SOE, there is an inherent, though perhaps sometimes latent, conflict of interest. As long as the site keeps its current rules, I think this can only make it better, even if it is inconvenient to LFG.

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As far as developer behavior, I’m definitely not happy with the idea that game developers would pass out information and/or favors selectively, so as to give their non-job-related toons an advantage. To most of us, it doesn’t really matter, we aren’t really about getting there first. But to the people that are trying to stay at the head of the pack, this is a significant advantage. The amount of material on Trakanon would probably take a guild several hours to deduce from logs, not to mention repair costs. This should not have happened.

I generally think it’s a good idea that game devs play the game in their spare time. It gives them a better idea of what goes on, and how the game really works for a player. The problem comes when they start using their insider information to help themselves in competitive situations. I am not in favor of this. Ideally, no information given out should be exclusive. If you’re going to tell one group, tell everyone. And no financial incentives to join a developer’s guild should be handed out, either. That’s a definite problem.

Unfortunately, retaliation has muddied the waters. SOE developers who were probably uninvolved, and perhaps even sympathetic were probably outed. SOE will certainly focus more on its own injury than on cleaning up its act. In the same way, the focus at Eq2Flames the focus has shifted from the initial, legitimate issues to the escalation.

Critical Analysis

I’ve been wondering how to trade off various items with enhancements to spell damage. There are three basic types of these items. First, there are items which add direct damage to all spell damage (There is an uncommon form of this that adds to only particular types of spell damage, such as poison or mental). This type of enhancement is sometimes known as BoE, for Bolt of Energy, which was the name this effect was given when it first appeared.

The second kind of enhancement is an increase in critical chance, e.g., “+2 damage spell critical chance”.

The third kind of enhancement is an item which procs a damage spell on a hostile spell.

I’d like to be able to do some math to get a rough idea of the contribution to total DPS each of these enhancements makes, as well as the contribution of increased INT. That is, is +1 crit chance better than +5 INT? This post will not resolve all these issues.

I gathered some data from my Ultraviolet Beam, a fast-casting, fast-recovery direct damage spell. I want to be able to relate the nominal damage on the spell to the actual damage, and try to figure out how much more damage, on average, a critical is worth.

I gathered data on 90 castings of Ultraviolet Beam. Examining the spell, it said that it would do “1120-1473″ damage. I split the normal and critical hits apart, and sorted each subset, then plotted them on a graph, which looks like this:

There are a couple of clear outliers. This data was gathered in actual combat versus Ya-leih in Jarsath Wastes. I suspect that the outliers were due to unusual happenstances in combat, mobs with higher resistances, and so on.

Still, the data appears uniformly distributed, whether critical or normal hits. Here’s a histogram plot of the same data:

Critical hits seem slightly non-uniform. This may simply be due to the effects of my debuffing mental resist, which I did not control for in this run. The whole dataset is online if you’d like to look at it.

Regardless, the normal hits had a mean value of 1426 with standard deviation 158, while the critical hits had a mean value of 1906, with standard deviation 207. I have seen reported elsewhere that a critical hit was worth 4/3 of normal spell damage, this data is consistent with that hypothesis.

How does the data relate to the “examine” data range, though? Recall that the “examined” range for this spell was 1140-1473. If we assume that damage is uniformly distributed within this range, that gives a mean damage of 1297, which is well below that of our data for normal hits, by roughly 130. This may be due to the effect of debuffs of mental resistance.

In any case, this gives us a rough formula for the value, in terms of DPS of an increase of one percent of critical chance. +1% critical chance is worth 4/3*.01*nominal DPS.

Incidentally, I have seen critical damage described as (max damage)*4/3. It turns out that the maximum “examine” damage is very close to the mean normal damage in our dataset, so this may be the source of that description.

Unfortunately this is too high. Criticals will only affect the first tick of a dot. So, if a large proportion of your dps comes from dots, criticals are going to be considerably less effective.

The next point to mention is that BoE damage seems to be incorporated into the “examine” value, since I had roughly a total of +500 spell damage equipped at the time. We don’t really see a shift of 500 in the means from examine damage to normal damage. I think a further experiment on this is in order.