Thursday, May 31, 2012

BlizzCon 2013 Predictions

"100% chance we'll see these costumes." or "BlizzCon dot j p e g"
A while back, much to the dismay of everybody, Blizzard announced that there would be no BlizzCon in 2012. They cited a lack of good information to dispense, since I guess game would either be to close or to far from completion to talk about. But they did assure us that they're planning on hosting on for 2013. Since it's never too early to speculate, here are my predictions for what we'll see at BlizzCon 2013.

At this point, I expect that Starcraft II's first expansion Heart of the Swarm will be released. We first got details about the game's new multiplayer units at Blizzcon 2011. The multiplayer for the game will be playable in June at the MLG Spring Championship and I highly doubt that it would take Blizzard another year from then to release the game. Especially since Starcraft II was released back in summer of 2010.

The big question for me at this point is whether we'll hear anything about a Diablo III or World of Warcraft expansion. Since Diablo III just came and people expect Mists of Pandaria to be released by the end of summer, both games would be a year of more past their release by the time BlizzCon would roll around. If we were to only get one announcement, I would expect a WoW announcement, since they are trying to stick to a schedule when it comes to WoW releases and since WoW is the largest property for BlizzCon.

 Titan. If for some reason we don't get a WoW, Diablo III, or Starcraft II announcement, then I'd have to bet we'll have a reveal of Titan. We're getting to the point with Titan where there is always hope, but little reliability of prediction. All I can say is that if we do get a reveal of Titan, I will be incredibly excited.

It's not games that I'm most looking forward to about BlizzCon 2012. What I'm really looking forward to most about BlizzCon is the potential of meeting my internet friends and guildies! Seriously, you all. I'll be so psyched to meet those of you that I can. I went to BlizzCon '07 and '08 but I've never gone to BlizzCon to meet guildies before so that will be a new experience for me.

We'll have to get together, alright?

Wednesday, May 30, 2012

Minipost: Fixed Post

For RSS feed readers: I fixed the post from earlier today. It turns out I had forgotten to add the javascript to it. Go there now and check it out!

WoW: MoP Drop Rate Statistics Calculators

Normal Loot

Drop Rate
Number of Kills
Probability of drop =
Kills Needed =
Average Next Drop Prob Median
??? ??? ≤???

LFR Drops

Drops per boss
Pieces eligible
Pieces Needed
Average Next Drop Prob Median
??? ??? ≤???

Explanation of the Normal Loot section
First, you'll have to enter in the drop rate. From that, the table below will populate. It will tell you the average number of kills needed for the piece to drop, the probability that it will drop on the next kill (which should be equivalent to the entered probability) and the median number of kills required to see the item drop. If, for example the median number of kills is 4, then there is a 50% or better chance it will have dropped on or before the fourth kill.

Second, if you enter in the number of kills that you've performed, then it will tell you the probability that the item should have dropped at least once in those kills. If you enter in something in the "Probability" field, it will tell you the number of kills needed to have that probability of the item dropping at least once.

For example, if you have a drop rate of .5 and 5 kills, there is a 0.968 (actually 0.9875, but the results are rounded) probability that the item will drop at least once in those five kills. If the drop rate is still 0.5 and you enter a probability of .90, it tell you that 4 kills are necessary to have a 90% or better chance of the item having dropped at least once.

Explanation of the LFR Drops section
This is based on the LFR loot system that will be introduced in Mists of Pandaria. An explanation can be found here. You just enter in how many piece of loot the boss will drop among the raid, how many pieces of loot in its table you are eligible for, and how many of those pieces you actually want. When you have that entered the table will populate with the same type of information that is in the above table.

I based this on the assumption that a boss will drop a particular number of pieces. If it is the case that you have a fixed X% chance to win loot, then I will alter it. It is also based on a 25 player group. Furthermore, the top section is about a piece dropping and not necessarily that you'll win it. The bottom section involves you winning a piece that you want.

If you have any questions about this or about loot drops, please don't hesitate to ask below. If you have comments, recommendations or requests, then please ask.

Tuesday, May 29, 2012

The Myth of Compound Interest

Banks and mathematics courses will talk about how monthly compounded interested is better than yearly compounded interest. You might even see a demonstration of it such as this one dealing with 6% yearly interest.

Which shows that a 6% interest rate, when compounded monthly, provides a slightly higher amount of interest. Now, the amount of increase you get is dependent on your base interest rate. In our example, a 6% interest rate becomes a ~6.17% interest rate. A 12% yearly interest rate becomes a ~12.68% interest rate, which is a far better gain than what 6% achieves. But a 12% interest rate is incredibly unlikely to get anywhere.

So why am I calling this a myth? Well, because it's only better than yearly interest under certain conditions. The example they give you presumes that you aren't depositing or withdrawing money from the account. And if you're not depositing or withdrawing money from an account, what good is it? It's either a small amount of money, in which case the additional interest in negligible. If it's a large amount of money, then the person is likely financially secure or wealthy, so they could benefit significantly from the increased interest.

Suppose you're depositing money into the account every month. If you have monthly interest, then a small amount of interest is applied to small amounts of money at the beginning of the year, and larger amounts of money at the end of the year. If, however, you have yearly interest, all of the interest is applied to a large sum of money at the end of the year. Why apply interest to a small amount of money when you could instead have the interest applied to a large amount of money?

The question then becomes, how big of a deal is this discrepancy? Well, I'm glad you asked. I used an R program to come up with some numbers for us. I used a 6% yearly interest rate and invested in the account at $300 per month. Now, the $300 figure isn't important, these results will hold true no matter what the amount is, $300 just seemed like a good figure to work with.

YearsNo InterestMonthlyYearlyDifference

From this, it would appear that the yearly interest is always better than monthly interest, but when you carry the calculations out you find that monthly interest will eventually exceed yearly interest.
Click to Enlarge
From this chart, if you have a 6% interest rate and deposit money at a constant rate, then monthly interest overtakes yearly interest at the end of the year only at year 27. Monthly interest accounts exceed yearly interest accounts in the middle of each year because of the interest that is applied during the year, but at the end of each year prior to year 27, yearly interest comes back. From this graph we see that yearly interest provides, at most, a $1161.17 advantage (with a $0 initial balance and monthly deposits of $300). This scales as long as your monthly deposit is the same. So the advantage maxes out at roughly four times your monthly deposit.

There is another situation where compound interest is better. When the amount of money in an account is in decline, it is better to have compound interest because then the interest will be applied when you have more money (before you lose said money).

So what affects whether monthly or yearly interest is better? The factors are your initial balance and how much you invest each month. If you have a high initial balance, then monthly interest should always be better. If you have little to no initial balance, yearly interest will be better for a long time. If your investment rate increases with time, such as starting by depositing $100 and depositing more and more as time goes on, then yearly interest will stay relevant longer.

So banks tell you about this wonderful thing known as compound interest when it isn't necessarily better for you. I know how you all must feel right now. I mean, how could the banks betray you like this? It's just so hard to believe that they could be like that. I mean, that something they would tell you is a good thing can actually be a bad thing (unless you are financially secure enough to save a large amount of money for a long time.

I think I'll do a followup post that investigates some other investment situations. Keep an eye out for that. 

Monday, May 28, 2012

10 Things I've Never Done in WoW

Turn into an ogre and swim in lava? Done it.
Bravetank posted a writeup of 10 things they've never done in WoW, and it has similarly inspired me to do the same. This may or may not have to do with me not writing about WoW in a long time.

Never have I ever...
  1. ...cleared any Cataclysm raids. The guild I started the expansion with wasn't capable, and I just haven't made an effort to get that done. This is all despite the fact that my current guild does raid every week. I just have trouble getting inspired to pull the time together to do so. No LFR. I only completed Baradin Hold when it had one boss in it.
  2. ...leveled a Horde character past the low 60s. My highest level horde character is a Forsaken warrior who's still in Hellfire Peninsula. I started playing as Horde, but fell out of playing Horde because Sarah and I wanted to level a paladin and a shaman together, and thus we rolled Draenei (since this was before Cataclysm when Tauren gained paladins).
  3. ...leveled through the 1-60 content after Cataclysm. I think this is mainly because I took a break during the middle of Cataclysm. I know that there is a ton of really great stuff out there and I really want to see it.
  4. ...leveled a plate wearer to 85. I have a level 80 Death Knight from Wrath that just kinda happened? I started it out of curiosity and that curiosity carried me to 80 where he stagnated. I'm currently leveling a Blood Elf warrior who is in his 20s.
  5. ...done the Molten Front. I'm working on it right now and I HAVE to do it. I have a thing about hippogryphs and bear pets. I got both of the hippogryphs from the Argent Tournament as well as the bear, squire, and the squire's horse. The Argent Tournament had a TON of great stuff.
  6. ...gotten a Amani Bear. I was upset that they removed the bear from Zul'Aman back in patch 3.0 and was so happy that they added the bear back into the revamped Zul'Aman. This is another thing that my guild is doing that I for some reason haven't gotten involved in.
  7. ...used a highly customized user interface. I use the base interface (I don't even have a boss mod or recount right now). I don't think I actually have any addons at the moment.
  8. ...been an auction house aficionado. I just post my stuff just below where other people have it posted. I've very rarely bought an item and flipped it for a higher price or bought something to make it into something else to sell at a higher price. An AH Baron, I am not.
  9. a Warcraft novel. The only WoW fiction that I've read was some of the comics. The Ashbringer series of comics was quite excellent and I highly recommend reading it. But there is no way that you could get me to read a novel.
  10. ...gotten any of the Cataclysm drakes. I just realized that while writing this. It seems like it'd be prudent to do so. I think I'd like to do this through the Glory of the Cataclysm Hero achievement. 
So what have you never done? My list is pretty decent and I really hope to accomplish some of these some day.

Sunday, May 20, 2012

How Many Diablo III Builds Are There?

In Diablo III you can have a an ability mapped to both of your mouse buttons and to the 1-4 keys on your keyboard. By default each skill in the game can only be placed on a particular button. For example, my Zombie Dogs have to be bound to the 1 key. This means that under the default settings you can't have some skills on your bar at the same time because they would have to be bound to the same key.

There is, however, an option called elective mode that removes this restriction and allows you to put whatever skills you want on whichever key/button you want. This has led me to wonder how many different builds you can get out of each particular mode. So to look at this, I will use my witch doctor, Tauzex, as an example. The number of skills I use in this post will come from him. Other classes have different numbers of skills, so these numbers will vary from class to class.

Some background on what goes into a build
  • You have 6 active skills and 3 passive skills at max level
  • Each active skill can have 1 of 5 runes attached to it. 
  • I will assume that you'd never want to use a skill unruned
  • In both modes at max level, you can pick any 3 of your passive skills with  no restrictions.
I will not be considering a build with the same skills but on different buttons as being a different build. 

For my witch doctor, the number of skills that I can attach to each key in standard mode is
  • 1 key: 4
  • 2 key: 3
  • 3 key: 4
  • 4 key: 3
  • Left Click: 4
  • Right Click: 4
  • Passive Skills: 15
In general, the number of builds in either mode is the number of choices you have for your active skills times the number of choices you have for your passive skills (since your active skill choices and your passive skill choices are independent of each other). In both modes, the number of passive skills that you can select is the same
The middle section is read as "15 choose 3" and is explained in the footnote*
To count the number of active skill choices, I will first count how many choices of skills you have and then factor in the different rune choices for those builds. If you have a selection of 6 skills and each of those skill has 5 runes, the number of ways that you can rune a particular set of skill is 
So now we just have to count the number of skill choices each mode has.

Active Skill Choices in Standard Mode
To figure out the number of builds in standard mode, I just have to multiply the number of choices I have for each skill slot. This comes out to
choices for your active skills. In whole, this brings active mode to 
builds for your character. That's over 16 billion distinct builds.

Active Skill Choices in Elective Mode
In elective mode, you aren't restricted by abilities needing to be placed in certain positions. So as a witch doctor I would just need to select 6 active skills out of my 22 total active skills. The number of choices in elective mode is 
choices for your active skills. In whole, this brings elective mode to 
builds for your character. That's over 530 billion distinct builds. This can be done for the other classes as well, which gives us the following table.

ClassGuided ModeElective Mode
Demon Hunter21,840,000,000717,670,078,125
Witch Doctor16,380,000,000520,451,796,900

We shouldn't forget our followers! They play an important role in single-player gameplay. So how many choices do we have for our follower builds. Well, there are 3 followers, and each one requires that you make 4 choices that each have 2 options. 

So that multiplies the number of distinct was to outfit your character by 48. Of course, since you don't have a follower in multiplayer mode, this doesn't apply there.

Wow, that's a ton of different builds for your characters, and elective mode has so many more builds. In fact, elective mode over 32 times as many builds as standard mode does. I don't believe I have to tell you that that's an impressive number of choices!

* As I said above, that particular notation is read as " choose ." In mathematics it's known as a combination (as opposed to a permutation) and is calculated as follows.

Thursday, May 17, 2012

Differential Equations and Support Tickets

Slope fields are very useful in Differential Equations.
This one approximates the situation described below.

"It's been 3 days and my ticket still hasn't been resolved, this is bullshit"

"Why don't they just hire some temp support staff? Then they could just work through the backlog and then fire them and we'd have instantaneous response times."

I'm back with another entry that nobody asked for. Here I'm going to be talking about yet another practical use for mathematics that relates to World of Warcraft.

We often have to deal with situations where we have to wait for something to get resolved by someone else. And we'll find ourselves wondering why it's taking so long. We wonder why the queue is so long. We wonder why they don't just hire somebody else to work through the backlog.

The truth is that it probably wouldn't solve the problem. But looking at that is probably a question for differential equations. Normal equations relate to quantities. Here we'd be looking at the length of the support queue as a function of time or some other factor. For the purpose of this analysis I'll be looking at time. Often times it's incredibly difficult or impossible to come up with a function that describes certain situations. However, it can be relatively easy to come up with an equation that describes how a particular value changes.

You may have taken a calculus class at some point in time. You may remember that the derivative of a function describes how that function changes with respect to its variables. If we let Q(t) be the number of messages in the support queue at any given moment in time, then we'd be more concerned with
which is the rate of which Q(t) changes over time. So now we just have to ask ourselves, what causes Q(t) to change?

Well, Q(t) increases whenever somebody has some sort of error to report. And Q(t) decreases every time a petition is answered. So we might be inclined to say that
Where p is the rate at which petition-able items occur, and a is the rate at which the game masters can answer petitions. But that's not true. If the queue size is particularly large, people become less likely to submit a petition. We may do this because we're impatient or because it may be the type of issue that could resolve itself in that amount of time (say with a bugged mob). So I'm more inclined to say that the function more closely resembles.
Where k(q) is a function is always positive but decreases as q (the length of the queue/wait time) increases. It is the probability that a person will report their issue given the length of the queue. Now, if we presume that p and a are constants, meaning that petition-able items and the rate at which petitions are answered aren't affected by anything here, then our function is a differential equation of one variable, q.

So what does this mean. Well, if the queue is long, then q is high,  k(q) is small, and the value of our derivative is negative, meaning that the queue will get shorter. If the queue is short, then q will be small, k(q) will be higher, and the value of our derivative will be positive, meaning the queue will get longer. It turns out that if p and a remain constant, then the length of the queue will tend towards a value for which
 When the derivative is zero, that means that the length of the queue stays the same. So the length of the queue will tend to wards a particular length and then remain stable, provided p and a don't change. This is especially true of more demanding queues, such as the post office, where you must physically wait in line. It's still true for passive queues, such as WoW reporting system.

So hiring temp workers to reduce the queue length won't work, because once those temp workers are gone the queue length will return to normal. This is why it's very important for Blizzard (and other agencies) to create more automated support systems, so that smaller, easier-to-fix problems can be handled automatically and bypass the queue.

Wednesday, May 16, 2012

Diablo III First Impressions

Diablo III came out yesterday (5/15/2012) and although it spent much time down because of the massive amount of traffic they were experiencing, I was able to spend a good couple of hours playing. I wasn't really sure what I wanted to play until a couple hours before doing so. I originally settled on the wizard but when I got to the character creation screen I went for the witch doctor. I feel like whatever attracted me to play him is the same thing that made me want to play a warlock in WoW.

I logged in and watched the great character intro scene. Once the game started I did the first thing necessary: turn down my graphics settings so it played at a decent framerate. I was a bit dismayed that my computer had as much trouble as it did, but it's from 2007 and its graphics card is from 2008 and well, what do you expect?

The witch doctor started out okay. I had Shoot Poison Dart and Stab With Knife for my two actions. I didn't really enjoy that very much. But Shoot Poison Dart was quickly replaced by Throw Jar of Spiders and I really started to love the flavor of the class. In short order I also received Grabby Zombie Hands, Summon Zombie Dogs, and Shoot Flaming Bats and I was quite happy.

The voice acting in the game is a wonderful addition. It allows you to take in the lore and story without slowing down and stopping, which is very important so that you can keep that Diablo pace without miss out on the story. I really enjoy the random spurts of lore you occasionally get from the "Lore" button that will occasionally appear in the bottom right of the screen. The more thorough questing system is a wonderful addition to the game. It still feels like Diablo (as opposed to WoW) but makes it much easier to keep track of what's going on.

I also think that the skill system in Diablo III is great. For those who haven't played it you have skills bound to left mouse, right mouse, and 1-4. Each of those buttons has a particular set of skills that can be assigned to it, and there is no overlap in what skills can go in each position. Furthermore, skills have runes that are accessed as you level up which augment them. And skills cannot be switched out mid-combat.

Having your skills locked to certain buttons gets me really excited. It's simultaneously simplifies the gameplay and challenges you. By not having access to all of your skills at a time you're forced to strategize outside and inside of battle. You have to figure out what skills go well together and execute them well. It allows for a great diversity of gameplay because switching out your skills and runes you can create a vastly different character.

And yes, the game still feels like a Diablo game.

With regards to the launch day issues: I don't feel contempt for Blizzard, because I do understand that there is a limited degree to which you can prepare for these things, but it is still their responsibility to prepare for it and I do hold them accountable. I understand all the reasons that they have for requiring the online connectivity and agree that it's the best choice, because it's not JUST a single-player game. There is an economy, of currencies both virtual and real, that is attached to this so that security is of paramount importance.

Interestingly, I read an article a short while back about Zynga's server structure. They have their own servers that they use to host all of their games that they have custom built and everything, like anyone with a large number of servers should. However, they also utilize Amazon's cloud servers to deal with spikes in their server needs. This way they can quickly react to changing server loads without having the type of errors that Blizzard is having. Now, I don't work for Blizzard nor am I particularly versed in server things, so I don't know if there may be something that could keep them from doing such a thing, but it's definitely something that, if I were an executive and Blizzard and I had heard about, I would have the right people look into it.

In short: amazing game :) but launch day issues :(

Friday, May 11, 2012

Minipost: My 2012 Sex Life

I saw this meme on tumblr, and since I don't have a tumblr (I subscribe via RSS) I'm doing it here. I hope it spreads in the WoW blogging community. The meme is as foloows
Pick up the nearest book to you. Turn to page 45. The first sentence describes your sex life in 2012.
Alright then. Let's do this. The closest book to me was Starcraft: Ghost - Spectres by Nate Kenyon. The first sentence (that begins) on page 45 is
Its alien rage ate away at her brain, a nearly mindless urge to destroy.
We'll have to see how 2012 plays out, but I'm definitely excited. What about you? If you do this, try and leave a comment below and tweet about it. If you're an adamant tumblrer, here's a link to where I saw it.

Wednesday, May 2, 2012

The Math of the Deeprun Tram

Moving Away At Other Station Coming Back Arrives At Your Station Leaves with you m w m w m How many times have you gone to the Deeprun Tram and it was there, waiting, but was gone before you could get to it? If you're a frequent Alliance player, probably tons of times. And whenever that has happened, have you said to yourself, "They should make it wait longer, then people wouldn't miss it so often and people would get to their destination faster." How would you feel if I told you that wasn't the case and that perhaps it waits too long?

On the left I have a little diagram, the part in orange is the part of your journey which you must always endure, the actual travel. The part in white represents where the tram may be when you are actually ready to board it (and not just running to be ready to board). When you are ready to board you may arrive at any one of those points. So your actual time spend waiting on the tram and traveling on it is
where X is a uniformly continuous random variable that ranges from zero to 2m+2w, where m is the amount of time spent moving from one side to the other and w is the amount of time the tram waits at each stop.

What we want to do is we want to minimize t. Or rather, we want to minimize the average value of t. We do this by calculating what's known as the expected value of t, E(t).
I'm fairly certain that I don't REALLY need to go through this next part, but it's a good indication of where calculus is helpful in real life type situations. That and I've spent a good amount of time teaching mathematics and I can't resist a good example. In order to minimize a function (which E(t) certainly is), you take the derivative and check the value of it when that derivative is zero, at endpoints, and at discontinuities. In this case, our variable is w, the amount of time spent at the station. The partial derivative of E(t) with respect to w is
This is because the partial derivative with respect to w of 2m is zero and the partial derivative with respect to w of w is 1.

Here we find that the derivative is never zero, so that means our function, E(t), must be minimized at an endpoint, in this case w=0. So with the goal of people arriving at the other side as fast as possible, it is optimal that the Deeprun Tram (and this can be said of other transports) not wait at all? Well, this is a mathematical model, and there were some limitations put on it to make it simple. What this tells us is that it is optimal for the tram to wait only long enough to let the people who are waiting for it board, which when you think about it, makes sense.

Why is that so? Wouldn't it benefit from waiting longer so that people who are close can get on? No, because if the tram waited longer, that would make its round trips longer and it would make the people who are on it and waiting for it to depart have to wait longer for it to leave.

This post was a fixed-up, more elaborate, better version of a blog post that I did when my blog was young. Many of those older posts have good content, but I was just terrible at writing/the web at the time and I feel they deserve a second chance. Furthermore, since it was old, I bet nobody saw it.