math
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Nintendo slipping DS handhelds into schools, McDonald's training sessions
What's a global gaming company to do once they've soundly dominated the portable market? Why, covertly get the DS into schools and restaurants, of course! Shigeru Miyamoto, who created undercover gems like Donkey Kong and The Legend of Zelda, recently informed the AP that his company would be rolling the DS out "in junior high and elementary schools in Japan starting in the new school year," though few details beyond that were available. We do know, however, that this invasion into the education sector is more than just a fluke, with Miyamoto noting that this very area is where he is "devoting [himself] the most." Of course, the Big N already has a nice stable of mind-bending titles, but getting actual teachers to embrace the device in the classroom would be another thing entirely. In related news, select McDonald's eateries in Japan will be using the DS to train part-time workers, though mum's the word on whether the Cooking Mama franchise will be cashing in here.
AddOn Spotlight: Automaton
AddOn Spotlight focuses on the backbone of the WoW gameplay experience - the user interface. Everything from bags to bars, buttons to DPS meters and beyond - your AddOns folder will never be the same! This week, Automaton takes some of the tedium out of little tasks! What's the only thing better than an addon with a beautiful and pristine interface that rivals all addons with its ease of use? An addon with NO UI AT ALL, minus the text commands. This week, I'm going to show you Automaton, an addon that is as light as they get while providing a host of awesome functions. It's bare-bones addon day today on AddOn Spotlight! Won't you join us?
10 billionth iTunes download going down today
Obama Pacman has done the math, and they claim that the 10 billionth song download on iTunes (which Apple is paying out a $10k gift card for) is going to happen today, February 24th. So if you've been waiting to buy some music, today's the day to do it -- go pick up some songs in the early to late evening, and you might end up being the lucky winner. Plus, contest aside, this means Apple will have sold 10 billion songs on their store. That's an incredible number, and it's a number that has changed this industry for sure. Fortune's Brainstorm Tech blog has a nice short look at just what that means for the store itself, including the fact that the store is now making over $520 million a quarter (even though Apple says that it's only slightly profitable for them, as they're more interested in hardware than content) and that the Black Eyed Peas have two of the top 20 best-selling songs of all time, the first and the third. Pretty incredible achievement for Apple, and with the iPad on the way, I'll bet the iTunes store will only get busier. We'll keep an eye open for the official announcement this evening. Good luck if you're trying for the prize!
Austin Independent School District makes deal to buy more video games for classrooms
We've seen educational video games show up in the classroom before, and it looks like one school district is coming back for more. The Austin Independent School District has ordered up another set of edu-games from a company called Tabula Digita that provides 3D, first-person action-based games to teach students how to do basic math and algebra. One sample scenario in the games has students calculating the location of an in-game weather station on a graph, and then using the data found there to make charts and track down alien creatures. The press release doesn't mention costs, but according to its website, 15 single-user licenses to the games cost the school $1049.25 each, making up a cost of just over $24,000 for the entire 350 student program. The students, who were part of a 10-day JumpStart program and had previously failed a math retest, were allowed to play the games for 30 minutes a day, and, afterwards, 82% of the kids said they had improved their understanding of the concepts. No word on how their k/d ratio came out.
15 Minutes of Fame: The Pi Guy
15 Minutes of Fame is WoW.com's look at World of Warcraft players of all shapes and sizes -- from the renowned to the relatively anonymous, the remarkable to the player next door. Tip us off to players you'd like to hear more about. Sorry, no typos in the headline. It's not the pie meme that's the topic of today's 15 Minutes of Fame. (You'll have to turn elsewhere for your just desserts.) We really do mean pi -- you know, 3.14159 ... We're not quite sure how pi and WoW go together. And frankly, neither are players on US Llane, where the mysterious Pi Guy holds court in Trade. "He's in Trade chat spamming pi and other fascinating formulas, like how 99.9 = 1," writes our tipster, "which makes sense after he shows you the steps ... which he does. He's got top-of-the-line gear, which in itself is a nice thing. But on top of that, he's a math genius. A very mysterious math genius." We suppose community fascinations have formed up around more bizarre memes than pi. But a mysterious mathematician lurking in Trade? How could we allow this stone to remain unturned? Without further delay, we offer up for your consideration the curious tale of Gauss, the Pi Guy.
Math problem: Average winning roll
Here's a question that occurred to me while I was walking home from the subway recently: What's the average winning roll in a five-man group, assuming everyone rolls? That is, if you randomly chose five numbers between one and 100, what is the expected value of the highest one? I know a bit of statistics, but I really don't know how to begin getting at that one. However, I do know how to write a script that will calculate the answer. (Yes, these numbers are only pseudorandom, but I did some limited testing with real random numbers (from random.org) and the results were the same. Besides, I'm pretty sure Ruby's Mersenne twister pseudorandom generator is good enough for testing distributions like this.) The average winning roll out of a group of five people is 82.8 83.8 83.3 (tested over many, many repetitions). Now can any mathemagicians tell me why? The graph above, in case it isn't clear, is average winning roll on the y-axis vs number of people rolling on the x-axis, tested over 100,000 trials for each group (the relatively small sample size is why the first point is not right at 50, and probably why the curve is a little wobbly).
A look behind the systems of Champions Online
If you're good with numbers or would like to obtain some understanding of Champions Online's various systems, then this new systems dev blog is right up your alley. There's plenty of math happening here, so when you start to feel confused don't worry so much -- you're not alone. Actually, the basics of what systems designer Brian Urbanek discusses aren't too convoluted. At least, the part where he explains the percentages of what influences a character's power isn't too bad. As it turns out, equipment makes up for 42.5% of your overall power, while talents take up 15%, "base" is 2.5% and super stats fill the rest at 40%. What that essentially means, is that your leveling choices in super stats and talents (which effect stats as well) make up a large part of where your character excels. This is all shortly followed by equipment, but creates a slightly bigger focus on how you design your superhero. Soon Brian will be discussing combat, which is sure to be a hot topic within the Champions Online community. Until then, we're going to re-read this first entry in the hope that someday we can grok it.
Using WoW for learning in schools
We've heard about WoW in schools before, but usually it's at schools of higher learning, where they're studying social networks or how society evolves. But a group in North Carolina is planning to put WoW in schools in a different way: by using situations in World of Warcraft to develop literacy, mathematics, and other competencies. WoWinSchools has math lessons and other tests based around WoW terms and knowledge: one example question asks "Which types of heals produce a greater number of recovered hit points during an encounter?" Another wants to know "Which buff (a spell that enhances a character's abilities) is more effective for your character, Blessing of Kings or Blessing of Might?" The idea is to use situations that the kids are familiar with in World of Warcraft (raiding, for example), and apply higher level thinking to those situations.There are even creative writing suggestions dedicated to the game, from writing an RP story about a character in Azeroth, to writing a song parody (that one should be taught by Professor Turpster) or designing a quest chain. And lest you think they're just joking around, there's a whole slew of research behind the idea, too, and it definitely makes sense: kids who play World of Warcraft are much more likely to be interested in problems about DPS and Healing rather than Susie and Bobby's apples that we added and subtracted back when we were kids in school.It seems like the only place this is implemented is in one afterschool program -- while there are lots of good ideas here, it's not necessarily being used in many classrooms yet (and my guess is that not every student in schools would vibe with a World of Warcraft-based curriculum, either). But it is a plan in development, and anything that better helps teachers understand what their students are interested in is probably worthwhile.
Solving the mathmatical tangles of ArPen
Armor penetration is probably one of the most misunderstood stats in the game, for a number of reasons. First of all, it's only become popular lately -- while it's been in the game since 1.10, it's only started showing up regularly on items in Wrath. And even then it's really only a meta-meta stat: the core abilities like Strength and Agility are easy to understand, the next level of abilities are things like hit rating and crit rating, and then armor penetration, you could argue, goes another level after that: it's a stat that affects a stat affected by a stat. It's for that reason, then, that Xanthan argues we need a more elegant solution.Armor penetration basically allows you to hit an opponent as if they're wearing less armor than they really are. That's not to hard to understand -- if you have a certain amount of armor penetration, then the opponent armor number in the equation that determines damage done is lower (edit: by a percentage, not a number) than it would usually be. But the confusion comes in when you see how armor penetration scales. It actually scales exponentially, not linearly -- if you have no ArP and you increase it by a little bit, you only get a little extra damage increase. But if you have a lot, and you add a little more onto that, then you'll get a bigger damage increase, due to the way the math works (I'm bad at math, but Xanthan has an excellent, clear description of the calculations in the forum thread, and we've posted some explanations before as well). Blizzard recently capped ArP at 100% (so you could never get into a place where you're reducing armor below the amount of armor that's there), but it's still possible to have the amount of armor reduced equal the amount of armor on a target, causing the equation of armor vs. armor penetration to divide by 0, and at that point, things get wacky, and terms like "infinite damage" come into play.
BobTurkey updates Priest theorycraft
Disc Holy MP5 1.0000 1.0000 Spirit 0.3317 0.6397 Intellect 0.7853 0.7480 SP 0.6000 0.6000 Crit rating 0.3564 0.3763 Stamina 0.2000 0.2000 Haste rating 0.2925 0.3059 I love theorycraft. One of my favorite things about WoW is the fact that you can do math about it, and that math can help you play better. One of the better examples of theorycraft out there was MK, author of A Dwarf Priest, who did some seriously cool work on Holy gear ranking for Wrath. However, MK hasn't been seen around lately, and hasn't updated the information for patch 3.1, with its big changes to spirit and to Priest talents. Fortunately, a blogger named BobTurkey has stepped in and thoroughly reworked all the numbers, at great and interesting length. It's times like these that I really love the WoW community.
The math behind random drops and rolls
Reader Sekhar P. sent us an interesting story of a strange roll seen in Naxx recently: Haunting Call dropped, and four people needed. The rolls came up, in order: 1, 2, 3, 4. The raid boggled at how unlikely that must be. Sekhar's tip set off a round of discussion among our WoW Insider staff: while it seems unlikely that four numbers would come up in sequence, the math on it isn't any more likely than any other four numbers (3, 69, 82, and 95, for example, or even 4, 8, 15, and 16). The odds come out to 24/100^4, about 0.00000024%, or about two chances out of 10 million. Of course, probability is tricky, so the chances that any one of those rolls would come up is still one out of 100 -- just like coin flips, previous die rolls won't affect the current die rolls (mistaking that is often called the gambler's fallacy) But the chances that any specific four numbers would come up are the astronomical chances above.Of course, math aside, that still doesn't keep us from trying to predict how random rolls might work. We also recieved word from reader Emily about a site she and some friends are working on that is trying to predict just how much you'll have to run a certain instance to pick up some of the rarest items in the game, like Baron Rivendare's mount. Unfortunately, it's not a relevant indicator -- it looks like all they're doing is "simulating" runs on the item, and then tracking when it drops in their simulator. They're putting the math behind the chance into practical numbers.
Blizzard LF numbers geek, pst
If your idea of fun in playing World of Warcraft is to mine the auction house or raid buffers for statistics and then turning them over every which way, then Blizzard may have a job that's of interest to you. Admittedly, the best candidate would also have a degree in "computer science, statistics, operations research, industrial engineering, and mathematics, or business administration, marketing, or management with strong quantitative focus" but we're sure there are some WoW Insider readers who fit their Data Analyst posting bill. Sure, it may not be the most glamorous position ever offered, but it's still working for Blizzard - and in this case, working away from the front lines. Think of the perks; the awesomeness of being able to get in on Blizzard games well before anyone else gets to; the cool gifts that Blizz seems to like to give employees; the ability to get in to BlizzCon without having to play tag with the mrglrfrling Failoc. All that, and hey - it's translating numbers to non-number-geek English, which seems to be a passion amongst many of the numbers geeks I know. So if you've got the chops and are looking for a job many would envy you for, what are you waiting for? Get to applying - and good luck![Via Virtual Economy Research Network]
Replenishment: What are the odds?
There was a recent flurry of interest surrounding the Replenishment mechanic due to Ghostcrawler's statement that "we assume that you have Replenishment available to your raid." He said that it doesn't mean raids will be undoable without it, but that they're tuned assuming you have it, and if you don't, you'll need to out-gear or out-skill the raid, or else you'll have problems. In this post, I'd like to look at just how easy it is to get Replenishment in your raid. There are three Replenishment specs: Retribution Paladin, Shadow Priest, and Survival Hunter. As you can see, they're all DPS specs. Historically speaking, these specs were probably selected because they had been viewed as suboptimal for raiding (in the case of Survival and Ret), or because they had been valued for their mana regeneration (in the case of Shadow), although at the moment all three of these specs have competitive DPS and don't really need group utility to prop them up. Unfortunately, GC never clarified whether he was talking about 10- or 25-person raiding, so I'll examine both. I will make the simplifying assumption that the 30 specs are equally distributed in the raiding population: any given character is 1/30 likely to be of any given spec. Put another way, each spec enjoys a 3.3% share of the character base. I know this is not actually true, but it's a very helpful simplification and I don't think it will distort my numbers too much. Edit: Yes, I'm also assuming every Survival, Shadow, and Retribution raider has the relevant Replenishment talents. I think this is a pretty safe assumption.
YouPlayorWePay claims to offer downtime insurance
I think this is a wild idea (even if it is something I wouldn't actually put my money in). We got tipped about a new site called "You Play or We Pay" and from the looks of it, these guys are offering none other than downtime insurance. That is: you pay a fee to them regularly, and then they "compensate" you for any downtime that your server has. They call it "third-party compensation," but that sounds like insurance to me.At any rate, we wouldn't quite recommend jumping in headfirst yet -- they haven't, as far as we can see, revealed any prices, and while you can register your characters, you can't actually get any sort of payout quite yet, as they say they're still working on the system. For all we know the site could be an elaborate scam at this point. But it is an intriguing idea, and if they're really ready to put their money where their FAQ is, these guys may have an actual business plan that depends on Blizzard keeping the servers up. Just like all insurance companies, they must have figured out that the servers stay up more often than not, and that there was money to be made there.It's quite an interesting plan, and we'll keep an eye on it to see if they ever announce a fee or explain themselves better. The math doesn't quite seem right here, but if somehow their fees are low enough and the payouts are high enough, it's possible that you really could be compensated for downtime by a completely separate company other than Blizzard. Very interesting.Update: The company has contacted WoW Insider, and we've requested an interview. Stay tuned.
Nintendo: Kids don't like math. We checked
Nintendo recently employed the services of Wakefield Research and had a survey conducted. The results of said survey show that 1 in 5 kids are more inclined to believe they'll be rich and famous than good at math. Who would've thought today's youth lacked so much self-confidence? Some other key items of interest include: More than 1/3 of kids surveyed say math is their most difficult subject Nearly 1/3 of the kids view math in a negative light; 18% called it "boring," while 13% called it "torture" 86% of parents surveyed say math is important to their careers, even though they thought they'd never need math back in school This, of course, segues brilliantly into Nintendo's newest game for the DS: Personal Trainer: Math. Oh, and will you look at this? Why, look what game released this week. What a coincidence!
DS releases for the week of January 12th
Moon, elves, chaos and madness -- it's just another week of new DS games, only this time, with actual games! January's been slow so far, but this week, Moon really is coming out, along with a few other titles. Looks like things are finally getting back to normal after the holidays. Jumble Madness The Lord of the Rings: Conquest Moon Personal Trainer: Math Gallery: Moon
Northrend's Gross Domestic Product: 719 million gold
Our friend The WoW Economist started a little project the other day: he added up, according to the top items lists, all of the products sold from Northrend across the servers, and then multiplied each by what he calls a "median" price (though exactly how that's reached, we're not sure), and landed on a huge amount of gold: 719,918,239.7. Obviously I'm not a WoW Economist (I'm not even that good at math), but that sounds to me like Northrend's gross domestic product: players are creating an economy of 719 million gold in Northrend from week to week.Unfortunately, that number alone doesn't tell us much, except that there's a lot of gold moving around in Northrend (it would be interesting to compare this to, say, Azeroth or Outland's equivalent, though the more useful numbers would probably be Outland before the new expansion hit, when everyone was still farming and selling items from there). And it will be interesting to see this tracked in the future: the real GDP is usually used as an indicator of both standard of living and a country's economic health, and while there are drawbacks to using that number to gauge both of those qualities, it's probably fair to say the economy in Northrend is booming. Maybe tracking this in the future will let us see how new content patches or item or even class updates can affect what the economy does there.Very interesting. EVE Online's creators, CCP, have actually hired an economist to help run their ingame economy, and while WoW's isn't generally seen as quite that complicated, there are still plenty of big numbers to play around with..
Encrypted Text: The fuzzy math of theorycrafting
Every Wednesday, Chase Christian of Encrypted Text invites you to enter the world of shadows, as we explore the secrets and mechanics of the Rogue class. This week, we'll be talking about the methods used to break down gear and talents into their fundamental parts, and compare them intelligently.While it's not recognized as an official term by the Oxford Dictionary, "theorycrafting" is definitely the biggest buzzword in the Rogue community. Originally coined by Starcraft players looking to use their mathematics knowledge to perfect their strategies and unit build orders, it refers to the idea of using math to guide your choices, instead of simply playing from your gut.From the lowest level of forum troll to the most serious raiders, many Rogues love to punch numbers into spreadsheets and talk about the PPM (proc-per-minute) chance of Mongoose. Theorycrafting is a largely arcane art, and unfortunately an inability to play ball with these math magicians can be grounds for ostracism from the discussion at hand. Asking for talent or skill help on the Public Rogue Forums will likely result in recommendations like "Check the spreadsheet or delete your character."Obviously you've become attached to your assassin of the shadows, so after the cut we'll talk about how to become a theorycrafter even if you weren't first in your algebra class.
Making/Money: Auctioneer Wishlist
WARNING - MATH AHEAD! A few weeks ago, a reader e-mailed me with questions about some Auctioneer data that they have been collecting. Though the question was regarding trying to determine inflation patterns on their server, it got me to thinking about what Auctioneer actually captures. And what other data points would be most helpful in making evaluations of item pricing or looking into economic trending. While I'm not about to go through all of Auctioneer's algorithm rules, I would recommend that anyone who uses this mod check them out on Norganna's Wiki. They explain where the recommended prices come from. Basically, it's a comparison of the historical data accumulated from all of your auction house scans and the most recent snapshot data. The market value ends up being either the median of historical or recent data, flavored with the user-set preferences for markup or markdown.
Phat Loot Phriday: Torch of the Damned
We've been a little husky the past few weeks here at Phat Loot Phriday, so this week we're aiming to fix that, and get back to what this column is all about: gigantic spiky, glowy things that you can kill with.Name: Torch of the Damned (Wowhead, Thottbot, Retribution)Type: Epic Two-hand MaceDamage/Speed: 396-595 / 3.80 (130.4 DPS)Abilities: +51 Strength, +45 Stamina Improves crit strike rating by 38, improves haste rating by 50. Great for Paladins, and any other class that uses weapon damage for certain abilities. Warning: this gets into some deep math, and you guys know I'm bad at that, so expect to see some more number crunching in the comments. Basically, Seal of Command, a Ret Pally talent, gives a chance to add 70% of the weapon's damage to any normal attacks, and since most weapons trade off speed for damage (as in, the slower the weapon, the higher the damage), slow weapons are better -- you'll get more damage output when SoC procs. And since this weapon is very slow and very powerful, you'll get more damage overall out of Seal of Command. The Haste rating is also good for Paladins, not because it will help with Seal of Command (SoC is a procs-per-minute talent, so no matter how many times you hit, you can't get it to proc more often), but because it'll let you hit more often, which means more white damage. Any class that benefits from big swing damage (Windfury is awesome when it procs with a huge weapon like this) will love this mace. Oh, and anytime we mention a two-handed weapon, Matthew Rossi's eyebrow twitches until we mention Titan's Grip. Imagine seeing a Warrior wielding this baby... and something else at the same time. Yeah. How to Get It: Drops from the Essence of Anger, which is part of the Reliquary of Souls in the Black Temple (which, trivia for you, was influenced heavily by Sinistar, an old arcade game). Essence of Anger is the third phase, so get your 25 man raid up to that point, be one of those silly Ret Paladins (silly Paladins -- DPSing is for Hunters, Locks, Mages, and Rogues!), and spend your DKP or win the roll, whatever you need to do. Then you too can haul around this big purple spiky Mace, swinging it at will and bringing your enemies to their knees with just one proc.Getting Rid of It: You probably won't, for a while. But it does disenchant into a Void Crystal, and vendors will buy it back for 18g 43s 86c
