Game Math and Redefining “Happy”
From http://xkcd.com/138/
Games are math.
Whether you play a logic game like Sudoku, an MMO like Star Wars: The Old Republic or Lord of the Rings Online, or CityVille on Facebook, you are using math to solve problems designed by developers.
I have mentioned before that I consider combat in MMOs to be like a problem of rates. All combat can be broken down into percents, coefficients, and factors. In the simplest terms, if ratedamage(me) * mitigation(you) > ratehealing(you), then I kill you.
Things like buffs, heals, shields, and debuffs all swing the rates one direction or another. The experienced raid leader looks at the field of battle and sees the rates shifting and swelling, and makes decisions based upon them. In PvP, this is also added to the issue of seeing when points are being captured, where the Huttball is, etc. Everything about the game becomes math, whether we realize it or not.
So two things today. One is a really neat article I found on Massively that has James Ohlen talking about some PvP formulae and their ramifications, as well as his approach to healer Sage/Sorcerer nerfs. The second thing I found was a website run by former Dev of Star Wars Galaxies and Ultima Online, Raph Koster. He shows his understanding of game theory and math in numerous articles, presentations, and Powerpoint slides.
James Ohler defines “Happy”
In the Massively article, James Ohler reveals his formula for Expertise and the way it interacts with players of different levels of Expertise.
The old formula pre-1.2 was damage * (1 + attacking player’s Expertise – defending player’s Expertise). This led to issues when one player had vastly more Expertise than another player. The exact reasons why are explained really well in the article, so I won’t go too deeply into them here. The main gist was that if one player’s damage was boosted by a 50% advantage, then his defense was boosted by the same amount, so the other player would simultaneously be taking 50% more damage and doing 50% less damage, making it a really tough fight. Players with the same Expertise were on equal ground, of course.
The new and improved formula post-1.2 is damage * (1 + attacker Expertise)/(1 + defender Expertise). This means that a player with a 50% advantage will gain a lesser defense advantage, making time-to-kill smaller for the defender. This evens the playing field a bit. Players with the same Expertise are still even though.
James Ohlen then discussed Sage/Sorcerer healing nerfs, which made them have more resource problems. Ohlen states that Sages and Sorcs had almost no regen issues before 1.2, even healing full-strength. That is obviously unbalanced, and he feels that the healers are closer to targeted strength than ever before. It was obviously a case of not working as intended and now it is fixed.
When it comes to overall balance issues, James Ohlen had the following to say,
Currently, we’re “happy” with where we sit balance-wise in a global aspect of the game, but all that really means is that we’re not up all hours of the night pulling out our hair screaming, “How do we fix this?!” Instead, we’re coming in to work each day calmly asking, “How do we fix this?” That’s the job, after all.
Players need to take this same stance. When you lose badly in a Warzone, think about all the factors, don’t just follow your knee-jerk reaction and go on the Forums to rage about it. It is likely you were outplayed or outgeared, not unbalanced. Submit reasonable, logical thoughts if you have them, and approach their game and balance the same way they do, with calm concern and open minds.
Math Makes Me Happy (in the original sense of the word)
I found a lovely site that I will be perusing for quite a while. http://www.raphkoster.com is a site run by game developer Raph Koster, who helped develop Star Wars Galaxies and Ultima Online. I haven’t even cracked the surface yet, but there are some really interesting articles about game theory and how it relates to MMOs and gaming in general. I found a lot of it pretty heavy with the theory and math (which I love), but there are some presentations that look like they were designed for the layman as well. Definitely check it out, and let me know what you think of it. I may post more about it when I get a chance to read more.
So what about you folks? Do you look at games like I do? Do you see the Matrix? Or are you like a musician enjoying his instrument without thinking about wave dynamics, just doing what feels natural and ignoring the behind-the-scenes stuff? I’d love to hear your thoughts!
The Fanatical Swordsman 
Viewing a fight as a math problem is not always seen that way in the battle but people do it all the time:
ex) my fighter is taking on a VERY large monster.
The monster hurts a lot. I am putting minor hurts on the monster. After a few round you should have a sense of whether you have a chance, knowing your heals and buffs versus his.
If you’ve been holding steady about half health with spikes up and down from buffs, heals and attacks, and the monster’s health is dropping slowly, you realize you can take him over time barring a nasty crit or other surprise.
On the other hand
ex) Your 6 member group goes to take on the Big Bad and he kills your two healers and tank as you enter the room. The other three suddenly realize, without much thought to the numbers, that they have no realistic chance and turn tail.