Scion said:
Numbers have a certain elegance to them, and are difficult to dispute when used properly, but everyones campaign world is different, generally drastically so.
Numbers have a certain simplicity to them. That is why we trust them so much. We can look at them and feel like we understand what is going on.
The problem, however, is that numbers are deceptive in their simplicity. When you apply numbers to a situation as complex as a role playing game, the numerical analysis falls far short of capturing a complete picture. At best, it can serve as an untrustworthy tool. At worst, it leads you to conclusions that are true for only a limited set of circumstances, but are applied to a far wider range of situations ... leading to common belief in falsehoods.
Those that fail to learn from history are doomed to repeat it ... unless they make their saving throw versus doom [DC15W].
In the 70s, there was this fad in economic analysis called forecasting (or econometrics). Economists looked at things going on around them, broke those situations down into numbers and then crucnched numbers to predict the future: they predicted the stock market, the market for certain products, unemployment, etc ... Some of the most brilliant minds in the world worked in this area, developing complecated formulas based upon heavily researched data.
A few decades later, current economists look back at that work and laugh - hysterically in some instances - at how poorly forecasting and econometrics has served us. Some economists continue to tinker in the area, but the 'revolution' that economists of the 70s expected never came. The data was fine and the formulas were well designed , but in the end, most of the world couldn't be broken down into simple formulas that captured enough of the world for forecasting to be accurate as a tool in more than limited situations.
You can run the numbers all you want. You can compare how much damage an optimal 32 point build character will deal in a full attack when designed as an archer or when designed as a melee fighter. You can look at the difference in damage potential between an optimal archer with and without IRS when doing a full attack action. Analysis like this only captures an insignificant portion of the equation we call balance. Each of these different comparisons implicitely makes assumptions about the situation in which they would be used by not capturing certain variables (and thus effectively holding them fixed).
Large scale game mechanics, like feats, are too complex to be broken down into simple numbers. Sure, you can easily break down the chances of a PC making one particular saving throw, but it is impossible to assess a comparitive value on a feat that grants a bonus on that saving throw until you have a context to know how often that saving throw will come up, what the effect of a failed saving throw will be, etc ... The determination of whether a feat is 'balanced' must be based upon trial and error experience rather than upon numbers that can not hope to catch all the significant variables involved.
Simply put: Math is going to lead you down the wrong path unless you can put it in context. Doing this type of analysis and putting faith into it without applying it to game situations is nothing more than mental masturbation. You may enjoy doing it, but in the end, nothing good is going to grow out of it. And you'll get mental hairy palms and go mentally blind.
Hear me! Math is your False God! Deny it and be blessed by the wisdom of Trial and Error!
I've had my say. You folks can go back to your analysis.
