Direct vs. Derived Statistics in RPGs
In the RPG space, there are generally two ways to handle character attributes or statistics.

Each stat is used and modified directly.
The first, simpler solution defines a set of stats that a character needs for the mechanics of the game to work, and then exposes them directly, allowing items, spells, level gains, and other modifiers to explicitly raise and lower these stats as necessary. Japanese RPGs tend to go this route, with simple stats like Attack and Magic, which are then directly modified by improved weapons or accessories. I will refer to this method of managing character stats as a Direct Stats system in this post.

Damage is derived from Power which is derived from Strength and Agility.
The second common solution, and more popular in western RPGs, is a system of primary attributes like Strength and Dexterity, which are often directly customizable as a part of the leveling process, but which generally do not affect game mechanics directly. Instead, these primary attributes control derived stats like Attack Power or Critical Chance, which are used directly in game mechanics, and which are calculated from the primary attributes according to some formula, which can vary depending on the character class. For example, in WoW, the Attack Power derived stat raises damage from physical attacks and is derived entirely from the Strength attribute for most classes, while Rogues instead use both Strength and Dexterity to compute it. I will refer to this method of managing character stats as a Derived Stats system in this post.
The benefits of a Direct Stats system are simplicity and understandability. As long as a player understands a stat's basic function, it is fairly easy for him to figure out how important it is to his character, and consequently, what items and abilities to concentrate on. If he wants to make a character that is exceptional at killing things by hitting them with a hammer, and knows that the Attack stat directly affects weapon damage, he knows to prioritize Attack over other stats.
A Derived Stats system, on the other and, can be a lot less understandable, since it tends to be cluttered with a large number of stats, some of which seem to represent similar concepts (Strength vs. Power?) and explaining the relationships between them is no small challenge. This is exacerbated when primary attributes are treated differently by different classes, meaning that even if a player learns how a stat works for one class, they may be in trouble when they try another.
The downside of a Direct Stats system is that with such clearly defined stats being the only defining characteristics of a character, it can be harder to differentiate characters. For instance, it is likely that all physically oriented characters will need the Attack stat, despite the fact that they are meant to have different flavors and different powers. With such a clear-cut set of stats, it's hard to put the stats to use in creative ways that still makes sense. Sure you could make a class that loses Attack instead of HP when it is hurt, for instance, but a lot of people are going to complain that such a weird mechanic ruins their immersion.
This is where a Derived Stats system can really shine, you can add a lot of variety to the mechanics governing your classes when you choose to derive stats differently for Rogues than Warriors, for instance. Furthermore, having both derived and primary stats available means that you can bind certain abilities or class features in unexpected ways, sometimes using a primary attribute for an attack, for instance, and primary attributes also work well for role-playing scenarios outside of combat.
The Right Tool For The Job
As is often the case with this kind of thing, neither of these two approaches to character development is necessarily better than the other, instead, there are specific situations where one may be more useful than the other.
The Direct Stats system most commonly shows up in Japanese RPGs which have simplified and distilled the systems they learned from early western computer RPGs like Wizardry and Ultima. Those games, on the other hand, adapted their mechanics from pen and paper RPGs, specifically Dungeons & Dragons, which through four editions has kept and refined the quintessential Derived Stats system of Strength, Dexterity, Constitution, Wisdom, Intelligence, and Charisma.
The origins of these two systems are not a coincidence, and considering them, we can quickly come up with some conclusions about the types of games best served by each system.
Derived Stats are often the best fit for games that share a lot of similarities with pen and paper RPGs. Games where the player only controls one character, for instance, can have complicated derived stat arrangements because the player will only have to master that one character's class to be effective, without having to worry how another class works. Such a system is especially important in a multiplayer game like WoW, where players often have to work together and share the loot they find. Since even classes with similar functions, like Rogues and Warriors again, need different primary attributes to grow their derived stats, you can easily create loot that is more useful to one than the other, reducing conflict over who should get an item.
A Derived Stats system is also a great fit for games which, like pen and paper RPGs, offer a lot of gameplay outside of pure combat scenarios, since the variety of available stats, all important to different types of characters, and all with specific flavors (my character is very Wise!) can be used in conversations with NPCs, in quests, or generally to advance the plot.
The Direct Stats system can be equally valuable, however, and it is often the best choice in games where the player must control or manage a large number of characters. Imagine that you have a roster of 20 characters, each has a slightly different class, and each class derives its relevant stats slightly differently. Do you want to have to remember exactly how each one of those classes uses the Strength attribute every time you need to decide who to give a sword with +Strength on it?
Similarly, a game with a heavy focus on combat, where battle is the primary gameplay mechanic and 90% of your time is spent fighting something is probably better served by a Direct Stats system. This is particularly true if the combat in question is highly strategic, and requires a lot of meaningful choices from the player at every turn. In a game like this, information is one of the most important resources at the player's disposal, and being able to clearly present information about the player's characters, so that it is always clear exactly what a stat does, and how the character will be affected if that stat is buffed or debuffed, can make the game a lot more satisfying and enjoyable.
So there you have it, each of these two systems has their uses, and the key is to consider what kind of game you want to make, and what you want the player's experience with the game to be like.
The next time you are playing an RPG, gentle reader, consider how the designers chose to represent your characters' attributes. Chances are there are good reasons they chose the system they did, and you can learn quite a bit by considering what those reasons might be.
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