Which leads to greater character diversity: more options or fewer? There are several moving parts there: the number of choices, the number of options for each choice, the importance of those choices, and the ability to change them. I should note that I will be considering the majority or the people who care; there will always be people in the tails of the bell curve who are trying to make the worst possible choices because of contrariness or a character concept.
The importance factor seems the easiest: the more important a choice is, the less likely there is to be diversity. If something really really matters, there will be one best way to do it or a few best combinations; even if you give me more options for that choice, anything less than the best means gimping the character. Contrarily, if the decision has no practical importance, the distribution will be random, and more options will lead to even greater diversity.
You can see this one easily in evolutionary biology. Do you have attached or detached earlobes? It really does affect your survival, so our species is random there. Can you roll your tongue? Innie or outie?
Take character appearance as an example. This will have few effects on your ability to play, and while some looks are more popular (Hey wow, another CoV villain in black with a skull motif. Think of that one yourself?), someone will like just about anything. In City of Heroes, you have a practically infinite number of options when creating a character, if you include all the possible combinations of body parts, colors, and sliders. You see more diversity there than in YAFMMORPG, where you have some options on a few parts.
Of course, in a heavily itemized YAFMMORPG, those initial appearance choices do not matter, both in the sense that they have no effect and that you will not see them. Your character will be covered in gear, which is where real diversity of appearance comes from. Now appearance is very important because it is a side effect of how effective you are. Now that it is important, there is one best set of gear for your class, so everyone is building towards that. Given enough time, everyone will look the same, and diversity in character appearance comes from who has spent less time farming.
Moving along, all things being equal, more options for each choice should lead to more diversity. Even if there is a central tendency, having a wider range leads to a broader spread. Having some options that are clearly better or worse will decrease the effect of this. Adding more useless crap does not increase diversity much.
Does having more choices increase diversity? This seems like a live option to me, particularly based on whether those choices are from the same pool or not, the range of options in those pools, and the other factors surrounding choices. Let’s get some examples to explore.
You choose one race from x races and one class from y classes. These are what I am calling separate pools: you pick one race and one class. If you can multi-class, you are still making one pick from the race pool, then one or more from the class pool. Then you have your skills, traits, spells, etc., which usually have many picks from many options, possibly from separate pools. If you have mutually exclusive pools, that is effectively another level of pooling, a sub-class.
You get one choice for race, unless your game has multi-racial characters or a system with more variables (kind of like a skills system for race instead of/in addition to class). Does this create the most diversity, or would having more choices? This will probably depend on the number of choices and their importance.
Trivially, being able to pick more than one race would lead to more options. If there are five races for each side in WoW, there are ten bi-racial choices, twenty if order matters. Having tri-racial characters, however, does not give you more options unless order matters: there are still ten combinations. Letting you pick four brings us back to having five combinations, and all five means just one. You increase that a bit if you allow both single-race and multi-racial characters. The same thing applies to classes: Guild Wars gets more diversity from its class options by making you pick two, and order matters there so they get even more.
What I am really interested in here is the question of when you have multiple picks from a pool with multiple picks. This could be skills in Asheron’s Call, powers in City of Heroes, talents in World of Warcraft, or traits in The Lord of the Rings Online™: Shadows of Angmar™. For any of them, order does not matter (much), importance is high, and the number of picks varies widely so we have multiples cases to consider.
First, remember the issue before with combining a small number of races: as the number of picks approaches 0 or all of the possible choices, the number of different options shrinks. If you pick all but one, you have the same number of options as if you pick only one. (If you want to try the math at home, see combinatorics.) The same applies here. If you can take almost everything, you do not get much diversity. Skills produce no diversity in WoW because you can buy all of them, and you expect everyone to do so.
This would seem like a trivial math exercise: with the number of options you have available, figure out which number of picks gives you the most options, done. The Lord of the Rings Online™: Shadows of Angmar™ has 19 virtue traits, so there are 92,378 options if you let people pick 9 or 10.
But wait, are any of them completely useless? Useless to your class? We can eliminate those. Are any of them obviously the best or effectively required for your class? Assume everyone takes those. Now you are no longer picking 9 from 19; if there are four “required” and four “worthless,” you are picking 5 from 11. That is still 462 options: not shabby, but far fewer than the 92,378 it looked like. Anyone want to bet on whether folks will do the math to get a perfect ordering of the traits, so that you really do have a required list for all of them with few to no choices?
You can make it so that there is no “best,” just “best at this.” Unfortunately, one sort of
Even if you do succeed in making a “best at,” you still have different classes. Being the toughest mage in the world means that you are now two-ply toilet paper. Go you. Being the warrior with the most mana is not going to do much for you, either. You are going with best at your role, so the diversity question falls back to how many roles your class design allows. Wow, all that work with classes, skills, and talents, and it all comes down to whether a Fury Warrior out-DPSes a Rogue.
Like many of my posts, this is getting long, so I am going to tie it off with the ability to change choices. Easier changing effectively increases the number of picks, because you change it for the situation at hand. You are no longer picking 9 of 19; you are picking 19 of 19, but only 9 at any given time. Gear is probably an easier way to think of this: you can wear your healing suit or your damage suit, your fire protection or your acid protection. You can switch gear in a moment, though, so unless this fight calls for you to be the primary healer and primary DPS against enemies dealing heavy fire damage and heavy acid damage, there is still going to be one best pick for you. Click a button to change it when the acid-spitting bugs replace the fire-breathing dragons. Now your range of options is limited only by pack space.
How is that working out in whatever game you are playing? What needs to be fixed?