Keeping the Icosahedron Rolling
Strange quantum effects aside, everything that happens in the real world is the result of a deterministic (if exceptionally complicated) chain of events that start's with one action and ends in an appropriate reaction. If I swing a sword, my ability to determine where to strike based on my target's gait, my physical ability to direct the blow correctly and with enough power, and the target's own reaction all determine clearly whether the blow connects and if so what the impact is. The factors one needs to account for are tremendous and have spawned many centuries-old traditions of training and expertise that require olympic-level skill to truly master. In you average RPG, however, the sum of these proud traditions is often reduced to a 5-10% bonus on a d20 to-hit roll.
While you certainly could create combat systems that account for a variety of stances, blows, counter-blows, parries, etc. (and many have!) a lot of times the details of such events are simply beyond what the game was designed to accomodate. When creating a game system, a designer has to carefully balance including details which may provide players with interesting choices or dramatic moments, while at the same time eliminating as much complexity from the actual gameplay as possible. This is not only to make the system easier to learn and play, but to keep the experience focused on what the game is designed for -- more rules means more decisions, and thus more play-time required to resolve each encounter and to move through the narrative. Combat rules can be rudimentary if the focus of an RPG is on stealth and subversion, while social interaction rules can probably be greatly simplified if you just want a straight forward hack-and-slash.
|Much like concrete and metallurgy, ascending AC was a secret known to the ancients but lost to civilization until only recently.|
In this context, then, the dice rolls serve as a simplification tool. The designer can shrug and say "this probably has a 30-70% chance of succeeding based on your character" without having to go into detail about all of the factors which might affect or determine the specific result. More importantly, the DM can use the same tool to fill in the rules where a player tries something that isn't clearly laid out. Instead of trying to root through a manual, or walk though a series of generally minor events and decisions, the DM can just set a difficulty target, ask for a die roll, and move on based on the result. Using dice like this allows the players to spend a majority of their decision-making time on important, high-level decisions, while simply glossing over the details that don't need to be played out in detail.
Roll Playing is Role Playing
I may get some disagreement here, but I think that -- far from being at odds -- die rolls serve an important purpose in establishing and developing a sense of character. It's true that "story-based" players and systems often try to minimize complexity and die mechanics in favor of more simple "narrative" approaches. The view is that those elements make RPGs feel more like a "game" that can be manipulated and beaten rather than a framework for players to use to tell the stories of their characters and the world they are in.
In contrast, though, I would argue that mechanics like skill and ability checks, feat bonuses, and the like serve to deepen the roleplaying experience by separating the players' decisions and capabilities from the characters ability to execute them. Yes, I may be an eloquent and persuasive speaker who should have no problem putting together a coherent argument as to why the king's guard should let us go and chase down the real villains; however, my character Ragnar the Blooded is not the type to talk out these sorts of things and so my decisions when playing as him must necessarily differ from how I would approach similar problems myself. The die rolls give us a little bit of a buffer between player, character, and world, and this space is filled with the unique traits of those characters and how they themselves interact with the environment.
There's also the often un-discussed aspect of the DM experience. By making important events die rolls with specific modifiers (instead of simple check-lists of activities) you reduce the DM's bias in what outcomes occur, forcing (but also allowing) him to fill the roll of impartial arbiter of events rather than tyrant lord of everyone's imagination. Yes the DM rules by fiat with absolute power, but so long as he is willing to relax that control a little, he grants the players greater agency by letting them manipulate the world themselves to change it without the DM's direct intervention, giving them a much greater sense of ownership.
Expecting the Unexpected
You could run standard D&D 4th Edition combat without a single die roll. You could use the expected values for to-hit, modify the expected damage by those, and just use a flat average for every interaction. It would certainly be a lot faster! However, a die roll is more than just a way of determining results from a complex set of statistics like to-hit, AC, base damage, strength modifiers, etc -- the randomness itself has an intrinsic value that is crucial to the play experience.
If I am rolling a 1d12 damage die, then the outcome has a very wide spread of possible degrees. yes it averages out to a flat 6.5 per hit, but if combat only lasts a half-dozen rounds then it is unlikely for my performance to approach that average within the time frame; thus, to some extent the outcome of the single battle really does have a lot to do with luck (or at least how I as a player react to my luck, be it good or bad). This is doubly true when it comes to a player hitting or missing with a crucial Daily attacks, or an NPC Brute scoring a critical hit and suddenly turning a comfortable victory into a desperate struggle.
Dice add drama and excitement to roleplaying because, while we as players know what should happen most of the time, it's not at all certain that that is what will happen. Everyone pays attention to the game when dice are rolled because the outcome can put them in exactly the right position to execute their clever schemes, or force them to completely reconsider. Again, this is important for the DM experience as well. Anyone who's DM'd a multi-adventure campaign will know that some nights you sit down and just have a check-list of events and encounters you need to run the players through to advance the plot. If you're the strong storyteller type you might not have much of a problem with this; however, if you release some control and allow for random elements to creep in, then what was a static experience of playing "host" to your friends now becomes a dynamic and interactive experience for the entire table, including yourself. It can definitely be worrying and lead to some brief moments of panic when your PCs somehow slay a key character you had plans for down the road; however, if you can resist the urge to overturn their victory one way or another and just roll with their decisions, you'll end up with a much more nuanced story that the players will feel much more involved in because (whether they know it or not) they are helping to shape it.
For the Fun of It
Rolling dice is just fun. There is the sense of drama and suspense when an encounter boils down to a few crucial rolls sure, but the actual act of picking up a hand full of polyhedra and throwing them on the table to determine your fate provides a surprisingly important physicality to what is otherwise a very abstract experience that sucks players in. Think about it, which would you prefer as a player -- rolling all your attack and damage die yourself, or letting the DM do everything behind the screen? By letting the players roll dice, they inherently feel more responsible for the outcomes (even if they are no less random) than if it were determined statically by their decisions, or rolled by the DM in secret. The barbarian grows accustomed to his large, swing-y d12 to represent his powerful but inaccurate great weapons, while the wizard palms a fist-full of d4s and d6s that almost mimic the explosive nature of a fireball or cone of frost. The dice provide an important physical grounding for the whole experience.
Why Don't We Roll?
Of course, not everything is determined by a die roll -- and with good reason. Die rolls take time, force players to look up modifiers, and cause the DM to have to ensure he knows how to react to any of the possible outcomes. As a rule of thumb, die rolls should be avoided when they don't accomplish the goals above -- when they slow down or complicate play rather than speeding it up, when they remove a player's sense of character rather than reinforce it, when there is no real suspense or sense of stakes or drama, or when players just aren't interested in this aspect of the adventure and are eager to move on to something else. A DM has the power to just say "This is impossible" or "That would trivially succeed" and should feel free to do so whenever he sees fit to keep the game interesting and moving. If a die roll would result in pretty much the same thing (or if the players have an unlimited amount of time and there is no consequence for failure) then just skip it; likewise, be careful not to ask for a die check if you don't actually know what would happen if the players fail. In either case, just don't be so overzealous about it that you make the players really feel like they are being railroaded down a specific path of decisions. Try and be as flexible and creative as you can while still staying a step or two ahead of the players.