The five attributes, including Bravery, which affect combat include modifiers to a character's speed and/or accuracy with various weapons. The Bravery attribute score increases or decreases a character's Speed and Accuracy, for example, providing a discrete, quantifiable impact on the character's performance in the game: a character with a high Bravery score is cool under fire, faster and more accurate than his counterpart with a low Bravery attribute value.
Consider a character who is a town marshal with a Coward Bravery rating and no Experience; maybe he got the job through a political connection, or maybe the townsfolk stuck the badge on him because no one else wanted it and he didn't have the guts to say no. Now a gang of bank robbers come to town, and it's the marshal's job to confront them.
Now here's the thing: there's nothing about the attribute itself rules-wise which determines if or how the marshal will confront the robbers; the attribute modifiers only speak to what happens if he tries to fire his gun at them. The attribute and the modifiers influence how successful the character is in a particular task; they say nothing about when or how the character decides to attempt the task.
So the marshal checks his six-shooters, grabs a double-barrel from the rack, and walks into the dusty Main Street to face-down the robbers. His hands shake like he has the palsy, sweat drips off his brow making his eyes sting, and his mouth is as dry as an arroyo in August so that when he shouts, "Throw up yer hands!" it comes out as little more than a hoarse whisper, and that is what is represented by the Bravery attribute modifiers, not the decision to confront the gang - that decision is solely the province of the player.
In thinking this through, I realised that the character's stats are reflected not in what the character does, but in how well he does it. By treating character attributes as a nothing more than a rules interface and not a determinant of personality, roleplaying and character stats exist independently of one another. Put another way, roleplay your character as you like, and let the stats take care of themselves.
Consider another example, this time the loquacious player who uses a 'social stat' like Charisma or Charm as his character's dump stat; whether you're using something as simple as a reaction roll-plus-modifier or something as complex as Duel of Wits, let the player be as charming and as eloquent as he likes, and let the dice handle the actual result. The player of a would-be warlord may deliver a stirring in-character speech, but if his Charisma modifier is in the negatives, however inspiring the player may believe it to be, the warlord isn't persuasive, for this is the limitation imposed by the character's actual ability, in the same way that his Strength or Dexterity may affect his effectiveness at fighting.
If the player wants the character to be better at something, then it's on the player to choose that for the character, by whatever means the system supports, whether that's adding skill points, raising an attribute, or whatever - a would-be Cassanova with a 5 Charisma needs to invest skill points in Bluff or Diplomacy or whatever, or accept that he's only going to get play when he's really, really lucky.)
I've floated this argument on different roleplaying gaming forums over the years, and I found it's one which reliably brings out the self-anointed real roleplayers to tell me I'm doing it oh-so-profoundly wrong, to accuse me of advocating 'roll-play over roleplay,' and on, and on, and on. Perhaps their most compelling - though by no means persuasive - argument is, 'But that's what the books say!' And pretty often they're right. There's a sort of schizophrenia between what some rule books say about attribute scores, and what they mean in actual play. One of the rules-rebuttals offered is the 2e AD&D PHB, in a section subheaded, "What the Numbers Man," which offers examples of interpreting character personality from the attribute scores.
I have two specific issues with this. First, in the case of many roleplaying games but AD&D in particular, the implications of the attribute scores don't relate well to other parts of the game. Take this, frex, from the page above: "His Dexterity is 3? Why? Is he naturally clumsy or blind as a bat?" Well, if he's blind as a bat, is his chance of detecting secret doors lower? Is his outdoor encounter detection range reduced? Or if he's clumsy, is his movement reduced when he runs? Does it affect his melee attacks? Interpreting the stats this way has knock-on effects through other parts of the game with which Dex 3 simply doesn't interact. In 1e AD&D, Dex 3 means the character must be a cleric, that she cannot be a half-elf, elf or halfling, and that she suffers penalties to her reaction time, missle attacks, armor class, and certain saves. And that's it. Neither "blind as a bat" nor "naturally clumsy" fit because of the way attribute scores relate to the rest of the rules.
Second, insisting that attribute scores define personality may limit the range of potential characterisations to 'playing to type.' For example, maybe Rath, again from the 2e example, is a thief who really wants to be the leader of a gang, so he's forever trying to recruit cutpurses and bandits. But of course he's not a natural leader at all, no matter how hard he tries - I know this because his reaction rolls and loyalty scores suck when he tries to lead. The fun thing is, his rare successes simply reinforce his perception of himself, or offer him hope, so he keeps trying.
Playing against type can make for memorable characters. I have a great example of this from my Flashing Blades campaign, Riordan O'Neill, King's Musketeer, would-be Casanova with (originally) Charm 11. Most of his attempts at courtship and seduction are an uphill struggle, and luck is a huge factor in his successes. It's his repeated attempts at being the great lover in spite of lacking the natural acuity reflected by his Charm score that make him so much fun in actual play.
Or how 'bout the lily-livered Boot Hill town marshal I wrote about earlier? Maybe he took the job of marshal out of a sense of responsibility to his community, and he's determined to overcome his shakes when faced with the bank robbers. Or maybe he's a braggart and a bully who likes lording the position of marshal over the rest of the townsfolk, but like most bullies, deep-down he's gutless - he goes to face the bank robbers because he knows if he doesn't, he'll be exposed as yellow.
There's nothing wrong with playing to type, of course, but by unhooking personality from ability, a broader range of characterisations becomes available to the players.
'But what about immersion?' the real-roleplayers complain. 'An Int 6 barbarian shouldn't solve puzzles as well as an Int 18 magic-user!' There are a couple of weaknesses to this rebuttal as well. I don't mean to keep picking on D&D here, but since this argument comes up so often with respect to The World's Most Popular Roleplaying Game™, D&D examples provide a convenient gamer lingua franca. First, let's look again at what the rules say Intelligence actually provides to the character. In 1e AD&D, frex, Intelligence covers the number of possible languages spoken, the minimum and maximum number of spells a magic-user may know by level, the chance to learn a given spell, and the minimum score required to learn spells of a particular level; in 3e, Intelligence covers languages again, skill points, and the modifier for a number of skills. There is no mention of puzzle solving in there at all, and referees who 'slip clues' to players running characters with a high Intelligence score are adding something to the game that simply doesn't exist to compensate for this.
Looking more closely at the rules, what Intelligence, Wit, &c often provide in roleplaying games are resources, not abilities. Perhaps the player of the Int 6 barbarian solves sudokus in his sleep, but he's not solving a puzzle in a language his character doesn't understand until or unless someone translates it for him. Skills may also be gatekeepers, in that a character must learn a certain skill simply to be able to perform a given task. A player who's a master at pike-and-shot wargames is still limited to making brilliant maneuvers in Flashing Blades by first taking the Strategy skill and then rolling under one-third of his character's Wit. In each case, the player's ability is constrained by the character's resources.
In truth, I admit I couldn't care less if a player isn't roleplaying her character's Wit 6. Maybe it comes from starting with D&D way back when, but honestly, I expect players to metagame, to rely on their resourcefulness and experience, and I design my challenges accordingly. I never expected players to pretend their characters didn't know, say, that fire kills trolls; if I wanted them to face an unexpected challenge, then I would simply change things up on them, like trolls which are killed with salt instead of fire. One of the characters in my Flashing Blades campaign nearly died because his player ignored a clue - a case of Anjou wine - which came straight out of The Three Musketeers novel. Easter eggs from books or movies aren't there out of laziness or to try to be clever - they're there because they're fun for the players, and I fully expect them to take advantage of them, or I wouldn't include them in the first place. We're playing a game, and the experience should reward smart play.
Second, because attribute scores are often disconnected from other rules, what tends to snap my suspenders of disbelief isn't an Int 6 barbarian is solving puzzles, but rather roleplaying him as the same stupid lunk at 10th level as he is a 1st level. The barbarian's explored ancient ruins, fought men and monsters, survived poisoning, travelled across trackless wastes, seen priests drive off and destroy undead with a word, felt the power of magic, raised a horde and sacked an evil temple, maybe even been turned to stone and restored to flesh, and yet a few gamers would have that Int 6 trump all of the actual play experiences of the character - and no, that's not hyperbole.
There are roleplaying games out there which integrate both who a character is and how that does what she does - Pendragon is one of my favorite examples of 'personality mechanics' in a roleplaying game. Ability scores, however, are not personality rules, in my experience, and unfortunately even the rule books themselves sometimes confuse this.