I can't tell if this is just being pedantic or something else. Perhaps an example will help illuminate. Attack rolls in D&D. Are they representational? I say they are. What are your thoughts?
Gygax's DMG says this (p 61):
The system assumes much activity during the course of each round. Envision, if you will, a fencing, boxing, or karate match. During the course of one minute of such competition there are numerous attacks which are unsuccessful, feints, maneuvering, and so forth. During a one minute melee round many attacks are made, but some ore mere feints, while some are blocked or parried. One, or possibly several, have the chance to actually score damage. For such chances, the dice are rolled, and if the "to hit" number is equalled or exceeded, the attack was successful, but otherwise it too was avoided, blocked, parried, or whatever.
This suggests that the roll to hit, in AD&D, represents how well the target, of that one attack that actually has a chance to land, does in attempting to avoid, block or parry it.
4e D&D says this (PHB p 273):
To determine whether an attack succeeds, you make an attack roll. You roll a d20 and add your base attack bonus for that power. A power’s base attack bonus measures your accuracy with that attack and is the total of all modifiers that normally apply to it.
That makes it clear that the bonus represents something - accuracy - but the roll itself seems to be a mere determiner. This is reinforced, it seems to me, by this on pp 276 and 278:
When you hit with an attack, you normally deal damage to your target, reducing the target’s hit points. The damage you deal depends on the power you use for the attack. Most powers deal more damage than basic attacks do, and high-level powers generally deal more damage than low-level ones. If you use a weapon to make the attack, your weapon also affects your
damage. If you use a greataxe to deliver a power, you deal more damage than if you use a dagger with the same power. . . .
When you roll a natural 20 and your total attack roll is high enough to hit your target’s defense, you score a critical hit, also known as a crit. . . . Rather than roll damage, determine the maximum damage you can roll with your attack. This is your critical damage. . . . Magic weapons and implements, as well as high crit weapons, can increase the damage you deal when you score a critical hit. If this extra damage is a die roll, it’s not automatically maximum damage; you add the result of the roll.
The attack roll is a mere determiner. But the
damage - whether rolled or fixed or a combination of both - represents how powerful/effective/devastating/etc the attack was.
This is also how 4e D&D allows for damage on a miss.
Anyway, my posts about this mentioned the rolling of tests in Burning Wheel, the rolling of dice pools in Marvel Heroic RP/Cortex+ Heroic, and the rolling of the hit location die in RuneQuest. Are you saying that those rolls represent something? If you are, are you able to say what you think they represent?