Role, Rules, and Rolls posted a “Simple Chase Rule” a couple weeks ago, where a character can forgo their normal movement rate for a turn in order to roll for a random movement rate. In D&D/Pathfinder terms, a character who moves 30′ in a round can move 10d6′ instead (or I guess you could simplify it to 6-spaces and 2d6-spaces if you cared to). This gives a range of 10′ to 60′ (with an average of 35′) which is a huge range to represent bursts of speed or mishaps/stumbling.
Right off, I like the idea that Roger is going for here: with static movement rates, you can determine the results of a chase before anyone moves anywhere; the faster party wins, or in the case of matched rates whoever can outlast the other. That’s rather dull, and adding in a roll shakes it up a bit.
That being said, I’m not sure it actually works, at least not in D&D and not with characters or groups who have different speeds. For example, a human can move 30′ or average 35′ (at the risk of moving only 10′ in a turn). A kobold can move 20′ or average 23′ (rolling 6d6+2), hoping to get as much as 38′ at the risk of only going 8′. Assuming a Human is running from a Kobold and chooses to NOT random-roll the chase, he will move away at a steady 30′ pace. If the kobold doesn’t random-roll the human will pull away at a relative 10′ per turn and the kobold has no chance to catch up. If the kobold DOES random-roll, he will average a speed of 23′ and the human will pull away at a relative 7′ per turn, and the kobold has no chance to catch up. Only early on, <i><b>if</b></i> the human and kobold are within 10′ of each other, does the kobold have a chance of catching the faster human, and then only if the koblod gets a particularly good roll and the human doesn’t put any special effort in to running.
Of course, this is all moot given that D&D/Pathfinder has a full-round “Run” action, where the character throws caution to the wind (granting combat advantage) and moves at a rate of 4x their normal speed (120′ instead of 30′). Combining these would give something silly like 40d6′ (between 40′ and 240′ depending on the whims of the dice) and it breaks down from there.