Here's a mechanic for pursuit in dungeons in Dungeons & Dragons 5th Edition that I stole from Lamentations of the Flame Princess (if you haven't noticed, I steal from LotFP a lot. How could I not? It's a work of sheer genius!) and shamelessly butchered. It will be added to the Back to Basics section of my House Rules. I wanted a set of rules for chases that were more specific than those outlined in the Dungeon Master's Guide, and more dynamic than just using movement rates.
Run Away! (Action): The party must declare that they are using this action when initiative is rolled. Once declared, this action can be used by any party member during the round. In order to use this action, you must have at least 1 foot of unspent movement. When this action is used, pursuit begins.
In order to participate in pursuit you must have at least 1 foot of unspent movement. Hereafter, the party that declared the Run Away! action is the "quarry," and any party that elects to chase the quarry is the "pursuer."
When the Run Away! action is used, the quarry decides if they are going to use the lowest pursuit roll among them, or the individual pursuit rolls of each party member. Then, members of the quarry can use interactions to drop a equipment or containers (perhaps to increase their movement speed, or to distract the pursuers with food or wealth), and use actions to create obstacles, each bestowing advantage on a number of pursuit rolls determined by the DM based on the nature of the obstacle.
When the quarry has finished preparing, each member of the quarry makes a pursuit roll, which is 1d20 + their movement rate divided by 5 (round up). The pursuers make one pursuit roll using the lowest movement rate in the party.
- Quarry Matches or Beats Pursuer: The quarry escapes from combat and end up in a random area that is a number of areas away equal to their movement rate divided by 5 (round up), in a random direction as determined by a d8 roll (1 is north, 2 is northeast, etc.). If the quarry elected to use the individual pursuit rolls of each party member, determine random areas for each party member, instead of the quarry as a whole.
- Pursuer Beats Quarry: The quarry does not escape from combat, and ends up in a random area that is a number of areas away equal to their movement rate divided by 10 (round down), in a random direction as determined by a d8 roll (1 is north, 2 is northeast, etc.). The DM distributes pursuers in the areas occupied by members of the quarry. If the quarry elected to use the individual pursuit rolls of each party member, determine random areas for each party member, instead of the quarry as a whole.
When writing this mechanic, it quickly got convoluted - not the mechanic itself, really, but how I had to phrase everything. Despite its wordiness, I appreciate how this mechanic accounts for player agency. The PCs can throw lit oil when trying to escape, they still make progress even if they don't escape, they can drop barrels of treasure that are weighing them down, they can leave slower characters behind, etc. Really, it's okay that this mechanic takes a couple read-throughs to comprehend when you consider just how much this mechanic covers.
And if you have any clarifying questions, you can always drop them in the comments!