|imagine this but much less colours|
The Quidditch Pitch is traditionally 500' x 180', although the size often varies wildly. There are three goalposts at either end of this pitch. The goal of the game is to throw the Quaffle into the opposing team's hoops.
Also on the pitch are two animated balls, the Bludgers, which fly back and forth to attack the players. There is also the Golden Snidget, a rare and fast-moving bird which must be caught before the game can end. (In ancient times it's said that the Snidget was replaced by a flying ball called a Snitch, but the manufacture of these delicate artefacts has been lost.)
The teams are made up of seven players - a Keeper who defends the goal, three Chasers who pass the Quaffle ball, two Beaters who defend against the depredations of the Bludgers, and one Seeker who pursues the Snidget. All the players are mounted on flying broomsticks.
Rules for D&D-type systems (totally un-playtested, ingest at own risk)
Assume that all the PCs will be playing in the game; if not, they should probably be skulking around the stands trying to cheat or whatever.
Use the same initiative system you would normally use for combat. One-roll initiative would probably produce different results to step-based initiative but oh well.
For purposes of abstraction, let us divide the game pitch into a series of zones and lanes. The zones are: Goal, Rear, Forward and Enemy Goal, each representing a 125' distance down the pitch. The lanes are Left, Right, Mid and High, each representing a different angle of attack. Each round, the players may move one zone down the pitch and move into a different lane, the only exception being that one cannot move directly from Left to Right.
As well as movement, each player can take one of the following actions each turn:
Pass: (Chasers/Keepers) Pass the Quaffle to another player. Make a ranged attack roll against AC 8 with the following modifiers:
Each Zone Distance: +3 AC (i.e. passing from Rear to Enemy Goal would give a +6 to the AC).
Passing between Left-Mid or Right-Mid: +2 AC
Passing between Left-Right: +3 AC
Passing to High: +3 AC
If the attack roll fails, the ball is Lost (see below). The ball is Lost in the zone of the person you were throwing to, unless you tried to throw across more than one zone/lane, in which case it falls in the middle between you.
Beat Back: (Beaters) Attack a Bludger with your club to knock it away. You must be in the same lane and zone as a Bludger to do this. Make a melee attack roll against AC 14 - on a hit, the Bludger is knocked away and must spend its next turn returning to the fray.
Beat Attack: (Beaters) Strike a Bludger with intent to send it at another opponent. This more difficult maneuver is reflected by a -2 penalty to the roll, but if successful it will cause the Bludger to make an attack against your target. The target must be within one turn's movement of the Bludger.
Tackle: (Chasers) Attempt to tackle an opponent and steal the Quaffle. You must be in the same zone and lane as them. Make a melee attack roll against the opponent's AC including their Dexterity bonus (armour is almost impossible to wear while riding a broomstick, which doesn't mean someone won't try it at some point.)
If you hit the opponent exactly on their AC, then you both drop the ball and it is Lost.
If you hit with a 20, you perform a vicious tackle that deals 1d6 real damage. Killing an opponent is not technically against the rules, but it is a good way to start a blood feud.
If you miss, you overshoot and must spend your next turn returning to the fray.
Score: (Chasers) Attempt to score at the opponent's goal. You and the Keeper secretly select a hoop to shoot for and to defend, respectively. If the Keeper defends the hoop you are shooting for, then your target AC is 15, otherwise it is 10. If you miss, the Keeper always takes the ball.
Behaviour of Bludgers: Bludgers have a very limited form of 'intelligence' which manifests in vaguely random movements. Each round, each Bludger has a 50% chance of staying where it is, a 25% chance of moving forward or back, and a 25% chance of moving to another lane. If the Bludger begins its turn in the same zone/lane as a player, or moves into the zone/lane of a player, then it will make an attack against them: +3 vs. AC, hit roll on the Bludger Attack Table. After making an attack the Bludger will move to another area rather than threaten the same player again. The Bludgers will never attack Keepers.
BLUDGER ATTACK TABLE (d12)
1-8: Struck painfully - take the indicated amount of subdual damage (1-8). If subdual damage brings you to 0, you are forced to retire.
9-10: Blown off course - you are sent flying in a tailspin and must spend the next round righting yourself.
11: Narrow escape - knocked off your broom but hang by one hand. You can spend a turn to climb up onto your broom... or you can keep flying but must make a CON check each turn to avoid falling.
12: Knocked off your broom - take 2d6 lethal damage from falling, or double that if falling from the high lane.
Lost Balls: When a ball is dropped through tackling or poor passing, it goes into freefall. All players within one turn's movement of the ball can roll to try and grab it (this happens immediately, screw the initiative order). The roll is d20 + Dexterity mod + 2 for players in the same zone/lane as the ball. Whoever rolls the highest catches the ball.
SNIDGET PURSUIT TABLE (d10)
1: The Snidget escapes, leaving no trace.
2: The Snidget dives and hides in the grass. Make a WIS check to find it again - failure indicates it has crawled away.
3: The Snidget flies high, higher than broomsticks are supposed to go. Make a CON check to keep up with it.
4: The Snidget hides in the crowd. Make a CHA check to get them out of the way or it will escape.
5: The Snidget flees right out of the pitch and into the surrounding countryside. Having broken the wards that keep it captive, it will now be much more difficult to catch and will probably go to ground in the nearest monster-infested forest.
6-9: Gaining on it! Add +1 to your next roll on this table.
10: Caught up to it! Make a DEX check to catch the Snidget.
It is customary for the Seeker to bite off the bird's head in celebration of victory, or to offer the morsel to his opponent in the case of defeat.
10 points are awarded for a goal. 30 points are awarded for catching the Golden Snidget. When the Snidget is caught the game ends and the team with the highest points wins.
As with the rules for combat in AD&D, these rules are hardly designed to cover all possible actions within the game. Improvisation within this framework is encouraged, as is outright cheating as long as you don't get caught.
Although broomsticks have survived the apocalypse better than many magical arts, they are still quite expensive and generally restricted to the use of the landed gentry. The exception to this rule is the masterless hill tribes, whose weird witches still remember how to craft the broomsticks.
Nevertheless, it is fairly common for peasants to play the game without any of the magical and valuable features that are afforded for the upper classes. In the peasant version of the game, the players are on foot and the hoops are at ground level. The Golden Snidget is replaced by a field-mouse painted yellow. The Bludgers are replaced by a pair of irate billy-goats.
If playing 'Low-Lying Quidditch', assume that the movement system is the same due to a smaller pitch, save that the High lane is eliminated. Make other adjustments as seems reasonable - for example, instead of being killed by falling after a Bludger attack, the players could risk being gored to death by goats.