Open-play wait time calculator

At a busy open play, waiting players line up their paddles in a rack and go on court in groups as games end. How long the line takes depends on three things you can count at the court: how many courts are in play, how many paddles are ahead of yours and how long a game lasts there. This calculator does that arithmetic. It uses no built-in averages: the game length is the one you enter, and the rotation choices are the ones parks departments post.

How open-play rotation works

USA Pickleball's Recreational Programs Guide calls the basic system "paddle-in-line" or the "paddle saddle": players lean their paddles against a wall or fence, or put them in a saddle, in order of arrival, and "once a court opens up, the next four players pick up their paddle and go to that open court." Dawson County Parks & Recreation in Georgia calls the same thing paddle stacking, "an easy, simple method to self manage player rotation on and off courts when all courts are full." (It has nothing to do with stacking, the legal positioning tactic.) The posted rules then differ on who comes off and when games get shorter:

Dawson County lets friends stack two or four paddles together "for a few games," but a stack may wait longer to complete a foursome and is "never a reason to jump forward in line." The full set of posted manners, from warm-ups to stray balls, is on the open-play etiquette page.

The formula

With C courts, game length G and S minutes between games, each court turns over every T minutes. W is the number of paddles ahead of yours, and k the number of players a finished game takes from the rack: 4 when everyone comes off a doubles court, 2 when winners stay (singles: 2 or 1).

T = G + S
games per hour = C × 60 ÷ T
openings you wait for: n = ⌈(W + 1) ÷ k⌉ (rounded up)
time between openings: I = T ÷ C
your wait: from (n − 1) × I to n × I; midpoint (n − ½) × I
average time in line = W × T ÷ (k × C)
games per player per hour = games per hour × players per game ÷ (W + players on court)

The time between openings assumes the courts' games end at spread-out times, which is what happens once open play has run a while; if games end in a bunch, the openings come in bunches but the totals are the same. The average time in line is Little's law from queueing theory: in a stationary system, the long-run average number waiting equals the rate at which people join the line (in a steady line, the same as the rate at which they leave it) times the average time each one waits. Here the rack holds W paddles and empties at k × games per hour.

Worked example: 4 courts, 14 paddles ahead

Say four courts are busy, 14 paddles are in the rack ahead of yours, everyone comes off after each game, you timed games at 15 minutes (the length Pittsburgh's waiting-system sheet says most games take) and walking on and warming up adds 2 minutes.

1. Court turn: T = 15 + 2 = 17 minutes.
2. Games per hour: 4 × 60 ÷ 17 = 14.1 for the four courts.
3. Openings you wait for: you are 15th in line, so n = ⌈15 ÷ 4⌉ = 4; your group is the fourth to go on.
4. Time between openings: I = 17 ÷ 4 = 4.25 minutes.
5. Your wait: 3 × 4.25 = 12.75 to 4 × 4.25 = 17 minutes, about 14.9 minutes in the middle. Little's law gives the same average: 14 × 17 ÷ (4 × 4) = 14.9 minutes.
6. Playing time: with 30 players in all (14 waiting, 16 on court) and everyone rotating, each plays about 14.1 × 4 ÷ 30 = 1.9 games an hour.

A fifth court cuts the midpoint wait to 3.5 × 3.4 = 11.9 minutes. Winners-stay rotation with the same line more than doubles the wait for players in the rack, to about 31.9 minutes, because each game takes only two players from it; that is one reason West Salem, Stamford and West Bloomfield switch to 4 on/4 off once 5, 6 or 7 players are waiting.

1. Front of the rack: the first four paddles (group A) take the next court that opens.
2. Your paddle (outlined): 15th in line, with 14 ahead.
3. Groups of four go on together under 4 on/4 off, so you wait for ⌈15 ÷ 4⌉ = 4 openings.
4. Openings: with 4 courts and 17-minute turns, a court opens every 17 ÷ 4 = 4.25 minutes on average.
5. Your group D takes the fourth opening: 17 minutes if you placed your paddle just after an opening, 12.75 if just before, about 14.9 on average.
6. Empty slot: the first player back from court 1 (or a new arrival) puts a paddle here and completes group D.

Where the inputs come from

• Game length is yours to enter, because published figures differ: Pittsburgh's sheet says most open-play games take 15 minutes, while pickleball.com's tournament scheduling guide plans about 20 minutes for one game to 11, win by 2. Shorter games to 9, which San Mateo, Dawson County and Wentzville switch to when the line is long, need their own timing.
• Minutes between games covers the walk and warm-up. San Mateo allows a 1-minute warm-up; West Salem and Wentzville allow up to 5.
• Rotation: the two choices match the posted rules in the table above. Two-game and three-match limits for winners are not modeled.

Limitations

• It assumes every court is busy and games end at spread-out times. At the start of a session, or when several games finish together, real waits come in steps.
• One game length stands in for all games. A long deuce game or a beginner court that plays slower shifts every number.
• Skipped paddles (Pittsburgh skips a player who is not there when called), friends waiting to complete a stack, and people arriving or leaving change the line as you wait.
• Venues that split courts by level run separate lines; enter only the courts and paddles for your level.
• Little's law holds for a line in a steady state. For a line that is still growing, use the "your wait" range.

For organized sessions with fixed partners and sit-outs, use the round robin generator; for planning how many courts fit a site, the court space calculator.