What Is Siteswap?
Siteswap is a notation system — essentially a mathematical language — that describes juggling patterns using sequences of numbers. Developed in the 1980s independently by several mathematicians and jugglers, it's become the standard way to communicate patterns across language barriers, write down new tricks, and even generate patterns algorithmically.
If you've ever seen a juggler write something like 531 or 97531 and wondered what it meant, this guide will decode it entirely.
The Core Idea: Each Number = a Throw Height
In siteswap, each number in a sequence represents how high (and therefore how long) a throw stays in the air. More precisely, each number tells you how many beats later that object will be thrown again.
| Number | Meaning | Example |
|---|---|---|
| 0 | Empty hand (no throw) | Pause in pattern |
| 1 | Fast pass to the other hand | Quick zip across |
| 2 | Hold — keep in hand one beat | Momentary hold |
| 3 | Standard cascade throw | 3-ball cascade |
| 4 | Straight up throw, same hand catches | Fountain throw |
| 5 | High cross throw | High cascade arc |
| 6+ | Increasingly high throws | Advanced patterns |
Reading a Siteswap Sequence
A siteswap sequence cycles repeatedly. The pattern 3 (just the number three, repeating) is the three-ball cascade — every throw is a standard crossing throw. The pattern 531 is a classic trick sequence that looks like this:
- Throw a high crossing throw (5)
- Throw a straight-up column throw (3 — actually a 3 in this context)
- Make a fast zip to the other hand (1)
- Repeat
How Many Balls Does a Pattern Use?
Here's a neat mathematical property: the average of the numbers in a siteswap sequence equals the number of objects being juggled. For example:
- 3 → average = 3 → 3 balls
- 531 → (5+3+1) ÷ 3 = 3 → still 3 balls!
- 97531 → (9+7+5+3+1) ÷ 5 = 5 → 5 balls
- 4 → average = 4 → 4 balls (the 4-ball fountain)
Odd vs. Even Numbers
Odd numbers in siteswap represent crossing throws (from one hand to the other), while even numbers represent non-crossing throws (the same hand that throws also catches). This is why the 3-ball cascade crosses and the 4-ball fountain does not — all 3s cross, all 4s go straight up.
Vanillas, Synchronous, and Multiplex Siteswap
The patterns described above are called vanilla siteswap — the simplest form. There are two more advanced variants:
- Synchronous siteswap: Both hands throw at the same time, written with parentheses like (4,4). Even numbers dominate here.
- Multiplex siteswap: Multiple balls thrown from one hand at once, written with brackets like [33].
Why Learn Siteswap?
Even if the math doesn't excite you, siteswap is practically useful. It lets you:
- Look up patterns in databases like Library of Juggling
- Communicate tricks precisely with other jugglers
- Use juggling simulators (like JugglingLab) to visualise patterns before learning them
- Understand why a pattern works the way it does
Start with the basics: recognise that 3 is your cascade, experiment with 423 (a popular 3-ball trick), and work your way up. Siteswap turns juggling into a language — and once you speak it, a huge library of patterns becomes readable.