Tips / Systems

Ball System Ball System · side-around

A side-around rule of thumb that reads the first object ball's reference line and the third-cushion target and combines thickness and spin. This page explains thickness in eighths and a slope correction of 1 per diamond.

Formula / route reference

Thickness number + tip number = first-object-ball line number + third-cushion number + slope correction

When to use it

When finding the thickness and spin that put the cue ball on the reference line after hitting the first object ball in a long → short → long side-around shot. Balls close together, large opposing angles and excessive follow or draw are hard to solve with the basic formula alone.

Written and edited by TTBoys · How we write and check sources · Report an error

Sources and diagrams reviewed: 2026-10-04. Rules of thumb are practice references for a specific diamond scale and stroke. Geometric constructions are kept separate from real trajectories, and nothing was measured on a real table. On mobile, the table stays in landscape so the directions in the text match the diagrams.

What do you read from the layout?

Line 4: the number of the reference line the red first object ball sits on.
Arrival 2: 1 per half diamond on the third cushion, a long rail.
Angle 0: the line you aim the thickness on is parallel to the short rail.

Slope and correction: Extend the aiming line to both long rails and count the difference along the long axis between its two ends. In this guide it is 1 per diamond, minus for a running angle and plus for a reverse angle. If you change the thickness, check the aiming line again.

See the worked example and layout See related practice

New to this? Start here

The Ball System puts different kinds of numbers into one formula. The first object ball is the ball the cue ball hits first, and the second object ball is the one it hits later. Start by reading “line number, arrival number, thickness and tips” separately.

The overlap of the two balls as seen along the cue ball's path. The balls do not actually sink into each other. Compare the yellow section with the ball diameter split into 8 parts. A thickness of 4 means 4/8, or half-ball, not 4 degrees or 4 tips.

In the next reference-line diagram, read line 4 where the first object ball sits, and in the arrival diagram read the third-cushion number 2 you want. The two numbers use different scale spacing.
Start with an example whose slope correction is 0. Make 4+2+0=6, then split it into a starting combination: thickness number 4 and 2 tips of running English.
Thickness number 4 is the 4/8 in the diagram below. First learn the thickness that sends the cue ball onto the reference line after hitting the first object ball, then adjust the spin. Not every combination that gives the same sum produces the same path.

Check yourself: You got a sum of 6. Should you just hit with 6 tips?

No. 6 is the sum of the thickness number and the tip number. The 4/8 + 2 tips in this example is only a starting combination; in practice you also have to match the separation angle that comes with the thickness, and the power.

The first-object-ball number is a line number, not a position coordinate

Basic lines 1–4 join bottom long rail 2→top 1, 4→2, 6→3 and 8→4. The red first object ball sits on line 4. The lines are references for reading, not the whole path after the stroke.

In the source, lines 1–4 join frame points on the two long rails. Read which line the first object ball is on, and between lines use the in-between value as a practice reference.
Lines 5–7 continue to departures from the short rail. The source distinguishes departure 5 in particular as a rail point. The beginner diagram shows only 1–4 to reduce confusion; for the extended lines, see the table in the source.
Don't use the cue ball position as the first-object-ball number, and don't think Five & Half's 40 is the same coordinate as Ball System 4.

Reading the third-cushion number and the thickness number

In this direction the third-cushion number goes up by 1 every half diamond from 0 at the left corner. One diamond = 2, two diamonds = 4. The spacing differs from the first-object-ball line numbers. If you flip the layout, flip the scale with it.

The thickness number is the numerator of the overlap in eighths. 2/8 is 2 and half, 4/8, is 4. It is not a coordinate for aiming at the ball center or an angle in degrees.
The tip number is the level of side-spin tip position defined by that material. Use the running-English side, and match the vertical height and stroke too. The 8 in the table is an arrival number, not an instruction to hit with 8 tips.
The third-cushion number is not simply a reading of the second object ball's horizontal position. Look at the path from the third cushion to the second object ball and first decide the arrival target at the cushion nose.

The slope reference and its sign

Here the slope is not how high you raise the cue but the direction of the aim line seen from above the table. In every picture below, the cue ball comes up from below, hits the left side of the first object ball and splits off toward the upper-left long rail.

Favorable angle −2

A and B are 2 diamonds apart horizontally. The cue ball comes in in a direction that helps the leftward travel, so −2.

4 + 2 + (-2) = 4

Parallel 0

A and B are at the same horizontal position: 0 diamonds. The aim line is parallel to the short rails.

4 + 2 + (0) = 6

Opposing angle +2

A and B are 2 diamonds apart horizontally. The cue ball comes in in a direction that works against the leftward travel, so +2.

4 + 2 + (2) = 8

Pick the thickness you want and extend the cue ball's aim line to both long rails. The blue dashed line is that line.
Bring ends A and B onto the same long rail and count the horizontal gap. It is not the distance between the balls or the difference between the marks right below them.
In this layout, which splits to the left, coming in from the lower right is a favorable angle and from the lower left an opposing angle. If you mirror the layout, mirror the balls, reference line and direction too.

The three pictures compare how to read the slope and the total. They don't mean all three layouts follow the same path at the same thickness. Changing the thickness changes the aim line, so read the slope again and check the spin left after impact and the entry to the first cushion.

The adopted material uses the line aimed at the actual thickness as the slope reference, instead of the line through the two ball centers. Extend this line to both long rails and count how many diamonds it is offset horizontally. Parallel to the short rail is 0.
Subtract for a favorable (with-the-path) angle and add for the opposite, opposing angle. With this method, line 4, arrival 2 and a 2-diamond favorable angle give a sum of 4; with a 2-diamond opposing angle the departure calculation is a sum of 8.
Some explanations use 1.5 per diamond of slope or use the ball-center line as the reference. Don't mix them with this page's 1 per diamond; practice the chosen material's reference line, tip position and stroke as one set.

Worked example: line 4, arrival 2, slope 0

4 + 2 + 0 = 6 → thickness 4/8 + 2 tips of running English

Line 4 + arrival 2 + slope 0 = 6 → a starting example of 4/8 thickness with 2 tips of running English. The yellow dashed line is the first object ball’s line; the blue dashed line is the thickness aim line. The white line is the rolling order cue ball → object ball 1 → long ① → short ② → long ③ → object ball 2.

Yellow 4: the first object ball’s line number and reference line
Blue 0: the slope of the thickness aim line
White 2: the arrival number on the third cushion

A sketch of the worked example's ball layout and travel order. Where the ball actually lands depends on thickness, spin and speed.

This is the arithmetic starting combination. Even with the same sum of 6, 3/8 + 3 tips doesn't guarantee the identical path. Changing the thickness also changes the separation angle, the speed and the spin created by the collision. First learn the thickness that separates along the reference line, then adjust the spin.

Conditions and practice order

First learn the direction of a no-English bank shot and a consistent power on reference lines 3–4. Then place the first object ball to check the thickness and separation angle that send the cue ball onto the reference line, and add spin and slope last.
The source describes a reference stroke that separates at about 45 degrees at 4/8 thickness. This is a condition of that practice method, not a law of every ball collision.
Large slopes, layouts with the cue ball very close to the first object ball, and object balls frozen to the cushion are sensitive to tip height and changes in separation angle. Calibrate on a real table starting from small slopes.
There is no dedicated simulator preset yet. The app's tip units and collision model have not been verified against this rule of thumb on a real table, so it doesn't provide a success path fitted to the calculated values.

The Ball System is a widely used side-around calculation, but it is not a single international standard or an exact law of physics. Use the source's system together with the references you learn on a real table.

Practice with the example layout

Back to the worked example and layout ↑

From 4 + 2 + 0 = 6, set 4/8 thickness and 2 tips of running English as the starting combination. In the worked example diagram, read the three balls, the angle reference line and cushions ①②③ together, and start by practicing the direction into the first cushion.

Point to the cue ball, the ball you hit first and the last ball, and say the cushion order.
Repeat the same layout 5 times and record where the first cushion and the calculated target actually land.
If the first cushion is already off, check your aim and thickness; if the first cushion is right but later ones drift, check spin and speed. Change only one thing for the next 5.

Sources and verification

하프스윙 · 볼시스템의 이해 — Reference lines 1–7, arrival numbers in half-diamond steps, thickness in eighths, the 1-per-diamond slope method and its limits.
처음처럼 · 옆돌리기 볼시스템 — Confirms the formula and 1 per half diamond of arrival; uses a different method with a slope factor of 1.5.

Sources may use different diamond scales and conditions. The text notes which scale it uses and the limits of what was checked; the diagrams are our own concept drawings.