Pool Bank Shots Made Simple: The Diamond Midpoint Formula

Pool players treat bank shots as black magic. Most actually-good bank shots are arithmetic, not intuition. Here's one formula that handles the majority of single-rail banks: aim at the midpoint between your start and target positions, in diamond units.

That's it. No spinning, no complex tables, no "feel." Just (start + target) ÷ 2. This article explains why it works, where it breaks down, and how to make it part of your pre-shot routine.

The Diamond Coordinate System

Pool tables have small inlay markers on the rails. They're not decoration — they're a numbered coordinate system for shot geometry. Standard 9-foot pool tables follow the same numbering convention:

• Long rails (the 100-inch sides): 3 diamonds between each corner pocket and the side pocket, plus the side pocket itself. Numbered 0–8 (corner-to-corner, with the side pocket at position 4).
• Short rails (the 50-inch sides): 3 diamonds between the two corner pockets. Numbered 0–4.
• Each interval between adjacent diamonds is one diamond unit. It's an abstract length, not a fixed distance in inches.

The Midpoint Formula

For a 1-rail bank — where your ball travels from a starting position, bounces off one cushion, and arrives at a target position — the cushion aim point is:

Aim point = (start diamond + target diamond) ÷ 2

That's it. Two numbers, average them.

Worked Example

Suppose:

• Your starting position (object ball position before being struck) is at long rail position 2
• You want the ball to arrive at long rail position 6
• It bounces off the opposite long rail: which point on that rail do you aim at?

Math: (2 + 6) ÷ 2 = 4. Aim at position 4 on the opposite rail. Position 4 happens to be the side pocket. So you aim directly at the side pocket.

Why It Works

The formula is the algebraic form of incident = reflection — the same physical law that governs light bouncing off a mirror. When a ball hits a cushion (with no spin), it leaves at the same angle it arrived, measured from the normal of the cushion.

If the cushion is at a fixed position, the reflection point that produces equal incident and outgoing angles is geometrically the midpoint between (start) and (target) along the cushion's axis. The diamond numbers are just a coordinate system along that axis. So averaging the two numbers gives the reflection point in those coordinates.

It's not a trick. It's geometry expressed in convenient units.

Where the Formula Breaks Down

The formula assumes a perfect mirror-like cushion bounce. Real-world cushions deviate from this in three main ways:

1. Sidespin Skews the Rebound

Adding sidespin (English) makes the cushion grab and release the ball at a different angle than the geometric reflection. Running English widens the rebound (ball comes out further down the rail); check English narrows it. The midpoint formula assumes a center hit. If you add spin, the formula's aim point will miss by 1–3 diamonds.

For beginners learning banks: no English. Center hit only.

2. High Speed Compresses the Cushion Differently

Cushions deform under the ball's pressure. At very high speed, the cushion compresses more deeply, and the ball's exit angle is steeper than the geometric prediction (the ball comes up short of where the formula predicts). At low speed, the cushion is barely compressed and the formula is more accurate.

Practical rule: moderate speed for banks. Hard banks deviate from the formula by 5–15%.

3. Frozen-Rail Object Balls Behave Differently

If the object ball is touching the cushion (a "frozen rail" position), the contact geometry changes. The midpoint formula assumes the ball travels free toward the cushion and bounces normally. Frozen-rail banks have their own techniques.

4. Multi-Rail Banks Need Different Systems

The midpoint formula is only for 1-rail banks. Two-rail and three-rail banks use different systems with different math:

• Corner-5 System (Allen Hopkins): 3-cushion kicks where the cue ball starts in one corner and hits 3 cushions to reach a target.
• Plus System (originally a carom system, sometimes adapted for pool): 3-cushion shots where the math is additive rather than averaged.
• Bob Jewett's Plus System (different from the carom system above): a pool-specific 3-rail kick system used for safety play.

Confusingly, multiple systems share names. When someone says "Plus System" make sure they mean the carom one or one of the pool variants. For most amateur play, the 1-rail midpoint formula handles 80% of bank situations.

How to Use This in a Game

Pre-Shot Routine for Banks

1. Identify your start position — where is the object ball? Estimate its diamond coordinate (0–8 along the long rail, 0–4 along the short rail).
2. Identify your target position — where does the ball need to arrive? Usually a pocket, so use 0 or 8 (corner) or 4 (side).
3. Average — `(start + target) / 2`. That's your aim point on the opposite rail.
4. Verify visually — does aiming at that point look reasonable, or wildly off? If wildly off, you may have miscounted the diamonds. Recount.
5. Center hit, moderate speed.

Beginner-Friendly Mental Shortcut

If counting diamonds is too abstract, use the mirror visualization instead — same math, more intuitive:

1. Mentally fold the table along the cushion you're banking off.
2. The target pocket appears at a "mirror" position on the other side of the cushion.
3. Aim straight at the mirror pocket. The cushion redirects the ball naturally.

The mirror method is just a visual way to do the midpoint formula. Same result; pick whichever fits your brain.

Common Bank-Shot Mistakes

1. Aiming at the Real Pocket

The most common mistake. The ball is bouncing off a rail, not going directly. Aiming at the real pocket sends the ball into the rail at the wrong angle. Always aim at the cushion midpoint (or the mirror pocket).

2. Adding Sidespin "for Insurance"

Some players add a touch of English on every shot out of habit. On banks, that touch ruins your aim because it changes the rebound angle. Bank shots should be deliberately center-hit unless you've explicitly chosen a side-spin bank technique.

3. Hitting Too Hard

"Harder must be better" is wrong for banks. High speed compresses the cushion more, and the rebound angle changes. Most pro banks are played at medium speed — just hard enough to reach the pocket cleanly.

4. Trying to Multi-Rail with the Midpoint Formula

The midpoint formula is 1-rail only. If you need 2+ rails, the math is different. For most bank situations in pool, 1 rail is enough. Save multi-rail attempts for the rare positions where they're needed.

5. Forgetting Banks Don't Work in Snooker

Snooker pockets are 25-30% tighter than pool pockets, with rounded jaws that reject misses. Banks that would drop on a pool table almost always rattle on snooker. In snooker, banking is mostly a safety tool, not an offensive one. Use it for hiding the cue ball, not for potting.

Practice Drills

1. Sit-down drill. Set up an object ball at long rail position 2, with no other balls. Bank it into the corner pocket at position 8. Compute: (2 + 8) ÷ 2 = 5. Aim at the opposite-rail position 5. Repeat 20 times. Track make percentage.
2. Variable target drill. Same setup, but vary the target each time — sometimes corner 0, sometimes corner 8, sometimes side 4. The formula doesn't care; just recompute each time.
3. Backward drill. Take a real-game position where you used a bank and missed. Now compute what the formula would have prescribed. Was your actual aim off? By how much?

The One-Sentence Summary

For 1-rail banks at moderate speed with no sidespin: aim at the midpoint between start and target diamonds. Everything else is variations on this same theme.

Related reading: How to aim in pool · The 30° rule · Lesson 3.2 · Diamond Midpoint · Lesson 3.1 · Mirror system

References: Bob Jewett, Billiards Digest bank-shot column work. Dr. Dave Alciatore, billiards.colostate.edu — Bank and Kick Shots.