The Fibonacci Scale

From Leonardo Fibonacci to Modern Planning Poker

What is the Fibonacci Sequence?

The Fibonacci sequence is one of the most famous mathematical sequences: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... Each number is the sum of the two preceding numbers. This seemingly simple sequence hides deep mathematical principles and surprisingly appears everywhere in nature – and in Scrum Poker.

History: Leonardo Fibonacci (1170-1250)

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The Mathematician from Pisa

Leonardo Fibonacci (actually Leonardo da Pisa) was an Italian mathematician who lived in the 13th century and is considered one of the most important mathematicians of the Middle Ages.

The Rabbit Problem (1202)

In his work "Liber Abaci" (Book of Calculation), Fibonacci posed a famous problem:

"A pair of rabbits is placed in an enclosure. How many pairs will there be after one year, if each pair produces a new pair every month starting from the second month of life?"

The solution? Month 1: 1 pair, Month 2: 1 pair, Month 3: 2 pairs, Month 4: 3 pairs, Month 5: 5 pairs, Month 6: 8 pairs... the Fibonacci sequence!

Fibonacci's Contribution

  • ✅ Spread of the Arabic numeral system in Europe
  • ✅ Replacement of Roman numerals (I, V, X, L...)
  • ✅ Introduction of zero as a number
  • ✅ Foundations of modern arithmetic

Influence to This Day

  • 📐 Architecture & Design (Golden Ratio)
  • 🌻 Nature (Sunflower seeds, snail shells)
  • 🎨 Art (Leonardo da Vinci, Parthenon)
  • 💻 Computer Science & Agile (Planning Poker!)

Mathematical Properties

⚜️ The Golden Ratio (φ ≈ 1.618)

The ratio of consecutive Fibonacci numbers approaches the Golden Ratio:

5 / 3 = 1.666...

8 / 5 = 1.600

13 / 8 = 1.625

21 / 13 = 1.615...

34 / 21 = 1.619...

→ Converges to φ = 1.618033988...

The Golden Ratio is considered an aesthetically perfect proportion and appears in art, architecture, and nature (e.g., nautilus shell, sunflower).

📈 Exponential Growth

The Fibonacci sequence grows exponentially, but not linearly. The gaps between numbers become increasingly larger:

Position Value Difference Ratio
F(5)5+2-
F(6)8+31.60x
F(7)13+51.63x
F(8)21+81.62x
F(9)34+131.62x

🌿 Fibonacci in Nature

Plants

  • • Sunflower seeds: 21 & 34 spirals
  • • Pine cones: 5 & 8 spirals
  • • Flower petals: often 3, 5, 8, 13
  • • Tree branching

Animals & Physics

  • • Snail shells (Golden Spiral)
  • • DNA double helix (13:21 ratio)
  • • Galaxy spiral arms
  • • Human body (finger joints)

Why Fibonacci in Planning Poker?

The Fibonacci scale is perfect for story point estimation because it reflects the natural uncertainty of larger tasks.

✅ Small Differences for Small Tasks (1→2→3)

For well-understood, small tasks, we can estimate precisely. The differences between 1, 2, and 3 story points are clearly recognizable.

✅ Larger Gaps for Large Tasks (8→13→21)

For complex, uncertain tasks, precise estimates are impossible. The jump from 8 to 13 signals: "Both are large, but 13 is significantly more complex." A linear scale (8, 9, 10, 11, 12, 13) would suggest false precision.

✅ Prevents False Debate

Without Fibonacci, teams debate endlessly: "Is this 16 or 17 points?" With Fibonacci: "5 or 8 points?" – The gap forces simplification: Is it more medium (5) or large (8)?

✅ Encourages Splitting Large Stories

The large jump from 13 to 21 signals: "This is too big!" Teams are encouraged to break down 21-point stories into smaller, manageable pieces.

✅ Psychologically Intuitive

Studies show: People can estimate magnitude (small, medium, large, very large) better than exact values. Fibonacci perfectly maps these magnitudes.

Alternative Estimation Scales

While Fibonacci is the standard, some teams use alternative scales:

🔢 Modified Fibonacci (0, ½, 1, 2, 3, 5, 8, 13, 20, 40, 100)

Adjustments: ½ for micro-tasks, 20 instead of 21 (rounder), 40 and 100 for epics.

When to use: Teams that need to estimate very small tasks (½) or very large ones (100 for epics).

👕 T-Shirt Sizing (XS, S, M, L, XL, XXL)

Advantage: Very intuitive, no numbers (avoids time conversion).

Disadvantage: More difficult for velocity tracking (how much is "L"?).

When to use: Rough pre-estimates or teams that are absolute beginners in Agile.

⚡ Powers of 2 (1, 2, 4, 8, 16, 32)

Advantage: Mathematically clear, always doubles.

Disadvantage: Very large gaps (4→8→16), less nuanced.

When to use: Engineering teams that prefer binary thinking.

📏 Linear (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

Advantage: Easy to understand.

Disadvantage: Suggests false precision, endless debates ("7 or 8?").

Recommendation: ❌ Not for Planning Poker – use Fibonacci!

Fibonacci in Practice

Typical Fibonacci Scale in Scrum Poker

Card Value Meaning Examples
0 No work Story already complete, only documentation needed
1 Trivial Text change, config update
2 Very small Small CSS styling, simple validation
3 Small New input field with backend connection
5 Medium API endpoint, simple CRUD operation
8 Large Feature with multiple components, complex logic
13 Very large Authentication system, complex feature
21 Epic (split!) Too large for one sprint – break it down!
? Unclear Requirements unclear, more research needed
Break Team needs a coffee break

Use the Fibonacci Scale for Your Estimations!

Start now with precise, consistent story point estimates.

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