Order Book Market

–more 4σ bars than a bell curve allows

–biggest bar so far, in typical bars (σ)

–worst fall within a day (24 bars)

–how much a big bar predicts a big next bar (BTC 0.28, a bell curve 0)

up bar down bar fair value (drifts gently, never jumps) market makers pulled out whale trading /crowd: trend followers / value traders

Book: bids (buy orders) asks (sell orders) market makers' share

How big the moves are

this market Bitcoin bell curve

Bars sorted by size, in σ (a typical bar). Log scale: each line down is 10× rarer. The bell curve dives; markets don't.

How often huge moves come

this market Bitcoin bell curve

Share of bars bigger than x σ, both axes log. A straight line is a power law.

Memory

size of moves direction of moves Bitcoin, size

Correlation with the bar k bars earlier. Direction: none, so you cannot predict the next move. Size: lots, so calm and wild spells cluster.

What each ingredient does

Market	bars	kurtosis	tail exponent	4σ bars vs bell	biggest	direction memory	size memory, 1 / 10 / 50 bars

Running the same market with pieces switched off, in the background…

Kurtosis is 0 for a bell curve and grows with fat tails. The tail exponent α says the chance of a move bigger than x falls like 1/x^α; real markets sit near 3 (the "cubic law"), a bell curve has no such tail (it shows as 5 or more here).

Run

Speed

bar (≈ one hour of Bitcoin)

100

price

–

spread (best ask − best bid)

4 of 4

market makers quoting

–

of the crowd follow trends

–

crowd activity vs normal

Be the whale

Block Spread over

You trade the block in small market orders. The book holds about – units within 1% of the price right now.

Ingredients

Market makers pull out when it gets wildand work off what they hold, which pushes the price further Speculators herdthey switch between following trends and buying value, mostly by copying the other camp Attentionthey trade more when the last few bars were wild Trend followers pile ineach has a trigger; a big enough trend makes them jump in, up to a full position Whalesnow and then someone sells or buys a big block

Changes apply at once. Switch herding and attention off and the spells and fat tails fade; the table on the left runs every case for you.

Who is trading

Share of all units traded with a market order since the start. Random traders also supply most of the resting orders the others trade against.

Why it matters

Benoit Mandelbrot noticed in 1963 that cotton prices jump far more often than a bell curve allows. Since then the same few patterns have turned up in every market: big moves far too often, no way to predict the direction, and calm and wild spells that last. Risk models built on the bell curve call a 10σ day a once-in-the-universe event; markets deliver them every few years.

Here nobody gets any news and the fair value only drifts gently, yet the crashes come. They come from the traders themselves: a crowd that copies itself, gets busier when it's wild, and market makers who step back exactly when they are needed.