Crypto order book slope: depth depends on distance

Crypto order book slope describes how displayed depth changes as you move farther from a reference price. To make it reproducible, calculate cumulative bid or ask quantity at declared basis-point distances, then divide each quantity increase by the distance increase. State the axes and units: capacity per basis point and price distance per unit of size have opposite interpretations.

A best quote answers where trading can begin. A depth curve answers how much displayed quantity lies inside a wider price boundary. Comparing those curves can reveal a difference that a spread or imbalance ratio hides, even when two books look identical at their entrances.

Define the axes before interpreting slope

This article uses price distance in basis points on the horizontal axis and cumulative base-token quantity on the vertical axis. One basis point is 0.01%. The curve is calculated separately for bids and asks.

For an ask curve, start at a reference price and move upward. For a bid curve, move downward. Distance remains positive on both sides. With a fixed book, widening either boundary can only add quantity or leave it unchanged.

The segment slope is the increase in cumulative quantity divided by the increase in distance. Its units here are tokens per basis point. A larger value means more additional displayed capacity across that particular interval.

An analyst can instead put cumulative quantity on the horizontal axis and price distance on the vertical axis. That produces basis points per token: a larger value then means a larger price concession for an additional unit. The two descriptions reverse which direction sounds liquid. A label such as “steep book” needs its axes, interval and formula attached.

These are descriptive finite differences between chosen boundaries. They are not a claim that the discrete book has a smooth, constant slope. A price interval containing no further displayed orders produces no capacity increase; the next occupied level can produce a large jump.

Build the curve from price-level quantities

For a midpoint reference, first average the best bid and best ask. At midpoint 100, a 20-basis-point ask boundary is 100 × 1.002 = 100.20. The corresponding bid boundary is 100 × 0.998 = 99.80.

Sum asks priced at or below the ask boundary. Separately, sum bids at or above the bid boundary. Include a level exactly on the boundary if that is your declared convention.

Use quantities at individual prices as the input. Summing a screen's already cumulative rows would count the same orders repeatedly. Binance Spot's documented depth response provides bid and ask price-quantity pairs, while its book ticker provides best-price quantities. The ticker alone cannot supply the deeper capacity curve. Binance Spot market-data documentation.

Keep the sides separate: ask capacity concerns an immediate buyer consuming offers; bid capacity concerns a seller consuming bids. Adding both sides would answer neither size question.

Two identical entrances, different capacity

The following is an original hypothetical spot-book comparison. Prices are USDT per token; quantities are base tokens at each price. Both books have a best bid of 99.90 containing two tokens and a best ask of 100.10 containing two tokens. Their midpoint is 100.

Assume the displayed ask range is complete through 101.00, including any unoccupied prices. Freeze the book for the calculation: no competing trades, cancellations or replenishment. Fees and venue trading filters are excluded.

Both books have the same 20-basis-point quoted spread. Their top-level normalized imbalance is also identical: (2 − 2) ÷ (2 + 2) = 0.

Now accumulate each ask side from the best offer outward:

Between 10 and 20 basis points, Book A adds six tokens over ten basis points, giving 0.6 tokens per basis point. Book B adds one token over the same distance, giving 0.1.

Between 50 and 100 basis points, the comparison reverses. Book A adds ten tokens over 50 basis points, or 0.2 per basis point; Book B adds sixteen, or 0.32. Book B concentrates much of its displayed quantity farther away.

With no asks at the midpoint, an end-to-end slope from zero distance to 100 basis points is 20 ÷ 100 = 0.2 for both. That single number loses the near-price difference. Retain several boundaries and their capacities alongside any summary statistic.

The order book imbalance calculation compares selected bid and ask totals. This example asks a different question: how quickly does one side accumulate quantity as its permitted distance expands?

Translate the curve into a size question

Suppose a hypothetical instruction seeks six tokens while allowing ask prices no higher than 100.20. Book A contains eight displayed tokens within that boundary, so the frozen snapshot has enough capacity. Book B contains three, so only half the requested amount is shown inside it.

At the published boundaries, six tokens require reaching 20 basis points in A and 100 basis points in B. That is a statement about the most distant required ask level. It is not an average fill price, a predicted execution cost or a recommended tolerance.

A buy price cap also needs an instruction for unfilled quantity. It might cancel, remain working where supported, or require an explicit later decision. Capacity alone does not select that behavior.

For average fill costs, use the separate slippage and order-book depth worksheet. For evaluation after a trade, the distinction between quoted, effective and realized spreads helps keep displayed conditions separate from executed results.

Base quantity also differs from quote notional. A's eight tokens inside 20 basis points represent 2 × 100.10 + 6 × 100.20 = 801.40 USDT of displayed offers. B's three represent 2 × 100.10 + 1 × 100.20 = 300.40 USDT. Label whether a curve accumulates tokens or price-times-quantity. A quote-spend instruction cannot be checked by treating either total as a token count.

Keep the distance reference stable

A midpoint band includes part of the spread before reaching the first order. A band measured from the best ask starts at that ask instead.

In the example, the best ask is already ten basis points above the midpoint. Ten basis points beyond the best ask gives a cap of 100.10 × 1.001 = 100.20010, whereas twenty basis points above the midpoint gives 100.20000. They happen to include the same rows here; the definitions differ.

Record the anchor and whether it changes at every observation. A moving midpoint can move a fixed order into or out of a band even when that order's price and size remain unchanged. A change in measured capacity may therefore reflect a changed boundary.

The last price versus midpoint guide explains why a recent transaction price is another distinct reference. Comparing books using different anchors can confuse spread differences with depth differences.

A fixed number of levels creates a related problem. Four occupied price levels can cover ten basis points in one book and hundreds in another. Use price bands when the question concerns a permitted price distance; keep the level count as a coverage diagnostic.

Check whether the apparent capacity survives observation

Return to hypothetical Book A. Suppose the six tokens at 100.20 are canceled before an instruction arrives, with everything else unchanged. Its capacities at 10, 20, 50 and 100 basis points become 2, 2, 4 and 14 tokens.

The top quotes and their quantities remain identical to the original snapshot. Top-level imbalance stays zero, but the six-token instruction no longer fits under the 100.20 cap. The capacity calculation was correct at the earlier instant; its input stopped describing the later book.

Observe capacity over multiple timestamps when evaluating persistence. Preserve exchange event time where supplied, local receipt time and observation age. A later refreshed curve cannot establish what was available when an earlier decision was made.

Data reconstruction matters too. Coinbase Exchange documents a level2 snapshot followed by updates whose size replaces the quantity at a price; zero removes that level. Adding every incoming size to the previous value would manufacture capacity. Apply the selected channel's own semantics. Coinbase Exchange level2 documentation.

Coverage can remain incomplete even when recent messages arrive. Binance Spot warns that its initial depth snapshot has a maximum of 5,000 levels per side and that untouched levels outside it remain unknown. Its documented missed-update procedure requires rebuilding the local book. Those are Binance-specific rules, with direct consequences for the validity of a band calculation. Binance local-book procedure.

An unobserved interval is unavailable, not empty. A boundary outside verified coverage needs an unavailable result rather than a confident zero or an extrapolation from the final visible row.

A worksheet for a reproducible comparison

Keep this record beside each pair of curves:

Validate one snapshot manually before evaluating a rule. Recompute each band's included rows, confirm cumulative capacity never falls as distance expands, and verify that the last capacity matches the sum of included quantities. Then remove a deeper level and repeat the calculation.

A negative segment slope within one fixed snapshot should trigger a units, sorting, summation or boundary check. Falling capacity across two different timestamps is entirely possible.

For comparisons across assets or venues, use aligned timing, compatible quote valuation and the same band definitions. Twenty base tokens in two different assets do not represent comparable economic capacity. Contract counts also require their instrument's multiplier and denomination before comparison.

Finish the check with the intended quantity and price boundary. Preserve the full capacity profile, then ask whether that quantity fits inside the verified range at the observation time. That record is more useful than a lone slope label because it states exactly how much displayed depth the conclusion depends on.