Log(A/B) Depth
Category: Structure
Formula
L(k) = log( Demand_k / Supply_k )
Per-bucket log-ratio of demand to supply liquidity. Positive = demand-heavy. Negative = supply-heavy. Zero = balanced.
Cumulative form: CumL(k) = log( CumDemand(k) / CumSupply(k) )
Intuition
Raw depth numbers are hard to compare — $4.2M of demand vs $3.8M of supply at bucket 5 requires mental arithmetic. The log ratio compresses this into a single number: positive means demand dominates, negative means supply dominates, and the magnitude tells you by how much. It turns a two-sided chart into a one-dimensional structural bias reading at every level.
What It Answers
Who dominates structurally?
The relative balance of demand vs supply liquidity at each price level, expressed as a signed log-ratio.
Visual Representation
- Panel: Log(A/B) chart — the histogram beneath the depth chart labeled
L(k) = log(A/B) - Display: Vertical bars per bucket — positive bars (demand-dominant) extend upward, negative bars (supply-dominant) extend downward
- Color: Bars colored by direction — teal/green for demand-dominant, orange/red for supply-dominant
- Displacement overlay: Vertical line showing current price displacement overlaid on the histogram
Behavioral Interpretation
| Condition | Interpretation |
|---|---|
| IF L(k) > 0 near mid | THEN demand dominates near current price — structural support for ratio to rise |
| IF L(k) < 0 near mid | THEN supply dominates near current price — structural pressure for ratio to fall |
| IF L(k) positive across most buckets | THEN broad structural demand dominance — the entire visible book favors the A-side |
| IF L(k) flips sign between near and far buckets | THEN structural regime changes with distance — near-mid and far-field tell different stories |
| IF L(k) magnitude increasing over time | THEN structural conviction growing — one side is building depth faster |
Failure Modes
- Log amplification at extremes: When one side is near-zero and the other is large, the log ratio spikes. A bucket with $50 demand and $5 supply gives L(k) = 2.3, but the absolute amounts are negligible. Always cross-reference with raw depth totals.
- Symmetric withdrawal: Both sides pulling liquidity simultaneously keeps L(k) stable while total depth collapses. The ratio looks balanced but the market is actually fragile. Check raw depth alongside log ratio.
Interactions
With Centroid: Log(A/B) shows the imbalance at each level. The centroid compresses this into a single location: where is the center of mass of that imbalance? Together they answer both "which direction" and "how close."
With Net Imbalance: Net imbalance is the sum across all buckets. Log(A/B) is the per-bucket breakdown. Net imbalance can be positive while individual near-mid buckets are negative — the aggregate hides the near-mid story.
With Displacement: Displacement shows where price is. Log(A/B) shows what structure supports. If displacement is positive and Log(A/B) is positive near mid, structure confirms the move. If they disagree, a structural trap may be forming.
With SLS: SLS RAW tracks the evolution of L(k) over time as a heatmap. The current L(k) snapshot is one column in the SLS surface.