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Capped Linear
CappedArithmetic growth with a safety ceiling.
At a glance
capped_linearsize(i) = base · min(i, cap) (cap = 5)What this curve is for
Linear growth with a hard ceiling: 1×, 2×, 3× and so on up to the cap, then flat. It is the most conservative genuine growth in the — enough averaging to matter, a maximum per-level commitment you choose, and a capital profile that stays affordable at depths where would be out of reach.
How the sizing rule works
Size at level i is min(i, cap), with the cap defaulting to 5× base. Below the cap the ladder is (with one order per level); at and beyond the cap it is a flat ladder at cap × base.
| Level | Per-order size | Orders | Level total | Cumulative | Entry price | Take-profit |
|---|---|---|---|---|---|---|
| L1 | 1.00× | 1 | 1.00× | 1.00× | 99.00 | 99.99 |
| L2 | 2.00× | 1 | 2.00× | 3.00× | 98.00 | 98.98 |
| L3 | 3.00× | 1 | 3.00× | 6.00× | 97.00 | 97.97 |
| L4 | 4.00× | 1 | 4.00× | 10.0× | 96.00 | 96.96 |
| L5 | 5.00× | 1 | 5.00× | 15.0× | 95.00 | 95.95 |
| L6 | 5.00× | 1 | 5.00× | 20.0× | 94.00 | 94.94 |
| L7 | 5.00× | 1 | 5.00× | 25.0× | 93.00 | 93.93 |
| L8 | 5.00× | 1 | 5.00× | 30.0× | 92.00 | 92.92 |
| L9 | 5.00× | 1 | 5.00× | 35.0× | 91.00 | 91.91 |
| L10 | 5.00× | 1 | 5.00× | 40.0× | 90.00 | 90.90 |
The ladder, as the engine builds it
Below is the 's own ladder and the trading terminal's chart engine, both driven by buildLadderPlan for this . Change the level count, spread or target and the rung prices, sizes, and chart lines recompute exactly as they would in the .
Ladder shape — Capped Linear
LONG · base 100.00 (illustrative) · 10 levels stepping down · 1% apart
Targets are stacked above the opening buy because a long grid exits higher than it enters.
Entry ladder
Limit buys below the base · L1 nearest, L10 deepest · every amount in USDT
| Level | Size curve | Entry buyUSDT | Exit sellUSDT | From base% | Sizebase lots | Orders | NotionalUSDT | MarginUSDT | Cum. capitalUSDT | Profit at exitUSDT |
|---|---|---|---|---|---|---|---|---|---|---|
| L1 | 20% | 99.00 | 99.99 | 1.00% | 1.00× | 1 | 100 | 100 | 300 | 1 |
| L2 | 40% | 98.00 | 98.98 | 2.00% | 2.00× | 1 | 200 | 200 | 500 | 2 |
| L3 | 60% | 97.00 | 97.97 | 3.00% | 3.00× | 1 | 300 | 300 | 800 | 3 |
| L4 | 80% | 96.00 | 96.96 | 4.00% | 4.00× | 1 | 400 | 400 | 1,200 | 4 |
| L5 | 100% | 95.00 | 95.95 | 5.00% | 5.00× | 1 | 500 | 500 | 1,700 | 5 |
| L6 | 100% | 94.00 | 94.94 | 6.00% | 5.00× | 1 | 500 | 500 | 2,200 | 5 |
| L7 | 100% | 93.00 | 93.93 | 7.00% | 5.00× | 1 | 500 | 500 | 2,700 | 5 |
| L8 | 100% | 92.00 | 92.92 | 8.00% | 5.00× | 1 | 500 | 500 | 3,200 | 5 |
| L9 | 100% | 91.00 | 91.91 | 9.00% | 5.00× | 1 | 500 | 500 | 3,700 | 5 |
| L10 | 100% | 90.00 | 90.90 | 10.00% | 5.00× | 1 | 500 | 500 | 4,200 | 5 |
What depth costs
Convex only for the first few levels, then linear at cap × base per level. Worst case is a two-term calculation, and depth is genuinely purchasable.
| Levels | Ladder cost | Deepest rung | Entry orders | Cost vs 5 levels | Coverage |
|---|---|---|---|---|---|
| 5 levels | 15.0× | 5.00× | 5 | 1.00× | 5% |
| 10 levels | 40.0× | 5.00× | 10 | 2.67× | 10% |
| 20 levels | 90.0× | 5.00× | 20 | 6.00× | 20% |
| 40 levels | 190× | 5.00× | 40 | 12.7× | 40% |
Read the cost vs 5 levels column as the escalation test. A flat ladder doubles when the depth doubles; anything materially above that is a whose coverage has to be bought rather than simply configured.
| Capital budget | Levels affordable | Adverse move covered |
|---|---|---|
| 10× base | 4 levels | 4.0% |
| 25× base | 7 levels | 7.0% |
| 50× base | 12 levels | 12.0% |
| 100× base | 22 levels | 22.0% |
| 250× base | 52 levels | 52.0% |
Averaging and recovery
With every rung , the volume-weighted average entry is 93.63 against a base of 100 and a deepest rung of 90.00 — so the average sits 64% of the way down the covered range. Getting back to flat from the bottom therefore needs a 4.03% , against 5.00% for a flat ladder of the same depth — 0.97% less work.
| Excursion | Levels filled | Deployed | Average entry | Mark | Unrealised | Bounce to flat |
|---|---|---|---|---|---|---|
| Shallow dip | L1–L3 | 6.00× | 97.67 | 97.00 | -0.04× | 0.69% |
| Half the ladder fills | L1–L5 | 15.0× | 96.33 | 95.00 | -0.21× | 1.40% |
| Full ladder | L1–L10 | 40.0× | 93.63 | 90.00 | -1.52× | 4.03% |
Grows linearly (1×, 2×, 3×…) until the cap (default 5×) and then holds. Predictable averaging with a hard maximum commitment per level, so deep ladders stay affordable.
Where the exposure sits
The last row is the metric that separates modes. Profit for a full cycle is the target of deployed capital in every , so it cannot discriminate. What differs is how much capital has to sit reserved to earn one shallow cycle: this mode 40.0× base to collect 2.5 bps of it when the first rung completes.
Which market pays this curve
Almost any regime, which is what makes it a sensible default for conservative mandates. In a range it averages; in a trend it degrades into a flat ladder rather than into a capital problem.
Grows linearly (1×, 2×, 3×…) but stops increasing once it hits the cap (default 5×). Predictable averaging with a hard maximum commitment per level — very risk-controlled.
The shape of the risk
Coverage exhaustion with mild escalation. Past the cap the carries the same risk as , at cap times the size.
Run it over real history
This is the product's grid backtester, not a summary of one. It fetches public candles for the you pick, rebuilds the ladder on the first candle of the , then applies the engine's own fill, take-profit, and stop-loss rules bar by bar. The caveat block inside the is part of the output — read it before trusting a number.
Instrument
BTCUSD
delta-india
Capped Linear · 10 levels @ 1% · target 1% · 100 USDT / level · 1× · long · no stop
What this does not model
- Exact intrabar ticks. Bullish/doji candles use open → low → high → close; bearish candles use open → high → low → close. Finer timeframes reduce sensitivity to this deterministic assumption.
- Queue position. Limit orders are assumed filled when touched, which flatters a maker grid in fast markets.
- Margin rejection and liquidation. Deep rungs fill here even if the account could not fund them — check the capital requirement.
- Slippage and funding. Only the fee you set above is charged; funding, borrow and slippage are absent.
Run the ladder over real history
The grid is rebuilt anchored on the first candle of the window, then the engine's own fill, exit, refill and stop-loss rules are applied bar by bar. You get the real fill sequence for this configuration on this instrument.
Measured against other modes
First the arithmetic, then the market. The below is computed from the size curves alone; the underneath replays every one of those ladders over the same real candle , with grid_mode as the only variable.
| Mode | Ladder cost | Deepest rung | Break-even bounce | Entry orders | Shallow cycle |
|---|---|---|---|---|---|
| Capped Linear (this mode) | 40.0× | 5.00× | 4.03% | 10 | 2.5 bps |
| Fixed | 10.0× | 1.00× | 5.00% | 10 | 10.0 bps |
| Linear Martingale | 55.0× | 10.0× | 2.38% | 55 | 1.8 bps |
| Exponential Martingale | 2046× | 1024× | 1.10% | 10 | 0.1 bps |
Nothing is precomputed here. Press run and the backtester fetches one candle window and replays 4 ladders across it — identical settings, identical bars, grid_mode as the only difference.
When to use it
- Risk-controlled averaging on any market.
- Conservative mandates that still require an adverse-move response.
- Deep ladders where would be unaffordable.
When to avoid it
- You need recovery from a deep — the ceiling is the , and it binds.
- The cap is set so high that the is simply .
Tuning
- Cap 3–5 is conservative; 10 is assertive; beyond that you are running with extra bookkeeping.
- Because post-cap cost is exactly cap × base per level, buy coverage by adding levels rather than by raising the cap.
This is parametric. The and the settings show only the dial(s) it actually uses, and changing one is a structural — the resting ladder is cancelled and re-placed at the new sizes.
Running it in production
- Record the cap with the . Two capped-linear strategies with different caps are different strategies.
- Watch the deepest level, not the P&L. Depth is the leading indicator; P&L is the lagging one.
- peak committed against the account, weekly. A growth that has never been deep has never been tested.
- Treat every level increase as a capital : adding levels to a growth is not a linear cost.
How it fails
- 1Coverage exhaustionBeyond the cap the ladder is flat, so a long trend still ends with a full position and no rungs left. Depth and the stop are the mitigations.
- 2Cap set too highA cap near the level count removes the ceiling entirely and reproduces 's capital profile.
Claims worth correcting
“Capped linear is too timid to matter.”
It measurably lowers the average entry versus while keeping the worst case a two-term sum. In the it is frequently the best risk-adjusted contender.
Interaction with the rest of the configuration
- Pairs well with deep ladders and trailing, because post-cap rungs are uniform and cheap to re-place.
- Spread sets how fast the ladder consumes depth. Widening it buys coverage for the same level count at the cost of fewer .
- Target sets what each cycle books. Below -trip fees plus slippage, a grid is a fee generator regardless of the .
- The is the only bound on the tail. Without it, the 's worst case is whatever the market does, not what you planned.
Questions this mode raises
- 1Capped linear or capped martingale?Capped linear for conservative mandates and deep coverage; when recovery speed from shallow excursions is the . Run both in the — they are close enough that the decides.
Where these numbers come from
- Sizes and capital:
levelMultiplier/gridModeCurveinlib/grid/gridModes.ts, fromgrid_modes.hppand the Python engine's lot calculator. - Rung and exit prices, , init targets and the stop line:
buildLadderPlan— the same builder the and use. - Backtest , cycles and P&L:
runBacktest/runBacktestSweepover public broker candles, applying the engine's fill, exit, and stop rules. - Price charts: the trading terminal's chart engine, with the ladder drawn through its own price-line API.
Related
- 1.Grid Modes — Overview — The full taxonomy and how to choose
- 2.Capped family — What every curve in this family has in common
- 3.Capital Allocation — Sizing an account to a Capped Linear ladder
- 4.Stop Loss — Bounding this curve's tail
- 5.Reading the Ladder Plan — Verifying the curve before deploying
- 6.Grid Structure — Levels, init batch and base size
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