QuantumPools · Deep diveTime in Range

LP education · how long a range lasts

How long will your range hold? The square law

My narrow range keeps going out. How long should a width hold the price?

The short version

Same 3% daily wiggle: the app's starting width (17.35%) holds price 7.11 days on average. The narrowest width (2.02%) holds it 2.67 hours.

Average hold = (h ÷ σ)² h ≈ distance from price to your edge σ = daily wiggle · price starts mid-range

One key variable: h, how far price must travel to your edge. At App start it's 0.08 (about 8%). With an example 3% wiggle: (0.08 ÷ 0.03)² = 7.11 days. A jumpier pair holds for less.

Small print: h = ½ × ln(1 + width). Standard random-walk math, no trend. Illustrative, not a promise.

1 · The wandering dot

Same wiggle, different stopwatch

One price path, two bands. The thin one loses price far sooner than its width suggests.

Two bands on one price scale follow the same illustrative price path. The Narrowest 2.02% band loses the price early and its stopwatch stops at out. The App start 17.35% band still holds the price at the end. Narrowest 2.02% price App start 17.35% ready ready ← lowerstarthigher →
Illustrative path

Same wiggle. The narrow band loses the price first.

2 · The square law

Twice the ticks, four times the hold

Hold time grows with the square of h. Double the ticks (1,600 → 3,200) and 7.11 days becomes 28.44 days.

Ticks are the app's tiny price steps, and they multiply. Each 200-tick rung is about 2%, so twice the ticks is 37.71%, not 34.70%.

17.35% → 7.11 days average, not a schedule

Table view
TicksWidthhAverage hold (σ 3%)
2002.02%0.01002.67 hours
4004.08%0.020010.67 hours
1,60017.35%0.08007.11 days
3,20037.71%0.160028.44 days
4,80061.60%0.240063.99 days
Halve your ticks and you'll leave about four times as often.

3 · The wiggle

Twice the wiggle, a quarter of the hold

Same 17.35% width, three wiggles. How jumpy the pair is matters as much as your width.

Wiggle 1.5% a day
28.44 days
Wiggle 3% a day
7.11 days
Wiggle 6% a day
1.78 days

Illustrative wiggle, not DELL's measured volatility

4 · The trade

Narrow earns more per dollar, for far less time

Per dollar, Narrowest sits 7.9× thicker at the price than App start (201× vs 25.5× in Configuration's range designer). Thicker means a bigger fee share while price is inside. The catch: it holds price 64× shorter.

Narrowest 2.02% vs App start 17.35% · log scale

Table view
Narrowest vs App startFactorFrom
Thickness per dollar7.9× thicker201× ÷ 25.5× (200.51 ÷ 25.50 = 7.86)
Time in range64× less(0.0800 ÷ 0.0100)² = 64
Narrow trades time for fee share. With Auto Snuggle on, the snuggle follows price when it leaves.
Watch a snuggle →

5 · Where the clock starts

The law assumes a centred start

It times price from the middle of your range. After a snuggle, the new range sits just past price with one token, earning nothing until price enters.

Centred start

Centred start: price in the middle of the band price in the middle

The formula applies.

After a snuggle

After a snuggle: price just past one edge of the band price just past one edge

The clock starts when price walks in, at an edge.

Edges snap to 200-tick rungs, so a fresh range can start up to a rung off-centre and leave sooner.

6 · Worked example

Three widths, one wiggle

σ = 3% a day, price starting mid-range.

Narrowest · 200 ticks

width 2.02%
edges +1.00% / −0.99%
h = 0.0100
(0.0100 ÷ 0.03)² days
= 2.67 hours

App start · 1,600 ticks

width 17.35%
edges +8.33% / −7.69%
h = 0.0800
(0.0800 ÷ 0.03)² days
= 7.11 days

Twice the ticks · 3,200

width 37.71%
edges +17.35% / −14.78%
h = 0.1600
(0.1600 ÷ 0.03)² days
= 28.44 days

Illustrative, not a promise.

7 · Try it

Try your width

Pick a width and a wiggle. See what doubling either one does.

1,600 ticks · 8 rungs of 200
A typical day's move, up or down. 3% is just an example.
Average hold
7.11 days
170.65 hours · price starting mid-range
Twice the ticks
28.44 days
37.71% width
Twice the wiggle
1.78 days
σ 6% a day
Edges from price
+8.33% / −7.69%
room each way before price leaves
Key variable h
0.0800
≈ distance to your edge

Try 2.02: the hold drops to 2.67 hours. Illustrative, not a promise.

Honest limits

A ruler, not a forecast

Useful for

  • Comparing widths on one scale.
  • Seeing how much jumpiness matters.
  • Hours or weeks? A quick sense.

Not for

  • Predicting your next exit. Real prices trend and jump.
  • Certainty. Many exits come sooner, some much later.
  • Fixed inputs. σ is a guess, and it changes.
  • Off-centre starts, after rung snapping or a snuggle.

What to do with this

Now you can size your range on purpose: pick the time you want, then the width.

Narrowest2.02%2.67 h at 3%14.4 min at 10%
App start17.35%7.11 days at 3%15.36 h at 10%
Twice the ticks37.71%28.44 days at 3%2.56 days at 10%

Average hold, price starting mid-range, from the formula. Illustrative, not a promise.

DELL has moved more than 3% a day. Put your pair's wiggle in the calculator above; the app's presets are tuned to the pool's measured volatility.

Compare widths in the range designer → Configuration
Next up Your range is a slow-motion order → When price runs through your range, what price did you trade at? While you're in range Your slice of the fee pie → Why a thicker range takes a bigger fee share while price is inside.

Educational content, not financial advice. Providing liquidity can lose money; nothing here promises returns.