The Lab

How we tested

• Bitcoin, Ether and Solana, every minute from October 2022 to September 2026: 48 months. The same coins, months, fees and bot rules as our study of rung counts, so the two line up.
• A long grid set fresh each month, with 8 or 20 rungs, on futures at a 0.02% fee, paying or receiving funding.
• The ladders:
  • fixed: 15% under the starting price to the same distance over, or 30%;
  • ATR gaps: each gap 0.5, 1 or 2 times the ATR, centred on the price.
• Re-centring:
  • none: the range stays all month;
  • up: when the price climbs one gap over the top, a new range is set around it. By then every rung has sold, so this costs nothing. Our own bots already do this. We call it the slide.
  • both ways: also when the price falls one gap under the bottom. Then the coins held are sold first, at the market fee.
• Fairness:
  • each setting is compared month by month with the fixed 15% grid of the same rung count, in each two-year half;
  • each month is also run 20 times with its hours shuffled;
  • the bar a setting had to clear was fixed in advance.

The maths, step by step

1. The ATR as a share of the price. The ATR ("average true range") is J. Welles Wilder's, from 1978. We use a simple form of it: average the last 14 days' high-minus-low, each divided by that day's close.

• Example: days that ran 90 to 110 and 95 to 105, both closing at 100, are 20% and 10%. Their average is 15%.

2. An ATR ladder. With an ATR of 10% and a gap of 1 ATR, each rung is 1.1 times the one under it. Three rungs around 100 sit at 100 ÷ 1.1 = 90.91, 100 and 110, and the top rung sells at 121.

3. When it re-centres up. One gap over the top: 110 × 1.1 = 121. At 121 a new range is set around the price.

4. Comparing with the fixed grid. For each month, take this grid's result minus the fixed grid's. Average those differences, and divide their spread by √48 for the standard error. The bar asked for:

• an average gain over twice its standard error;
• a gain in both halves;
• a gain bigger than in at least 18 of 20 shuffled versions;
• no more months wiped out at 3x leverage.

What we found

1. Re-centring up helps, a little and every time. Against the same grid left alone, it never lost more than 0.01% a month on any coin, rung count or ladder. It helped most on the narrow range, which the price leaves more often.

• Bitcoin at 20 rungs and Ether at both counts cleared the bar. They gained in both halves and beat 19 or 20 of 20 shuffles, with no more months wiped out at any leverage.
• Solana gained the most, but unevenly: in the second half, −0.29% and +0.16% a month.
• It barely changes how much coin the grid holds (Ether: 25% to 26%). The gain comes from trading again after a break-out, instead of sitting in cash for the rest of the month.

2. Re-centring on the way down buys safety, not profit.

• It cut Solana's worst month from −34% to −15% (8 rungs), and the months wiped out at 10x (Solana 38% to 33%, Ether 17% to 12%).
• But its gain wasn't steady. At 20 rungs it did worse than the fixed grid on Ether (−0.15% a month) and Solana (−0.39%).

3. Setting the gaps by the ATR didn't beat a fixed range.

• On Bitcoin, every ATR ladder that stayed put did worse than the fixed grid: −0.20% to −0.37% a month.
• On Ether and Solana the wider ATR ladders did better. But they held much less coin (7–17% of the money, against 18–27%). That is the effect of a wider range, which our earlier studies already found: less risk, not more skill.

4. Against luck. 13 of 90 coin-settings beat 19 or 20 of their shuffles, where luck alone gives about 9. Only 4 cleared the whole bar, and all 4 were re-centring up.