At 100x, the Median Position Dies in 2 Hours — With Zero Directional Edge

Most of what I've written on this blog answers "how far can price move before I'm liquidated." This one answers a different question: "how long, in calendar time, before that move actually happens" -- if I assume I have no edge at all. No trend read, no setup, nothing. Just a coin flip and volatility doing what volatility does. The result: at 100x, the median position doesn't survive two hours. Not because the trade was wrong. Because the barrier is that close and volatility doesn't care about your thesis.

The model, in one paragraph

Price is modeled as a driftless random walk -- zero expected direction, which is the honest assumption for "no edge." Daily volatility is set to 3%, roughly BTC's typical realized level (annualizes to about 57%). The liquidation buffer is the same formula I've used before: 1/leverage − maintenance margin rate, with a 0.4% maintenance margin rate on a major pair. The probability that the price path has touched that barrier by day N is a standard result from random walk theory -- the reflection principle: P(breach by day N) ≈ 2 × (1 − Φ(B / (σ × √N))), where Φ is the standard normal CDF. It answers "when does the path first touch the line," not just "where does it end up on day N" -- which matters, because a position can get liquidated on day 2 and still look fine on day 7's closing candle.

Buffer by leverage

Breach probability by holding period

Here's the probability that a position gets liquidated at some point within the first N days -- again, assuming zero edge, pure volatility:

Read the 20x row slowly. By day 7, better than a coin flip's chance the position is already gone -- and that's with no directional view at all, just volatility crossing a 4.6% line. This is why I stopped treating "20x isn't that aggressive" as a safe assumption for anything I plan to hold longer than a few hours.

The number that actually surprised me: median survival time

Flipping the table around -- solving for the day where breach probability crosses 50% -- gives a single number per leverage tier that's easier to feel in your gut than a probability table:

Between 25x and 50x, median survival drops from 3 days to 15 hours. That's not a gentle slope, it's a cliff, and it sits exactly where a lot of traders think they're still in "aggressive but reasonable" territory. At 100x you'd need to be watching the position more or less continuously just to see it happen, because the median outcome is gone before a single daily candle closes.

Does the model actually hold up against real data?

I didn't want to publish a clean formula and call it a day, so I checked it against a completely separate piece of work: my 120-day empirical candle replay, where I simulated 2,486 real entries on actual Bybit price history rather than a theoretical random walk. That backtest found 20x longs liquidated 59% of the time within a one-week hold. This zero-edge random-walk model, built from nothing but a volatility number and a formula, predicts 56.2% for the same leverage and horizon. A 2.8 point gap between a pure math model and real market data is closer than I expected going in -- and it's a decent sign that the volatility assumption is doing its job, not that real markets are somehow "nicer" than the math suggests.

What this changes for me practically: I already don't run size above 20x, but I used to think of that cap in terms of price distance -- "I can survive a 4.6% move." This model reframes it in terms of time -- "the median 20x position has about five days before volatility alone finds it, with zero credit for being right." Five days is roughly how long I want to be able to walk away from a screen. Above that leverage, I'm not sizing a trade anymore, I'm sizing how many hours I'm willing to babysit it. Run your own volatility assumption and leverage against the time to liquidation calculator.