+1 d
Median return +0.17%Completed observations: 22
- Middle 50%
- -4.36% … +3.57%
- Positive returns
- 55%
The Sandbox · Sigma Moves
Closed-period price moves, measured against their own history. One engine. Five markets. No forecasts.
Latest closed period
The Sandbox's latest move against its own history.
SAND Exceptional
+53.54%
+10.83σ
Not previously observed in 5 years
0 comparable moves / 1,826 observations
What happened afterwards
All history-qualified moves of at least 2.5σ. Results after the event are descriptive statistics, not trading instructions.
+7 d
Median return -1.34%Completed observations: 21
- Middle 50%
- -13.38% … +2.61%
- Positive returns
- 38%
+30 d
Median return -6.49%Completed observations: 21
- Middle 50%
- -21.28% … +10.03%
- Positive returns
- 43%
Every rare move, in context
Instrument: binance:spot:SANDUSDT
| Date | σ | Move | Observed rarity | +1 d | +7 d | +30 d |
|---|---|---|---|---|---|---|
| 2 Oct 2026 | +10.83σ | +53.54% | Not previously observed in 5 years0 comparable moves / 1,826 observations | +8.56% | — | — |
| 21 Aug 2026 | +3.60σ | +12.22% | About once every 107 days17 comparable moves / 1,826 observations | -8.02% | -20.05% | -17.60% |
| 19 Aug 2026 | +2.78σ | +7.27% | About once every 46 days40 comparable moves / 1,826 observations | +5.74% | +2.61% | -6.49% |
| 20 Jun 2026 | +5.07σ | +17.92% | 4 times in 5 years4 comparable moves / 1,770 observations | -7.65% | -21.86% | -21.28% |
| 5 Jun 2026 | -2.58σ | -9.42% | About once every 36 days49 comparable moves / 1,755 observations | -1.87% | -1.11% | -2.48% |
| 2 Jun 2026 | -4.46σ | -10.84% | About once every 250 days7 comparable moves / 1,752 observations | -0.50% | -17.85% | -21.74% |
| 5 Feb 2026 | -3.47σ | -19.12% | About once every 82 days20 comparable moves / 1,635 observations | +9.28% | +6.73% | +0.51% |
| 17 Jan 2026 | +4.72σ | +20.82% | About once every 269 days6 comparable moves / 1,616 observations | -5.19% | -1.06% | -41.38% |
| 13 Jan 2026 | +2.99σ | +10.11% | About once every 54 days30 comparable moves / 1,612 observations | +1.76% | +10.06% | -32.96% |
| 10 Oct 2025 | -10.25σ | -29.42% | Not previously observed in 4 years0 comparable moves / 1,517 observations | +3.68% | +7.15% | +10.03% |
| 23 Jul 2025 | -3.25σ | -10.98% | About once every 63 days23 comparable moves / 1,438 observations | -1.81% | -5.08% | +0.36% |
| 23 Jun 2025 | +2.72σ | +9.98% | About once every 40 days35 comparable moves / 1,408 observations | +0.04% | -5.98% | +18.62% |
| 8 May 2025 | +3.81σ | +14.72% | About once every 124 days11 comparable moves / 1,362 observations | +6.23% | +1.97% | -11.88% |
| 6 Apr 2025 | -2.67σ | -11.26% | About once every 37 days36 comparable moves / 1,330 observations | +3.23% | +11.01% | +16.43% |
| 3 Mar 2025 | -3.16σ | -17.01% | About once every 59 days22 comparable moves / 1,296 observations | +0.30% | -13.98% | -14.75% |
| 2 Mar 2025 | +2.58σ | +14.09% | About once every 34 days38 comparable moves / 1,295 observations | -17.01% | -25.58% | -24.01% |
| 24 Feb 2025 | -2.89σ | -13.27% | About once every 43 days30 comparable moves / 1,289 observations | +0.79% | -1.34% | +1.34% |
| 2 Feb 2025 | -3.01σ | -15.73% | About once every 53 days24 comparable moves / 1,267 observations | +5.57% | -8.06% | -26.22% |
| 24 Nov 2024 | +6.67σ | +76.44% | 1 times in 3 years1 comparable moves / 1,197 observations | -9.50% | -12.94% | -17.15% |
| 16 Nov 2024 | +7.35σ | +35.37% | Not previously observed in 3 years0 comparable moves / 1,189 observations | -11.71% | +11.02% | +81.63% |
| 25 Oct 2024 | -2.51σ | -8.63% | About once every 32 days37 comparable moves / 1,167 observations | +1.85% | +0.33% | +217.58% |
| 18 Oct 2024 | +2.51σ | +8.66% | About once every 32 days36 comparable moves / 1,160 observations | -0.07% | -13.38% | +23.99% |
The number has a method behind it
Sigma measures the size of a log return relative to volatility estimated before the period. Rarity is counted from actual historical standardized moves, not inferred from a normal distribution.
σt = ln(Ct / Ct−1) / vtvt ← t−1, t−2, …
Volatility adapts to the market regime with EWMA (λ = 0.94 for daily and weekly observations). Current-period returns are excluded. Each historical σ uses its own prior volatility.
Both directions count toward rarity. Reference history spans up to five years. A period with no prior exceedances is labelled unprecedented in the observed sample; it is never given an invented recurrence interval.
Stock observations use split-adjusted price returns, without dividend reinvestment. Commodities are explicitly labelled ETF price proxies; they do not represent spot commodity prices.
Questions behind the sigma
What does a 3σ move mean?
The period log return is three times the volatility estimated from earlier periods. Sigma is signed: negative for declines and positive for rises.
Why not calculate rarity from a normal distribution?
Market returns have heavy tails and changing volatility. We count actual past absolute sigma exceedances for the same instrument and period.
Does “once every 200 days” predict the next event?
No. It is the number of historical observed periods divided by comparable moves. Events can cluster and the market regime can change.
How much history is required?
At least three years of valid standardized observations, after a one-year volatility warm-up. This normally requires approximately four years of source history.
Are all instruments directly comparable?
The engine is shared, but each instrument has its own prices, calendar, volatility and reference sample. Commodity cards use explicitly labelled ETF proxies.
What happens on quiet days?
The page shows the largest covered standardized move, the complete rarity scale and recent records. Missing data is reported separately from market calm.
For information only. Historical observations are not investment advice and do not predict future moves. A rare move can be followed by another rare move.