What Is a Z-Score When One Bitcoin Close Scores Minus 1.07 and Plus 0.88?

Bitcoin's Saturday 12 September close of 77,284.92 scores minus 1.07 on a 20-session z-score and plus 0.88 on a 50-session one, each a count of standard deviations from average. It's the arithmetic inside John Bollinger's own band definition, run here on Phemex spot closes, and the lookback you pick decides the sign.

Every close in the 20-session window from 24 August came after Bitcoin's 18-21 August jump, and those 20 closes average 78,597.06. The 50-session window from 25 July still carries 25 closes from before the price climbed from 64,726.53 on 18 August to 78,338.02 on 21 August. Across the 225 Phemex spot pairs with a 12 September bar and 200 sessions of history, 83 flip sign between the same two lookbacks.

Bitcoin Z-Score at a Glance

How Does the Z-Score Formula Work on a Bitcoin Close?

The z-score formula takes a close, subtracts the average of every close in your window and divides that gap by the standard deviation of the same closes. A reading of zero means the close matches its average, and minus 1 means it's one standard deviation below it. If you searched for the Altman Z-score, that's a separate model that grades a company's bankruptcy risk from its financial ratios, and it has nothing to do with price.

Two choices set the answer, the lookback and the way you take the standard deviation. The population basis divides the squared gaps by the number of closes, while the sample basis divides by one fewer. That makes the sample figure slightly larger and every score slightly smaller. Our guide to standard deviation works through both calculations.

Method: every score on this page uses the sample basis on Phemex spot daily closes, ending with the Saturday 12 September close. John Bollinger's page says his bands use the population calculation, and on that basis the same close scores minus 1.10 over 20 sessions and plus 0.885 over 50. Switching basis rescales a score by 2.6% on 20 sessions and 1% on 50, and it never changes the sign.

Bollinger Bands lie two population standard deviations either side of a 20-period average, so a band touch is a z-score of plus or minus 2. On 12 September the 20-session bands ran from 76,214.99 to 80,979.12, and Bitcoin's %b reading came in at 0.225. Subtract 0.5 from that and multiply by four, and you get minus 1.10, the population z-score again. That's because %b measures the same thing on a scale that runs from zero at the lower band to one at the upper. The Phemex guide to Bollinger Bands covers trading around those lines.

Why Does the Lookback Period Flip the Bitcoin Z-Score?

Change the z-score lookback period and you change the question the score answers. Twenty sessions compare the close with the market since 24 August, and 50 sessions reach back to 25 July, which on 12 September means two different markets.

The 20-session window is the tight one. Its closes ran from 76,568.88 on 10 September to 81,268.26 on 3 September, a range of 4,699.38, and 17 of the 20 finished above the 12 September close. A standard deviation of 1,221.97 turns the 1,312.14 gap under the average into minus 1.07.

The 50-session window opens on 25 July, and its first 25 closes come from a market that never closed above 65,399.99. Those older closes drag the average down to 70,942.64 and stretch the standard deviation to 7,239.39. So the close that looks soft on 20 sessions reads 0.88 standard deviations rich on 50.

That 70,942.64 is also Bitcoin's 50-day simple average, which crossed above the 200-day on 8 September on Phemex spot closes. At the anchor it ran 1.17% above the 200-day's 70,125.12. Over the full 200 sessions from 25 February the close scores plus 1.10. Our explainer on the Bitcoin golden cross sets out why traders watch that pair of averages so closely.

What Does a 50-Session Z-Score Measure After a 21% Step?

It measures the step. Bitcoin closed at 64,726.53 on 18 August and at 78,338.02 on 21 August, a 21.03% climb in three sessions. The 50-session window holds 25 closes on each side of that move. The 25 closes from 25 July to 18 August averaged 63,987.80 and never left a band from 62,822.94 on 1 August to 65,399.99 on 26 July. The 25 from 19 August to 12 September averaged 77,897.48. Score the 12 September close against that second half alone and it comes out at minus 0.26, below its average and on the same side as the 20-session reading.

So the plus 0.88 records a regime change and tells you very little about a stretched price. On the population basis, about 94% of the 50-session variance comes from the distance between the two halves' averages. Only the remaining 6% reflects how prices moved inside each half.

A standard deviation inflated that way also overstates volatility if you read it as one. Our guide to historical volatilitybuilds that reading on a moving average and the standard deviation around it, so run the same window check before you trust it.

The distortion has an end date. The 50-session window that closes on 7 October runs from 19 August and holds no close from before the step. From that bar on, the 50-session score describes a single market.

How Many Phemex Spot Pairs Flip Z-Score Sign Between 20 and 50 Sessions?

Bitcoin has plenty of company. I ran both lookbacks on all 234 Phemex spot pairs with a bar on 12 September. I kept the 225 that carry at least 200 sessions of history, so each one also has a 200-session score.

Eighty-three of those 225 flip sign between 20 and 50 sessions. Seventy-eight follow Bitcoin's pattern, below the 20-session average and above the 50-session one, and five run the other way. The count is 83 on either basis, since the choice of standard deviation can't move a close across its own average.

Conflux (CFX) is the edge case. Its 12 September close of 0.0475 lands exactly on its 20-session average of 0.0475, a z-score of zero. With no sign to flip, it stays out of the 83.

That's more than a third of the board reading cheap on one lookback and rich on the other, and a single-lookback screen picks one answer without saying so.

How Do You Use a Z-Score in Trading Without Misreading the Window?

A z-score trading rule for a position you'll hold a week or two belongs on a short window such as 20 sessions. A view measured in months belongs on 100 or 200 sessions, where Bitcoin's 12 September close scores plus 1.56 and plus 1.10.

Before you trust any score, look at the window's own range. If the lowest and highest closes land on either side of a single jump, as in Bitcoin's 50-session window, the average falls between two markets and describes neither. Drawing that average on the chart shows the problem at a glance, and our guide to moving averages explains how the length of an average changes what it tracks.

The Federal Reserve meets on 15-16 September with a Summary of Economic Projections. Its 29 July statement held the target range at 3-1/2 to 3-3/4 percent, and all three dissenters preferred a quarter-point rise. A close from that meeting weighs one part in twenty on the 20-session window and one part in fifty on the 50-session one, so the short score reacts faster. The 3 September high of 81,268.26 leaves the 20-session window on the 23 September bar, and any close below it pulls the 20-session average down.

On a leveraged position the score marks a location and never works as a trigger by itself. Bitcoin's 20-session standard deviation of 1,221.97 comes to about 1.6% of the 12 September close, so a two-standard-deviation band on that window spans roughly 3.2% each way. At 20x, a 3.2% move against you costs about 64% of the initial margin before fees.

Frequently Asked Questions

Does a z-score of plus or minus 2 equal a Bollinger Band touch?

On the population basis Bollinger uses, it does. On the sample basis a 20-session band touch reads about 1.95, because the sample standard deviation runs slightly above the population figure over 20 closes.

At what lookback does Bitcoin's 12 September close turn positive?

Every lookback from 4 to 26 sessions scores it below average on the sample basis, and every one from 27 sessions to 200 scores it above. The 25-session window holds exactly the post-step closes from 19 August, which is why it lands on the same minus 0.26.

How many of the 225 pairs score beyond plus or minus 2 on 20 sessions?

Nine of them clear that line on the sample basis. Three score below minus 2 and six above plus 2, and the most stretched pair reads plus 3.78.

Bottom Line

A z-score is a claim about a window. Bitcoin's 12 September close read cheap against the market it trades in and rich against a market that ended on 18 August. The sign you see depends on which of those two markets you let into the average.

From the 7 October bar every close in the 50-session window postdates the jump. A positive score on that bar will mean the close is above the average of everything Bitcoin printed from 19 August. That's the reading the plus 0.88 of 12 September looks like it gives and can't.

Disclaimer: This article is for informational purposes only and is not financial advice. Cryptocurrency trading involves substantial risk. Always do your own research before making investment decisions.