Sticky States, Brief Transitions: A Markov Map of the Composite Score

Of the 678 state changes the composite score has recorded since July 2010, more than half are reversed within three days. The score crosses a threshold, sits across it for a day or two, and crosses back. Whatever the verdict appeared to say, it then unsays.

Treat the composite as a Markov chain, a discrete-state process where today's verdict is the input and tomorrow's verdict is the output. The dashboard already publishes five verdict states with hard cutoffs (5.5 for STRONG BUY, 4.5 for ACCUMULATE, 4.1 for HOLD, 3.8 for REDUCE, anything lower for TAKE PROFIT). Counting how often the score moves between those states across 5,790 days produces a transition matrix. The matrix is dull in places, surprising in others, and untrustworthy in a few specific cells that ought to be flagged rather than smoothed over.

What follows is the descriptive version of that exercise: what 15 years of daily verdicts have done, with the caveats kept visible.

The Score Lives in Two States

Start by counting days. Since July 2010, the score has read STRONG BUY on 2,635 of its 5,790 days and ACCUMULATE on a further 2,348. Together that is 86% of the historical record. HOLD has been recorded on 166 days, TAKE PROFIT on 598, and REDUCE on only 43.

The lopsided distribution is partly a function of bitcoin's trajectory: the score is built from indicators that flag accumulation opportunities, and a fifteen-year asset in long-term uptrend offers a lot of them. It is also partly an artifact of the verdict thresholds themselves. The HOLD band is the score range 4.1 to 4.5, a corridor 0.4 wide. REDUCE is 3.8 to 4.1, narrower still at 0.3. The composite score's empirical standard deviation is 0.76, which means the score's typical daily wobble is wider than either of the two intermediate bands. The verdict scheme catches buying opportunities, catches profit-taking opportunities, and treats the in-between as an afterthought.

That should affect how the rest of this analysis is read. The transition rows out of REDUCE come from 18 historical episodes. They are reported here because the calculation is well-defined, not because the numbers are dependable.

The 1-Day Matrix Is Nearly Identity

The first cut at the data is the simplest: what fraction of days at state s are followed by a day at state s'? The answer, for the dominant states, is almost always s again.

STRONG BUY days roll into STRONG BUY days 90.8% of the time. TAKE PROFIT into TAKE PROFIT, 91.1%. ACCUMULATE into ACCUMULATE, 86.8%. The composite score is a smoothed quantity, and smoothed quantities do not jump around. A reader who wants to know what the dashboard will probably say tomorrow can read it today and be right nine times out of ten.

The two transitional bands, HOLD and REDUCE, behave differently. Their diagonal probabilities are 66% and 58%. These are not stable regimes. They are thin corridors that the score crosses on its way somewhere else. Most of the off-diagonal mass out of HOLD goes back to ACCUMULATE (22.3% next day). REDUCE is too thinly sampled to characterize confidently; its largest off-diagonal cell is HOLD at 18.6%, on a base of 43 days.

The takeaway from the daily matrix is not the diagonal. It is the rate at which the matrix decays when the horizon is lengthened.

Persistence Half-Life

Extending the horizon to seven, thirty, and ninety days shows how long today's verdict carries information about future verdicts.

The dominant diagonals decay roughly linearly out to thirty days, then more slowly. By ninety days TAKE PROFIT has half-collapsed into adjacent states: a P(TAKE PROFIT | TAKE PROFIT) of 24% is barely above the empirical base rate of 10%. ACCUMULATE and STRONG BUY hold up better, partly because they together cover 86% of the sample and partly because their states are wider score bands less susceptible to drift.

The useful number here is the rough half-life of "memory" in the score: about ninety days, depending on the state. After three months, today's verdict has roughly as much predictive power over the next verdict as the long-run base rate does.

Half of All Transitions Are Noise

Now the uncomfortable finding. Of the 678 state changes recorded across the full history, 351 are reversed within three days. The score moves from A to B, sits in B for a day or two, and returns to A. The composite did not change regimes. It oscillated across a threshold.

That is exactly what the wide standard deviation of the score (0.76) and the narrow widths of the HOLD and REDUCE bands (0.4 and 0.3 wide) would predict. A score that wobbles by half a point on a quiet trading day can flip across the HOLD/ACCUMULATE boundary at 4.5 and back, generating two formal "transitions" that mean nothing. Half of the score's recorded transitions are this kind of churn.

One option is to smooth the verdict with a hysteresis rule: require the score to move past a buffer beyond each cutoff before the verdict flips. That fix introduces a free parameter (how much hysteresis), and any choice is arbitrary. The descriptive analysis here keeps the noise visible rather than papering over it: the daily transition matrix should be read with the understanding that roughly half its off-diagonal mass is threshold artifact.

To see the genuine structure, collapse runs of consecutive identical verdicts into episodes, and ask what each episode transitions to when it ends.

Profit-Taking Recovers in a V, Not a Slope

The full 15-year history contains 679 episodes, runs of consecutive days at the same verdict. Episode-to-next-episode transitions remove the daily diagonal entirely and surface the score's underlying topology.

One row is more interesting than the rest. When a TAKE PROFIT episode ends, it transitions to ACCUMULATE 69.8% of the time, to STRONG BUY 11.3%, to HOLD 13.2%, and to REDUCE 5.7%. The most common path out of profit-taking is not a gradual climb through REDUCE and HOLD on the way back to ACCUMULATE territory. It is a single jump.

That is consistent with how bitcoin's reversals tend to look on the price chart. Bottoms are V-shaped more often than they are U-shaped. The score's lowest band is followed not by a measured recovery through every intermediate verdict but by a fast jump back to "buying opportunity" territory, skipping the middle entirely. There are 53 historical TAKE PROFIT episodes, so this finding is anchored on enough observations to take seriously, even if not enough to bound tightly.

The mirror image is the STRONG BUY exit row. When a STRONG BUY episode ends, it transitions to ACCUMULATE 95.9% of the time, with the remaining 4.1% scattered across the bear states. Tops are not V-shaped. The score grinds down through ACCUMULATE rather than jumping. The asymmetry between bullish and bearish exits is structural in the data, not an interpretation.

The 70% headline needs a sanity check against the unconditional base rate. Across all 679 episode-ending transitions, ACCUMULATE is the destination 45.7% of the time regardless of where the episode came from. The 69.8% conditional from TAKE PROFIT is therefore a 1.5x lift over the base rate, not a 7x one. The more distinctive feature of the TAKE PROFIT exit row is what it avoids: direct jumps to STRONG BUY happen at 11.3% conditional against a 35.7% base rate, a lift of 0.32x. The structural fact is not that profit-taking recovers to accumulation territory. It is that profit-taking almost never recovers directly to high conviction. The score has to step through an intermediate state first.

The HOLD and REDUCE rows of this matrix should be read more cautiously. HOLD has 56 historical episodes and REDUCE only 18. Three of REDUCE's four off-diagonal cells are at 22% or below, drawn from samples of two to eight observations. The pattern looks suggestive (REDUCE exits to HOLD or TAKE PROFIT more often than to the buy side), but at this sample size the rank order of the cells could easily reverse in another fifteen years of data.

Dwell Times Are Short on the Median, Long in the Tail

The other quantity worth reporting is how long the score sits in each state per episode.

Every state has a median dwell of two or three days. The means are much higher because the distributions have heavy tails: a single STRONG BUY episode in early bitcoin's history ran 289 consecutive days, dragging the mean to 10.9. TAKE PROFIT's longest episode ran 104 days. The takeaway is that most regime episodes are brief (a flickering across thresholds, in line with the boundary-churn finding), punctuated by occasional long, stable runs. Both behaviors are present in the same data.

A reader looking at today's verdict and asking "how long will this last?" is asking the wrong question. The median says two or three more days. The mean says a week. The distribution says it could be either of those, or it could be three months. The signal is not predictive at the level a calendar-based question implies.

The Matrix Holds Up Across Macro Regimes

A first-order Markov chain assumes the transition matrix is stationary across time. Bitcoin's history covers a wide range of macro conditions, from a 4.6% M2 contraction in 2022 to a 26.8% expansion at the COVID peak. Stratifying the matrix by macro regime tests whether the unconditional version is hiding state-dependent dynamics. The expectation, set out earlier in the article, was that it would.

The cleanest split is M2 year-over-year growth. Across the joint history of M2 and the daily signals, the YoY series ranges from -4.6% to +26.8% with a median of 5.7%. Splitting daily transitions by whether the from-day sits above or below the median produces two matrices of 2,919 and 2,870 transitions: roughly balanced halves of the history.

The headline finding is that the matrices are nearly identical. Most cells differ by one to four percentage points. STRONG BUY → STRONG BUY reads 92.3% in loose-liquidity periods versus 89.1% in tight (3.2pp gap). HOLD → ACCUMULATE is 18.6% loose versus 25.0% tight (-6.4pp). TAKE PROFIT → TAKE PROFIT is 92.5% loose versus 89.2% tight (3.3pp). These are small differences, not zero, but not the regime-dependent drift the earlier caveat in this article anticipated.

One cell breaks the pattern, and it is the kind of break that demands a footnote rather than a celebration. REDUCE → REDUCE reads 70.0% in loose conditions and 30.8% in tight: a 39pp gap. But the loose figure rests on 21 transitions out of 30 REDUCE-from days in that regime, and the tight figure on 4 transitions out of 13. With samples that thin, the standard error on the loose diagonal alone is roughly 8pp, on the tight diagonal roughly 13pp. The two intervals overlap. The gap is not a finding; it is the dominant statistical noise in the entire stratification.

The negative result is the more important one. The unconditional matrix is doing more work than the original caveat assumed. Either the score is genuinely indifferent to macro conditioning at the verdict-state level of granularity, or M2 YoY is the wrong stratifier. Both are possible. The first is the simpler explanation, and in the absence of a stratifier that produces visibly different matrices, the analysis has to default to it.

What This Analysis Cannot Tell You

Three caveats matter more than the numbers above.

The first is sample size. Fifteen years is four full bitcoin cycles. The transition matrix for the dominant states has thousands of observations behind it. The matrix for REDUCE has 18 episodes. The 7-day cells for the REDUCE row are computed from single-digit counts. Any reader who looks at a transition probability of 0.116 for REDUCE → STRONG BUY at the 7-day horizon should remember that figure represents five observations across fifteen years. Cells with fewer than ten transitions are shown in lighter grey in the matrices above for that reason.

The second is look-ahead bias in the underlying composite. The SHAP weights used to construct the composite score were fit on the full price history. The historical verdict series is therefore computed using a weighting scheme that knew about the future at the time of each historical observation. A user dashboarding the score in 2015 would not have seen the same series the analysis here is based on. The transition matrix is descriptively accurate for the post-hoc series; it is not a snapshot of what a real-time user would have observed.

The third is the Markov assumption itself. A first-order Markov chain says today's state contains everything needed to predict tomorrow's. Bitcoin's actual dynamics depend on cycle position, macro liquidity, and halving proximity, none of which appear in the verdict alone. The M2 stratification above tests the macro-liquidity slice of this concern and finds the matrix mostly intact, but cycle position (only four cycles in the data) and halving proximity (four events) cannot be stratified with statistical power. The Markov assumption survives one test in this article. It is not yet a defended assumption.

What It Can Tell You

Four things, with appropriate confidence levels.

First, the score is sticky on short horizons. If today's verdict is STRONG BUY, tomorrow's verdict will be STRONG BUY about 91 times out of 100. Daily check-ins on the dashboard reveal almost nothing that yesterday's check-in did not already reveal.

Second, half of the score's recorded transitions are not transitions in any meaningful sense: they are boundary noise from oscillation across hard cutoffs. Users acting on every flip of the verdict will be reacting to threshold churn as often as to actual regime change.

Third, when genuine regime changes happen, they are asymmetric, but the asymmetry is in what the score avoids more than in what it heads toward. Profit-taking episodes recover to ACCUMULATE at 1.5x the unconditional base rate, which sounds dramatic stated as 70% and modest stated as a lift. The more distinctive pattern is the avoidance of STRONG BUY: profit-taking jumps directly to high conviction at only one-third the base rate. The score takes an intermediate step on the way back up. This finding is also the one most exposed to the look-ahead caveat, since the indicators that flag profit-taking overlap with those that flag accumulation.

Fourth, the matrix is mostly stable across macro liquidity regimes. Splitting the history by M2 YoY changes most cells by one to four percentage points. That is a weaker test of stationarity than splitting by cycle position would be, but cycle position cannot be split with four data points.

The transition matrix is a description of where the score has been. It is not where the score is going. Anyone who reads it as a forecast is misusing it. Anyone who reads it as a map of the score's own behavior, with the gaps and unreliable cells visible, will find it modestly useful and unsurprising in most places.

The interesting cells are the ones where the data is thin enough to be wrong.