Author: Mario Schröck, Glassnode; Compiled by: Tao Zhu, Golden Finance
Introduction
Bitcoin's transparent blockchain allows for detailed analysis of token movements and holder behavior. By examining the age of unspent transaction outputs (UTXOs) and their spending probabilities, we gain insights into the dynamics of the Bitcoin ecosystem. This paper explores the power law relationship between UTXO age and buying/selling probabilities, revealing predictable patterns of holding and spending tokens over time.
Why this analysis is important
Understanding the UTXO spending behavior of Bitcoin provides powerful insights for traders, investors, and analysts. By revealing predictable patterns that control dormant currency, you can:
Enhance investment strategies: Predict potential liquidity shifts and better gauge market sentiment.
Improve on-chain analysis: Utilize a mathematical framework to complement traditional LTH/STH metrics.
Predict holder behavior: Determine when tokens might re-enter circulation, informing the timing of trades or decisions.
Whether you are optimizing trading algorithms, analyzing market trends, or refining investment strategies, this framework can provide you with a clear, data-driven advantage in the Bitcoin ecosystem.
What are UTXOs and spending probabilities?
At the core of the Bitcoin blockchain is the UTXO model. UTXO stands for Unspent Transaction Output—essentially, Bitcoins that have been received but not yet spent. Each Bitcoin transaction consumes existing UTXOs as inputs and creates new UTXOs as outputs. These UTXOs can be thought of as tokens stored at specific addresses, waiting to be used in future transactions.
By analyzing the duration of these UTXOs (the number of days since creation), we can infer the behavioral patterns of holders in the network. A fundamental concept in this analysis is spending probability, which measures the likelihood of a UTXO with a given age being spent on any given date. This metric quantifies how Bitcoin moves within the ecosystem and how holder behavior evolves.
Methodology
Dataset and UTXO counts
Our analysis is based on Bitcoin UTXO data from 2015 to November 2024. Each day during this period, we calculate the number of UTXOs for each possible coin age, from one day to 10 years (approximately 3,650 days). We limit the maximum coin age to 10 years to avoid inherent noise in extremely old UTXO data.
Calculating spending rates
To determine spending probabilities, we compare the number of UTXOs of a specific coin age on a given day with the number of UTXOs of the next higher coin age the following day. The consumption portion is calculated as follows:
Spending score = 1 - (Number of UTXOs aged N for T days) / (Number of UTXOs aged N-1 for T-1 days)
This formula represents the proportion of UTXOs aged N-1 that do not appear as UTXOs aged N the next day, indicating that they have been spent.
We then calculate the average spending rates for each age group across the entire dataset, along with the standard error of the mean. Figure 1 visually displays the average spending rates segmented by coin age.
Power law dynamics in log-log space
To better understand the relationship between UTXO age and spending rates, we plotted the data in log space. This transformation is beneficial because power law relationships appear as a straight line in log-log space, making it easier to identify and analyze. Figure 2 shows the double-logarithmic plot of spending rates.
Fitting the power law
We perform linear regression on log-log data to quantify the power law relationship. We use weighted least squares for the regression, where the weights are proportional to the square of the UTXO count divided by the square of the mean standard error. This weighting accounts for variations in the reliability of data points due to differences in sample size and variance.
The slope of the regression line corresponds to the power law exponent, indicating how quickly the probability of consumption decreases with age. Figure 3 shows the fitted regression.
Analyze residuals to evaluate fit quality
To evaluate the fit quality of the power law across different coin age groups, we analyze the residuals, which represent the differences between the observed average spending rates and our model's predicted values. Plotting the residuals helps us identify patterns or systematic biases in the model. Figure 4 shows the functional relationship of residuals with UTXO coin age.
We observe minimal residuals for UTXOs around 200 days old, indicating that this cohort has high predictability. This aligns with the gradual transition from short-term holders (STH) to long-term holders (LTH). An S-shaped function models this transition to yield a smooth shift in holder behavior. The inflection point of this transition is marked at 155 days, representing a 50-50 ratio between STH and LTH classifications. At around 200 days, the completion rate of the transition from STH to LTH is 99%.
Our analysis indicates that the power law model fits STH tokens almost perfectly until they fully transition to LTH. For LTH tokens aged 3-4 years (the second transition zone), the model still holds well (with minor deviations). These deviations suggest that the spending probabilities for the mid-term LTH group are slightly higher than those predicted by the model.
However, for ultra-long-term holders (ULTH)—tokens older than about one halving cycle—we observe more significant deviations from the model. Specifically, the observed spending probabilities are lower than those predicted by the power law. This suggests a greater tendency to hold these tokens, possibly due to strong holding beliefs or the likelihood that some of these tokens have been lost.
Power law arranged by time
We examine whether the power law dynamics of token spending probabilities change over time from a different perspective. Instead of averaging the UTXO counts for each coin age across all dates, we track cohorts of UTXOs born on the same day. Based on these date groups, we can analyze how the spending rates of tokens evolved across different periods in Bitcoin's history.
For each cohort, we calculate the consumption rate day by day as the cohort's coin age increases. Then, we perform linear regression on the log-log spending probabilities for each group. Ignoring data groups with survival times less than 10 days results in about 3600 remaining groups and corresponding linear regressions.
The coefficient of determination (R2) for each regression indicates how well the power law model fits the data for that cohort. The slope of each line helps us understand the rate at which the consumption rate decreases as the age of the coin increases. Figure 5 plots the R2 values and line slopes over time for each date group.
Overall, the power law is highly applicable across different dates, confirming the consistency of this dynamic over time. However, specific periods exhibited lower fit quality, despite no clear correlation with price fluctuations during those times. We observed that throughout 2019, spending probabilities (with smaller slope values) were extended in advance. One possible explanation is that investors who bought during the -80% drop from the 2017 ATH were in it for the long term, thus their spending rate was higher than usual.
Impact on on-chain analysis
These findings provide a continuous perspective on coin age and spending probabilities, complementing existing LTH/STH frameworks. The power law relationship embodies the gradual shift from active trading to long-term holding.
Notably, the model fits younger tokens almost perfectly and still holds well for tokens around four years old (with only minor deviations). Beyond this coin age, model deviations become more significant, indicating that other factors may affect the spending behavior of ultra-long-term holders.
A power law with a slope close to 1 provides a clear and intuitive heuristic: for every tenfold increase in token age, the probability of it being spent decreases by roughly ten times. The approximate model values in the table illustrate this.
This predictable decay in spending probabilities highlights a behavioral pattern: younger tokens are actively traded or speculated upon, while older tokens become increasingly dormant over time. By adopting this continuous perspective, analysts and investors gain a richer understanding of the gradual decline in spending activity as tokens age, enhancing interpretations of on-chain data and investor behavior.
Quantifying supply hypotheses
Based on our data, we evaluate a simple predictive heuristic:
If the UTXO is less than 7 days old, it is assumed that the UTXO will be spent on that day. Otherwise, it is assumed that it will not be spent.
Using historical data, the accuracy of this heuristic approach reaches up to 98%, indicating that it correctly predicts whether UTXOs will be spent in the vast majority of cases. However, due to the imbalance in the dataset, high precision numbers can be somewhat misleading—there are large numbers of unspent UTXOs on any given day.
Summary
Our analysis suggests that Bitcoin UTXO spending behavior is governed by strong power law dynamics, with the likelihood of older tokens being spent gradually decreasing. The power law relationship fits younger tokens almost perfectly, and still holds well for tokens up to four years old (with only minor deviations). For ultra-long-term holders with coins older than this, the deviation from the model becomes more pronounced, indicating that spending probabilities are even lower than predicted by the model. This suggests that other factors, such as strong holding beliefs or lost tokens, may influence the spending behavior of these oldest UTXOs.
This finding enhances the existing LTH/STH framework by providing a continuous mathematical perspective on the gradual transition from active trading to long-term holding. The power law offers a precise heuristic: for every tenfold increase in token age, the probability of it being spent decreases by roughly ten times. This predictable decay in spending probabilities provides valuable insights into investor behavior and token dormancy over time.
As Bitcoin continues to evolve, the power law model provides a mathematically-based framework for on-chain analysis, enabling deeper understanding of UTXO lifecycle dynamics.
