Author: Mario Schröck, Glassnode; Compiled by: Tao Zhu, Jinse Finance
Preface
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 can gain deeper insights into the dynamics of the Bitcoin ecosystem. This article explores the power law relationship between UTXO age and buying/selling probabilities, revealing predictable patterns in how tokens are held and traded over time.
Why this analysis is important
Understanding Bitcoin's UTXO spending behavior provides powerful insights for traders, investors, and analysts. By revealing predictable patterns in currency dormancy, you can:
Enhanced investment strategies: anticipate potential liquidity changes and better gauge market sentiment.
Improved on-chain analysis: leverage a mathematical framework to complement traditional LTH/STH metrics.
Predicting holder behavior: determine when tokens may 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, Bitcoin blocks 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 held at specific addresses, waiting to be used in future transactions.
By analyzing the duration of these UTXOs (days since creation), we can infer patterns of holder behavior in the network. A fundamental concept in this analysis is the spending probability, which measures the likelihood that a given UTXO will be spent on any given date. This metric quantifies how Bitcoin moves within the ecosystem and how holder behavior evolves.
Methodology
Datasets 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 age, from one day to 10 years (approximately 3,650 days). We limit the maximum age to 10 years to avoid inherent noise in extremely old UTXO data.
Calculating spending rates
To determine spending probability, we compare the number of UTXOs of a specific age on one day to the number of UTXOs of the next higher 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 rate for each age group across the entire dataset, along with the standard error of the mean. Figure 1 visually displays the average spending rates broken down 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 logarithmic space. This transformation is beneficial because power law relationships appear as a straight line in double logarithmic space, making them easier to identify and analyze. Figure 2 displays the double logarithmic plot of spending rates.
Fitting power law
We perform linear regression on the double logarithmic 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 average 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 fast the consumption probability declines with age. Figure 3 shows the fitted regression.
Analyze residuals to assess fitting quality
To assess the fitting quality of the power law across different coin age groups, we analyze the residuals—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 between residuals and UTXO coin age.
We observe that UTXOs around 200 days old have very small residuals, indicating that this cohort is highly predictable. This aligns with the gradual transition from short-term holders (STH) to long-term holders (LTH). The S-curve models this transition for a smooth change 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 transition completion rate from STH to LTH is 99%.
Our analysis indicates that the power law model fits almost perfectly for STH tokens until they completely transition to LTH. For LTH tokens aged 3-4 years (the second transition zone), the model still performs well (with minor deviations). These deviations suggest that the spending probability for the mid-term LTH cohort is slightly higher than predicted by the model.
However, for ultra-long-term holders (ULTH)—tokens older than roughly one halving cycle—we observe a more significant deviation from the model. Specifically, the observed spending probability is lower than that predicted by the power law. This suggests a stronger inclination to hold these tokens, possibly due to strong holding beliefs or the likelihood that some of these tokens are lost.
Chronologically ordered power law
We examine from a different angle whether the power law dynamics of token spending probabilities change over time. Instead of averaging the UTXO counts for each coin age across all dates, we track groups of UTXOs born on the same day. Based on these date groups, we can analyze how the spending rates of tokens have evolved during different periods in Bitcoin's history.
For each group, we calculate the consumption rates day by day as the group's coin age increases. Then, we perform linear regression on the double logarithmic spending probabilities for each group. Ignoring the data groups with recorded survival times of less than 10 days results in about 3,600 remaining groups and corresponding linear regressions.
The coefficient of determination (R2) for each regression indicates the fit of the power law model to the cohort data. The slope of each line helps us understand how the consumption rate declines as the coin's age increases. Figure 5 plots the R2 values and line slopes over time for each date group.
Overall, the power law applies well across different dates, confirming the consistency of this dynamic over time. However, specific periods exhibit lower fitting quality, although there is no apparent correlation with price movements during those times. We observed that spending probabilities throughout 2019 (with lower slope values) were prolonged 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 rates were higher than usual.
Impact on on-chain analysis
These findings provide a continuous perspective on coin age and spending probability, complementing the existing LTH/STH framework. The power law relationship embodies the gradual transition from active trading to long-term holding.
Notably, the model fits almost perfectly for younger tokens and remains good for tokens around four years old (with only minor deviations). Beyond this age, the model's deviations become more pronounced, suggesting that other factors may influence the spending behavior of ultra-long-term holders.
A power law with a slope close to 1 provides a clear and intuitive rule of thumb: for every tenfold increase in the lifespan of a token, its probability of being spent decreases by about tenfold. The approximate model values in the table illustrate this.
This predictable decay in spending probability 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, thereby enhancing interpretations of on-chain data and investor behavior.
Quantifying the heat supply hypothesis
Based on our data, we evaluated a simple predictive heuristic:
If the UTXO is less than 7 days old, it is assumed that the UTXO will be used on the same day. Otherwise, it is assumed that it will not be spent.
Using historical data, this heuristic method has an accuracy rate of up to 98%, indicating that it correctly predicts whether a UTXO will be spent in the vast majority of cases. However, due to the imbalance in the dataset, high precision figures may be somewhat misleading—there are a large number of unspent UTXOs on any given day.
Summary
Our analysis indicates that Bitcoin’s UTXO spending behavior is controlled by strong power law dynamics, with the likelihood of older tokens being spent gradually decreasing. The power law relationship fits almost perfectly for younger tokens and remains good for tokens up to four years old (with only minor deviations). For ultra-long-term holders with ages exceeding this, the deviation from the model becomes more pronounced, indicating that the spending probability is even lower than the model predicts. 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 shift from active trading to long-term holding. The power law offers an accurate rule of thumb: for every tenfold increase in a token's lifespan, its probability of being spent decreases by about tenfold. This predictable decay in spending probability provides valuable insights into investor behavior and the dormancy of tokens over time.
As Bitcoin continues to evolve, the power law model provides a mathematically grounded framework for on-chain analysis, enabling deeper insights into the lifecycle dynamics of UTXOs.
