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 (UTXO) and their spending probabilities, we can gain deep insights into the dynamics of the Bitcoin ecosystem. This article explores the power-law relationship between UTXO age and buy-sell probabilities, revealing predictable patterns of how tokens are held and sold over time.
Why This Analysis is Important
Understanding Bitcoin's UTXO spending behavior provides strong insights for traders, investors, and analysts. By revealing predictable patterns that govern currency dormancy, you can:
Enhanced Investment Strategy: Predict potential liquidity changes and better measure market sentiment.
Improved On-chain Analysis: Utilize a mathematical framework to complement traditional LTH/STH metrics.
Predicting Holder Behavior: Determine when tokens are likely to re-enter circulation, informing the timing of trades or decisions.
Whether you are optimizing trading algorithms, analyzing market trends, or refining investment approaches, this framework provides you with clear, data-driven advantages 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 stored at specific addresses, waiting to be used in future transactions.
By analyzing the tenure of these UTXOs (the number of days since creation), we can infer behavioral patterns of holders in the network. A fundamental concept in this analysis is the spending probability, which measures the likelihood of a given UTXO being spent on any given date. This metric quantifies how Bitcoin moves within the ecosystem and how holder behavior evolves.
Methodology
Dataset and UTXO Count
Our analysis is based on Bitcoin UTXO data from 2015 to November 2024. Every 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 coin age to 10 years to avoid the inherent noise in extremely old UTXO data.
Calculate Spending Rate
To determine the spending probability, we compare the number of UTXOs of a specific age on a given day with the number of UTXOs of the next higher age the next day. The consumption portion is calculated as follows:
Spending Score = 1 - (Number of UTXOs aged N on day T) / (Number of UTXOs aged N-1 on day T-1)
This formula represents the proportion of UTXO with an age of N-1 that do not appear the next day as UTXO with an age of N, 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 represents the average spending rates by coin age.
Power Law Dynamics in Log-Log Space
To better understand the relationship between UTXO age and spending rate, 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 it easier to identify and analyze. Figure 2 shows the double-logarithmic plot of the spending rate.
Fitting Power Law
We perform linear regression on the double-logarithmic data to quantify the power-law relationship. We use weighted least squares for regression, where weights are proportional to the square of the UTXO count divided by the square of the standard error of the mean. This weighting accounts for variations in data point reliability due to differences in sample size and variance.
The slope of the regression line corresponds to the power-law exponent, indicating how quickly the consumption probability declines with age. Figure 3 shows the fitted regression.
Analyze Residuals to Assess Fit Quality
To assess the fit quality of the power law across different coin age groups, we analyze the residuals, which are the differences between the observed average spending rates and our model's predicted values. Plotting the residuals helps us identify patterns or systemic biases in the model. Figure 4 shows the functional relationship between the residuals and UTXO age.
We observed very small residuals for UTXOs around 200 days old, indicating that this cohort has high predictability. This is consistent with the gradual transition from short-term holders (STH) to long-term holders (LTH). The 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 short-term holder (STH) tokens almost perfectly until they fully transition to long-term holder (LTH) status. For LTH tokens with ages of up to 3-4 years (the second transitional band), the model still performs well (with small deviations). These deviations suggest that the spending probability for the mid-term LTH cohort is slightly higher than the model's predicted probability.
However, for ultra-long-term holders (ULTH) – tokens held for more than approximately one halving cycle – we observe a more significant deviation from the model. Specifically, the observed spending probability is lower than the power-law predicted probability. This suggests a greater tendency to hold these tokens, possibly due to strong holding beliefs or the likelihood that some of these tokens are lost.
Chronological Power Laws
We examine whether the power-law dynamics of token spending probability change over time from another perspective. Instead of averaging the UTXO counts of each 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 have evolved through different periods in Bitcoin's history.
For each cohort, we calculate the spending rate day by day as the cohort's age increases. We then perform linear regression on the double-logarithmic spending probabilities for each group. Ignoring data groups with survival times of less than 10 days results in about 3,600 remaining groups and their corresponding linear regressions.
The coefficient of determination (R²) for each regression indicates how well the power-law model fits the data of that cohort. The slope of each line allows us to understand the rate at which the spending rate declines as the coin ages. Figure 5 plots the R² values and line slopes for each date group over time.
Overall, power laws apply very well across different dates, confirming the consistency of this dynamic over time. However, specific periods exhibit lower fit quality, with no apparent correlation to price fluctuations during those periods. We observed that the spending probability throughout 2019 (with lower slope values) was prolonged. One possible explanation is that investors who bought during the 80% drop from the ATH in 2017 were aiming for long-term investments, resulting in a higher spending rate compared to usual.
Impact on On-chain Analysis
These findings provide a sustained perspective on UTXO age and spending probabilities, supplementing the existing LTH/STH framework. The power-law relationship embodies a gradual transition from active trading to long-term holding.
Notably, the model fits younger tokens almost perfectly and still performs well for tokens around four years old (with only minimal deviations). Beyond this age, the model's deviations become more significant, indicating that other factors may influence the spending behavior of ultra-long-term holders.
Power laws with slopes close to 1 provide 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 below illustrate this:
This predictable decline 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 sustained perspective, analysts and investors gain a richer understanding of the gradual decline in spending activity as tokens age, enhancing the interpretation of on-chain data and investor behavior.
Quantitative Hot Supply Assumption
Based on our data, we evaluated a simple predictive heuristic:
If UTXO is less than 7 days old, it is assumed that the UTXO will be used that day. Otherwise, it is assumed it will not be spent.
Using historical data, the accuracy of this heuristic method 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 of the dataset, high-accuracy numbers 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 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 performs well for tokens up to four years old (with only minimal deviations). For ultra-long-term holders beyond this age, the deviations from the model become more pronounced, suggesting that spending probabilities may be even lower than predicted by the model. This indicates 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 the lifespan of a token, its probability of being spent decreases by about tenfold. This predictable decline in spending probability provides valuable insights into investor behavior and token dormancy 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.
