Bitcoin Metcalfe Value Monitor

Method

Following Peterson (2018), Bitcoin is treated as a token currency whose network value is proportional to the square of the number of users, while supply dilution is handled by dividing by coins in circulation. The per-coin Metcalfe value is MET = k × n² / S, where S is total bitcoin in circulation and k is fitted by least squares on log price over the chosen fit window.

The choice of n matters more than anything else on this page. Peterson's demand variable was the number of wallets, a stock that only grows. A cumulative count of unique addresses used since 2009, built by integrating Blockchain.com's daily series, behaves like that stock and yields a network exponent close to two. Daily unique addresses are a flow, not a count of unique people or users: they run near 460 thousand as of September 2026, about where they were in 2017 to 2019, so a model built on them returns that era's price level (roughly $6,000 to $23,000 depending on window) with an R² near zero since 2017 and out-of-sample error above 140 log points. That definition was tested and rejected, and it is deliberately not offered on this page. Users also leave, so a decay option is provided: each day's unique addresses join the user stock and then decay exponentially with a chosen half-life. A half-life of zero collapses to the daily flow and an infinite half-life to the raw cumulative count. On this data the fit improves monotonically as the half-life lengthens, and the undecayed stock fits the 2014 onward era best, which is why it is the default; "Best fit" runs that comparison and reports the winner. Every year of half-life removed lowers the Metcalfe value, so decay is a conservative adjustment, not a neutral one. When the daily snapshot is available, the count of addresses holding a non-zero balance (Coin Metrics) is offered as well; it is the adoption proxy used in the published power-law decomposition and the closest public analogue of a wallet count. Unspent outputs are a further proxy for holders. The Gompertz option follows Peterson (2019): the user series is replaced by a fitted sigmoid growth curve, so the Metcalfe value becomes a smooth curve and the premium series isolates what the paper calls non-economic deviations, the 2011, 2013 and 2017 episodes among them.

Lost coins enter through supply: S in the formula is the surviving supply, not the mined total. The reader chooses the total assumed lost today, from the published range (Chainalysis 2.3M to 3.7M, later estimates near 3.8M, a 5.6M ceiling for coins dormant ten years or more, most analysts centring on 3 to 4 million), and a loss profile. The page then calibrates a per-year loss hazard on each vintage so that the profile reaches that total, and rebuilds the surviving supply day by day. Two facts govern how much this matters. A share of supply lost uniformly throughout the fit window changes nothing, because the constant k absorbs it; only the change in the lost share across the window moves the value. And the profile is what sets that change: coins were overwhelmingly lost in the early years, when they were mined for cents and discarded, and rarely today, when supply sits with custodians. The profile offered by default is front-loaded (a hazard that halves every three years above a small floor); it lifts the value about 2% at the central estimate on the 2017 window and about 4% on the 2011 window. The adjustment is off by default so that the headline is directly comparable with published figures, which do not state a supply adjustment. A constant-rate profile is offered for comparison and lifts it about 7%, because it assumes losses continue at the early rate. The better input would be measured dormancy from the chain (supply last active ten or more years ago), which is not in the public feed used here. Two diagnostic forms appear in the comparison tables but are not offered as valuations. The fitted-exponent form lets the data choose the network exponent instead of fixing it at two; on the default window it returns an exponent close to two, which supports the law, but as a valuation it is unstable across annual refits. The activity-adjusted form adds the 30-day average transaction count as a second regressor; it fits marginally better in sample and predicts worse out of sample. A macro overlay in the spirit of Cane Island's Macro Model Value, adding the broad trade-weighted dollar index and the effective federal funds rate as regressors, was tested the same way on monthly data: it raised in-sample R² from 0.85 to 0.93 on the 2014 window and raised out-of-sample error from 55 to 69 points, with the value for today swinging across a six-fold range between annual refits. It is not offered here. Nor are price-only constructions such as power-law floors in calendar time or seasonal-year profiles: they contain no user count, and this page is a network valuation. The Gompertz option is the counterpart of adoption-curve estimates, and it is kept as a diagnostic because it predicts less well than the observed user stock.

The premium series is 100 × ln(price / MET). Standard units divide that by the standard deviation of residuals in the fit window. Regimes are cut at the 10th, 30th, 70th and 90th percentiles of the fit-window premium rather than at multiples of σ, because the residuals are right-skewed: bubbles push price far above value for months, while discounts are shallower and longer. All distribution statistics (percentile, extremes, regime shares, forward returns) are computed over the fit window; earlier years are drawn on the charts, shaded as out of sample, but not fitted.

Validation. Every model and window is also scored out of sample: fit on data through each 31 December from the window start, predict the following year, and repeat. On this data the fixed-exponent model on a cumulative user stock, fitted from 2014 or 2017, predicts with about 50 log points of error and small bias, and its value for today moves less than ±10% across annual refits. The fitted-exponent and activity-adjusted forms fit better in sample but predict worse, and their value for today swings by a factor of ten across refits, because the extra parameter is not identified by a series that grows six orders of magnitude. The full-history fit overvalues systematically. These results, not in-sample R², decide the defaults, and the dashed line on the main chart shows what the chosen method would have said on each date.

The full-history calibration is a steep function of its start date: the first months of exchange trading in 2010 fit the law worst by a factor of fifty and pull the constant up. Starting the fit on 1 January 2011 removes that distortion and reproduces the published Cane Island Metcalfe value within a few percent; that window is the default so that the headline is directly comparable with published figures. The 2017 window, covering three halving cycles, is the one recommended by validation and is one click away. Before 2014 the address stock is still forming, so n² understates the young network's value by orders of magnitude; fitting through those years inflates the residual σ and, because the early residuals are positive, pulls the constant k upward. A 2014 start keeps the 2017 bubble at the front of the window and leaves a strongly right-skewed residual. From 2017 onward the specification comparison converges: all four model forms on the cumulative user series land within about ±10% of each other, the fitted exponent is close to two, and residuals are near symmetric. Earlier windows are left available for comparison.

What this page tells you, and what it does not

Descriptive: the relationship between the network-size proxy and price has held on the mature network, and its fit statistics are printed. Forecasting over a defined horizon: the page tests one-year-ahead prediction with annual refits and prints the error and bias; that is the strongest predictive claim it makes. Not claimed: a price target, or causation. Address counts respond to price as well as drive it, since bull markets bring users on chain and bear markets send them away; a cumulative stock damps that feedback but does not remove it. The model contains no calendar term, and the one fitted curve in time, the Gompertz option, is labelled a diagnostic for that reason. Use the value as one lens beside capital flows, holder behaviour and liquidity, with position sizing that assumes the stated error is real.

Sources

Unique addresses, transactions, circulating supply, and daily price history from the Blockchain.com Charts API. Spot price from Coinbase, refreshed every minute while the page is open. Data is cached in this browser for six hours.

References: T. F. Peterson, "Metcalfe's Law as a Model for Bitcoin's Value," Alternative Investment Analyst Review, 2018, SSRN 3078248; T. F. Peterson, "Bitcoin Spreads Like a Virus," 2019, SSRN 3356098. Peterson writes value as pairwise connections, n(n-1)/2; that is indistinguishable from n² here, the factor of one half being absorbed into k.

Companion page: the Bitcoin Power Law Monitor, where the Metcalfe exponent is one half of the identity β = β_A × β_M that decomposes the price power law in time.

Metcalfe value measures demand-driven network effects against a fixed-supply asset. It is not a price forecast and nothing here is investment advice. Address counts are an imperfect proxy for users and are affected by exchange batching, ordinals, and privacy tooling.