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I am building some new metrics to better understand the Bitcoin economy and one that seems to be useful is a probabilistic notion that a Bitcoin has been lost. I'm aware of the bitcoin days destroyed, but has anyone done any modeling to gain a sense if a Bitcoin has been destroyed as a result of a lost key or a transaction to a bad address?

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There is no way to determine (that I can imagine) the number of lost private keys, you would have to make a guess that after x years without movement the private key is lost but that would just be a guess.

  • Thus the notion of probabilistic measure. I'm certain with some modeling, we could develop a reasonable metric – Charles Hoskinson Apr 18 '13 at 3:57
  • @CharlesHoskinson How? I can't imagine you could get any useful data on which to base a prediction. – Jeremy Banks Apr 18 '13 at 4:07
  • Take the set of all accounts and measure the transaction volume over a fixed period of time. Build a distribution and examine the outliers. Certain accounts will be high volume others no volume. Create a notion of average time within an account and if an account is several standard deviations outside the time range, then it is either a high frequency account or a dead account – Charles Hoskinson Apr 19 '13 at 0:26
  • This analysis would also be useful for studying iceberging techniques for moving large chunks of bitcoins without having the market discover the divestment – Charles Hoskinson Apr 19 '13 at 0:28
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A digital currency with user-defined anonymity will cause any estimates to simply be guesstimates.

There are other areas where studies have attempted to quantify something and simply have concluded there is no reliable way to come up with the number so rather than provide misinformation there simply is no estimate made.

Essentially you could give a rough guesstimate of the upper bound. Any coin that hasn't moved in the past year, for instance, might go under the possibly lost for a year or more. That data is available and reportable. But who knows if the real level of coins that haven't moved for over a year is because they were lost or simply are being saved and not spent. Maybe it is 98% saved and 2% lost. Or not. Who knows.

  • Yes and what do you think the distribution would be? Poisson? – Charles Hoskinson Apr 18 '13 at 4:37

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