This project analyses different aspects of the time it takes to mine a new block.

What people currently know is the average block time. The monitoring sites ethstats.net and etherscan.io provide a good overview in realtime for this metric. Before Ethereum will be upgraded to Proof of Stake, the time to mine a block, the average block time is ~14 s. But block times over a minute are not uncommon. For certain applications, precise knowledge of the variance of the block times is vital, for example, realtime gambling applications where a user must wait for a result in a smart contract.

The difference of two Block timestamps is made and this difference is analyzed. First, the quantiles are calculated to have a first glance of the distribution, then the frequency density and cumulative density curves are calculated. Finally a Monte Carlo simulation describes how the IID distributions for multiple confirmations would look like. The IID should be considered to be purely theoretical. In reality, the independence of blocktimes is not given!

Blocktimes.csv contains a data set of collected between the Ethereum Homestead release and 10 June 2016. Each row represents the POSIX Date of the block mined since the first Homestead block (13000).
You can collect your own data with the collectBlockTimes.js script.

geth --exec 'loadScript("./collectBlockTimes.js")' attach http://localhost:8545

Figure: the distribution of observing block times and their density. Peak block time is around 2.9 s, median 10 s and average 14 s, maximum observed 2 min 54 s.

The quartiles are:

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 1.00    5.00   10.00   14.35   19.00  174.00

In laymen’s terms: block time is at least 1 s, because seconds is the granularity of the timestamp 25% of all transactions are ⩽5 s Median gives you an average that does factor out the outliers (174s) Mean gives you an average that includes outliers 75% of all transactions are ⩽19s The biggest Outlier 174s measured since Homestead (16 March - 11 June 2016).

Blockchains solve the double spending attack vector by concatenation of multiple confirmations of randomly selected mining nodes. Having one confirmation means trusting the current miner. For smaller amounts, this might be a good idea. How can we relate the transaction amount and the confirmation times?
In an article Buterin lays out 2 potential attack vectors:

1. Byzantine fault tolerance model: a certain percentage of all miners are attackers, and the rest are honest altruistic people.
2. Economic model: there is an attacker with a budget of $X which the attacker can spend to either purchase their own hardware or bribe other users, who are rational.

Amounts under minimal mining rewards of 5 ETH Here we can safely accept 1 confirmation, which is mined in about 1 min.

Fig: A 99% sure confirmation is reached after 61 s ( 1 min)

Amounts over 5 ETH

[...] the 17-second blockchain will likely require ten confirmations (~three minutes) to achieve a similar degree of security under this probabilistic model to six confirmations (~one hour) on the ten-minute blockchain. -- Vitalik Buterin on “the Normal Attack”

A Monte Carlo Simulation was conducted to show the potential development of confirmation times.
WARNING: this shows how the confirmation times would be if no block time adjustment would be undertaken. Ethereum, as also Bitcoin, adjusts the block times depending on the time of the previous blocks to gain constant confirmation times. The result is that variance is mutch more restricted and converges to constant times for multiple confirmations.

Figure: Monte Carlo distributions of confirmation times

Smart contract developers must take into consideration that blocktimes can vary substantially. We observed many blocks that were mined under 1 s but in rare cases, a block time can pass 1 m 30 s. The more confirmations the more uncertainty. This consequence is mitigated by an adjustment algorithm that we shall explore in a future article. ∎