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For the first four years of bitcoin, 50 bitcoin were being mined per block. There was a feedback loop to adjust difficulty so that blocks would be mined every ten minutes, on average. So why is the graph of "Total bitcoin in circulation" so far from a straight line? See image:
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When a large amount of hashing power enters or leaves the network, the difficulty adjustments (capped at 4x in either direction) often aren't enough to keep the average block difficulty at 10 minutes. When a lot of hashing power comes into the network, block time is more often going to be less than 10 minutes while the opposite means it's more often going to be more than 10 minutes. This in turn means that coins are generated faster in the former case and slower in the latter.
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If the Bitcoin would have had a constant amount of hashing power that whole time, we could have expected the straight line that you postulated.
However, the Bitcoin network's hashing power has been growing substantially, for some stretches even exponentially.
As the difficulty on the Bitcoin network only gets adjusted every 2016 blocks, i.e. every 14 days at a 10 minute interval, the difficulty has only been in line with the amount of hashing power right after a difficulty change.
Yet, as the hashing power has been increasing, blocks were found quicker, reducing the average block time below the target of ten minutes. – It actually dropped below eight minutes at peak hashing power growth rates.
As each block puts new bitcoins into circulation, a high growth in hashing power will cause a greater increase of bitcoins into circulation. Therefore, the growth of hashing power is related to the slope of "Total Bitcoins in circulation".
On the other hand, the hash rate in 2015 so far has been decreasing from a peak of 328 Petahashes/s to about 300 Petahashes/s, causing a current average block interval of just shy of 11 minutes.
Thanks for your answer. I guess a second question then is why is the slope generally increasing in the first four years? If the general trend was increased hashing power preceding increased difficulty I would expect early over-production and a decreasing slope. – Alex Millar – 2015-02-02T16:43:27.683
If you were to have exponentially increasing hashing power, you would expect some fluctuation within a given two-week period, but roughly the same # of coins produced in any given two two-week periods. Thus, the slope of the line would be higher, but it wouldn't necessarily increase. For that, you would need faster-than-exponential growth in the network. The slight dip in slope in Jul 09 to Jan 10 is probably a decrease in hashing power and the ramp up to Jul 10 looks more than exponential. After that to the first halving in Jan 13 looks like a straight line to me, as you would expect. – Jimmy Song – 2015-02-02T17:23:52.593