A miner controlling a fraction p of the mining power has a probability p to mine each block. This follows a Bernoulli distribution and the variance is given by p(1-p). Since all blocks are independent, and since in a year there are 365 days of 24 hours of 6 blocks each, the annual variance is 365.24.6.p(1-p) while the expected return is 365.24.6.p
The reason of course is that mining costs are fixed. A miner must thus compare the relative standard deviation of this revenue and his expected revenue. A miner projecting to obtain an expected return on investment of 10% and controlling 0.19% of the hashing power would have about a 16% chance of losing money by the end of the year.
The relative standard deviation is the square root of the variance divided by the expected return, that is:
But why is variance so important? After all, statistically it all boils down to the same expection. Are people so risk averse?
Does it mean that the mining landscape is doomed to be dominated by a monopoly? Not necessarily. The solution is for miners to outsource the risk taking, not the mining. This is what P2P mining achieves. P2P mining acts as a distributed insurer which offer miners a swap between between their expected returns and their actual returns.
If the Sharpe ratio falls, the risk-reward ratio becomes less attractive. At one point, it becomes better for the miner to just invest in the stock market rather than to attempt mining.
If you control 10% of the hashing power in the network, your annual relative standard deviation is 1.3%, control only 1% and it climbs to 4.3%, control a measly 0.1% and it’s 13.8%… for a tiny miner representing 0.01% of the pool (mind you, that is still a miner averaging 11 bitcoin of monthly revenues) the variance is a whooping 43.6%
One can form the ratio of these two numbers, this is known as a Sharpe ratio (interest rates should figure in there, but they’re near 0 anyway).
In bitcoin, miners join pools for two reasons. One is to avoid the hassle of running a full node — this could be mitigated by requiring miners to include proofs of blockchain retrievability. The other is to reduce the variance of the return in their mining.
The largest miners benefit from higher Sharpe ratio than their competitors. Thus, they are encouraged to invest more in mining, pushing the margins down and squeezing competitors out of the market.
Setbacks And Naysayers Begone! Bitcoin Breaks $8,000 On Investor Confidence
Bitcoin broke through the $8,000 price mark this morning, reaching an all-time high of $8,100, thumbing its nose at the growing chorus of doomsayers reacting to the financial industry’s rising interes
Bitcoin Price Achieves New All-Time High at $8,100, Market Confident in Institutional Investors
The bitcoin price has officially achieved a new all-time high price at $8,100, surpassing its previous high at $8,050 established earlier this week. $10 Billion Awaiting to be Invested in Bitcoin
Newsflash: Bitcoin Price Reaches $8,100, a New Record High
Bitcoin price has struck a new all-time high of $8,100 during Sunday’s trading, continuing its rally from the previous Sunday’s lows.
The world’s first cryptocurrency has hit a new record high of $
Prominent VC Investor: Be Aware of ICO Pump and Dump Schemes
Jason Calacanis, a highly regarded venture capital investor who has invested in 150 successful technology startups such as Uber, Evernote, and Swell cautioned investors in the cryptocurrency sector in
UPS-Backed Blockchain Consortium Seeks to Disrupt the Freight and Logistics Industry
As blockchain becomes ubiquitous across consumer and enterprise applications, we will continue to see more and more large scale disruption of traditional sectors that are critical parts of the global
Manhattan’s Real Estate Eyes Up Bitcoin for Property Payments
Manhattan’s real estate market is embracing bitcoin for property payments as the digital currency increases in value.
One property developer who is hoping to capitalise on the recent digital curren
Karpeles Looks to Revive MtGox, Seeks $245 Million
Does anyone have $245 million to revive MtGox? Mark Karpeles, who has pleaded not guilty to charges of money laundering and embezzlement, claims reviving MtGox offers a way to allow creditors to get s
Billionaire Investor Novogratz: Ethereum En Route to New All-Time Highs
Mike Novogratz, the billionaire hedge fund investor and former executive at Fortress, believes Ether, the native cryptocurrency of Ethereum, is poised to achieve new all-time highs in the short-term.<