Welcome to Jester's Trek.
I'm your host, Jester. I've been an EVE Online player for about six years. One of my four mains is Ripard Teg, pictured at left. Sadly, I've succumbed to "bittervet" disease, but I'm wandering the New Eden landscape (and from time to time, the MMO landscape) in search of a cure.
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Tuesday, August 16, 2011

Fermi estimate

In engineering, and in my business, great faith is put on Fermi estimates when you're faced with a difficult or insoluble number that you need to estimate.  The most famous Fermi estimate is "How many piano tuners are there in Chicago?"  The idea behind a Fermi estimate is that you estimate each factor that would give you an answer, then multiply all of those factors.  If you are not biased in some way toward getting the answer that you want, and as long as you produce estimates for a lot of different factors and not just a few, any errors in your estimates will tend to cancel each other out and your estimate will tend to be pretty close.

That way, even if you know nothing about Chicago or pianos or how long it takes to tune them, you can still produce a reasonably reliable estimate of the number of piano tuners there by estimating how many people live in Chicago, how many of them have pianos, how many of them get those pianos tuned regularly, how long it takes a piano tuner to tune one piano, how many hours a piano tuner works in a year, et cetera.  Even if you know nothing about each individual factor, your errors will tend to cancel each other out because some of your estimates will be high and some will be low.

With that in mind, let's estimate how many trillion ISK per month are being paid in high-sec incursion bounties.  Warning: scary math follows.

The factors are the following:
  • the number of high-sec incursions;
  • the number of 10-, 20- and 40-pilot fleets active per incursion;
  • a factor to adjust this number based on how active EVE is over the course of a day;
  • a factor to adjust for the fact that larger fleets will be much more likely on weekends;
  • a factor to adjust how efficient a given incursion fleet is;
  • the amount of ISK generated per incursion fleet per hour; and,
  • the number of hours EVE Online is available in a month.
Let's start with the easy ones.  There are roughly 23 hours per day that you can play EVE.  Let's say in a given month, there are 22 weekdays of 23 hours each and 8 weekend days of 23 hours each.  That's 506 weekday hours and 184 weekend hours.  But of course, EVE players aren't 100% efficient.  They try to be, of course, and they're often pretty close, particularly as the game approaches down-time.  But, it does take time for a sufficient number of people to log in, and to find partners with which to form fleets.  Let's say EVE players are 90% efficient at using EVE's available time for incursion-running.  So that's 455 weekday hours and 165 weekend hours.

The fastest high-sec incursion fleet there is peaks at around 100 million ISK per hour, but I've been in a fair number of 50 and 60 million ISK per hour fleets as well.  Let's say the average is 70 million ISK per hour per incursion-runner.

At any given moment, there are between one and three high-sec incursions.  When things compress down to one incursion, the number of incursion fleets steps on each other and there's a lot of competition, which lowers demand.  When things open up to three incursions, there's currently a bit of difficulty in gathering a fleet because the players that are active incursion-runners are split across wide areas of space.  Two is the average number of high-sec incursions at any given moment and seems to be the ideal for efficiently finding and running fleets.  Given that, let's say that at this moment, there are 1.75 incursions active throughout a given month: two incursions, minus a small factor to reflect the fact that one incursion or three incursions is less efficient than two.

An incursion fleet itself is not 100% efficient, of course.  The fleets lose members, gain members, take breaks, change systems, have to stop to mine for ore (don't ask)... there are all kinds of things that can slow down an incursion fleet.  Let's say a typical incursion fleet is 85% efficient.

On weekend days, there are three types of fleets running: 10-, 20-, and 40-pilot fleets.  Per incursion, there seems to be about a 50% chance of a 40-man shield fleet on weekend days, plus about a 33% chance of there being a 40-man armor fleet.  There also seems to be an 80% chance of a 20-man shield fleet, and a 40% chance of a 20-man armor fleet.  On weekends, there seem to be between seven and ten 10-man incursion fleets running at any given moment.  Let's say the average is eight.  We'll also estimate the size of 10-, 20-, and 40-pilot fleets to be 10, 20, and 40, respectively.  They'll sometimes vary a little, but in equal measure up and down.

On weekday days, there are two types of fleets running: 10- and 20-pilot fleets.  40-pilot fleets seem to be rare or non-existant on weekday days, so we'll say there's a 5% chance that one is happening at any given hour.  20-pilot fleets are somewhat more common, but seem to mostly occur in Euro TZ.  We'll say that there's a 60% chance of a 20-pilot fleet, then reduce it to 30% to reflect that the Euro TZ represents about half of the EVE day.  On weekdays, there seem to be between six and eight 10-man incursion fleets running at any given moment.  Let's say the average is seven.

So, at any given moment on a weekend day, there are eight 10-pilot fleets (80 pilots total), plus a combined 83% chance of a 40-pilot fleet (0.83 * 40 = 33.2 pilots total), plus a combined 120% chance of a 20-pilot fleet (1.20 * 20 = 24 pilots total).  That's 137.2 pilots total, which we multiply by 1.75 high-sec incursions, and the average 85% fleet efficiency.  So there are 204 pilots running incursion fleets every weekend hour, making 70 million ISK per pilot per hour, over 165 weekend hours in a month.  That's 14.28 billion times 165 hours, equals 2.36 trillion ISK in a month.

At any given moment on a weekday day, there are seven 10-pilot fleets (70 pilots total), plus a 5% chance of a 40-pilot fleet (0.05 * 40 = 2 pilots total), plus a combined 30% chance of a 20-pilot fleet (0.30 * 20 = 6 pilots total).  That's 78 pilots total, which we multiply by 1.75 high-sec incursions, and the average 85% fleet efficiency.  So there's 116 pilots running incursion fleets every weekday hour, making 70 million ISK per hour, over 455 weekday hours in a month.  That's 8.12 billion times 455 hours, equals 3.70 trillion ISK in a month.

Therefore, if this Fermi estimate is close, that's a little over six trillion ISK per month currently flowing into the EVE economy from high-sec incursions.  Feel free to adjust the factors I used to come up with your own estimate if you don't like mine.

For reference, in Q4 2010 (the last quarter for which we currently have data), there were 75.7 trillion ISK in pirate ship bounties paid (source: QEN 4Q2010, page 18).  Unfortunately, we have no way of knowing with public data what percentage of those bounties were paid in high-sec versus null-sec or low-sec.  We have only one clue: agent mission reward and time bonus reward per month amounted to four trillion ISK total per month in 3Q and 4Q 2010.

There's a few players here and there already grumbling over this massive flow of new ISK into the EVE economy, but the more I think this through, the more I think incursion ISK is healthy ISK, for four reasons:
  • it is self-limiting;
  • it is self-sinking;
  • it is not without risk; and,
  • it is social, merit-based ISK.
Each of those deserves some discussion, but this post is already pretty long, so I'll get to those four discussion points tomorrow.


  1. Does the 70 million isk/hour include approx value of the LP rewards?

  2. No. LP rewards are an ISK sink, as I'll explain tomorrow. In this post, I'm only considering the faucet.

  3. I like your idea on the estimation of ISK generation however I think you maybe slightly over the top as the 85% fleet efficient is too high. You have factored a number of delays but in my mind the big gap is fleet formation / composition. I have known many a time that fleets have been sitting at planets for over hour waiting for an illusive logistic to come available.

    Conversely the more people joining incursion running improves availability and the greater number of "shiney" fleets available as people re-invest thier ISK improves the completion time to sub 5 mins for some Vanguard sites. AT the moment my view is a more conservative 75% efficency


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