Expected Value

Sayings
There's one saying that has always bothered me in EVE.
"You've lost your ship as soon as you undock in it"

There's another thing that bothers me in EVE.
People claiming that they are making 100M ISK/hr. Not that I don't believe it's possible, it's more that I don't believe that they are actually doing the math to _really_ figure this out over the long run. We'll come back to this later.

While strictly believing the first statement seems like it might be in line with my "usual" line of "assume the worst case", I feel like it doesn't fully consider all of the factors involved.

Survivability: An Example
Here's what I mean. You just undocked in Nullsec, and let's assume you have zero support. You get out into the system at large, and start travelling toward hisec. Now, consider this situation in two cases:

- One, you're flying an armor-tanked Armageddon with a full flight of heavy drones (filling up your drone bay). Cost: ~110M
- The other, you are flying a Rapier, with a covops cloak. Cost: ~170M

I hope that you'd come to the conclusion that the first is a worse idea than the second. Why? Because it has significantly less survivability, if something bad were to happen, than the first. A single interceptor could make your day very, very bad by holding you down while he rallies support from his nearby allies.

The rapier doesn't have this problem. There are some things that could potentially kill the Rapier that couldn't kill the Armageddon as easily (Battlecruiser class ships come to mind, as do certain HACs) in open combat, but the Rapier has an advantage that the Armageddon doesn't have: evasive cloakiness.

So why should you consider both of those ships equally lost when you undock? My answer is that this is a very good question to ask, and that the "saying" doesn't cover the whole picture. By the logic of the saying, the Rapier is a worse idea to undock in, because it's more expensive, but this doesn't line up with the reality of the situation at all.
Yes, you can lose your ship anytime you undock, but you can also have a reasonable expectation of survivability in a lot of situations, if you are flying smart. So, to this end, I go to some light math.

The Math
Let us assume that you have the option of buying two ships, and are interested in a money-making opportunity that requires one of those ships. Ratting, missioning, this doesn't matter. The figures are also fictionally low, just used here to illustrate.

The first ship costs you 150M, and earns you 10M an hour, with a 5% chance of dying every given hour.
The second ship costs you 200M, earns you 5M an hour, and has a 1% chance of dying every given hour.

Over a large number of trials, ship 1 will earn you on average 50M profit per hull (200M gross - hull cost). Ship 2 will earn you 300M profit per hull (500M gross - hull cost)

The first hull is expected to last 20 hours, while the second is expected to last 100 hours.
Ship 1 then earns you approximately 2.5M per hour.
Ship 2 then earns you approximately 3M per hour.

So ship 2 is a better idea, given that all of these numbers are correct, even though you "earn twice as much while you are working" with the first ship, and even though the second ship represents a bigger possible loss. Those losses hurt, big time, and reducing the chance of them helps a lot. Survivability is key.

"But I'm in Highsec!"
Now, there are certain times where you might say that the chance of losing your ship is "zero" (highsec missioning, etc.), but this is never strictly true. If enough players get together and decide to gank you, no amount of tank will help. This, perhaps, is the reason behind the saying mentioned at the top, but in reality, this is just something to consider in the math above. Instead of 0 chance of loss, maybe that goes to .001% per hour.

If you can figure out those three numbers, you can figure out the relative profit of any money-making opportunity you can come up with... so let me break it down.

Raw ISK/hr = ISK/hr not considering ship death.
Hull_and_fitting_cost = how much lighter your wallet would be after fully replacing the ship you are using.
Chance of death = a percentage, expressed between zero and one, of how likely it is that your ship will be destroyed during an average hour of whatever it is that you are doing for the Raw ISK/hr.

Actual ISK/time = ( (Raw ISK/hr)/chance of death - Hull_and_fitting_cost ) * chance of death

If you don't know one of these numbers, guess! Estimations are better than nothing, as long as you are realistic about them. You might be surprised about how some of your favorite ISK-making activities might stack up here.

Other Considerations
It's worth noting that ISK isn't everything, and that constantly doing this math can make some activities that you like to do seem less fun, so don't forget to factor fun into the equation. If you are making marginally less ISK, but are having tons more fun, that's well worth it. EVE is a game, after all, even if it is ridiculously in-depth.

Also, I use this as an example for PvE, but you can do similar calculations on PvP to figure out how many hours you can expect out of your favorite ships, to figure out which ones really are "budget" ships, and which ones are the expensive ones (losing a 5M T1 cruiser every day in PvP might be more expensive than flying a 100M T2 cruiser that is more survivable). Again, though, take this with a grain of salt.

As one closing note, however, this works mostly for active combat-type activities; things that might be limited by "passive time", like industry, planetary interaction, or the like, get more complicated to look at, but for those in short: if you have a slot for something, figure out how to use it. More on this later.

[Future Link to Industry for non-Industrials]

TL;DR:
Every ship that you undock in can be destroyed, but that doesn't mean it will be. Each ship has a chance to be destroyed in a given situation, and this differs from ship to ship or loadout to loadout.
This chance of destruction affects how expensive flying that ship or loadout is over a long period of time, and these numbers might work out differently than you would think.