Evasion Math question

[shark]

A random number is generated by the game, it's evaluated if it's <= than your evasion value and if it is, you dodge. otherwise you get hit. A programmer and a mathematician will give you the same answer to this question.

Mathematician me:
For other statistical tests which *EXCLUDE* mental gymnastics, I'll recommend you do the Hi-square test and see if the numbers thrown out by the game conform to a random model. Add to that the floating-point roundoff error and the fact that you cannot shoot someone 1.5 times (meaning it has to be a round number to make it count) throws off your math quite a bit.

Because 1% evasion is the same as 2%, which is the same thing as 3%. they all sum up to 31 shots. I understand where you're going with this - increasing returns.

If you are going to discuss statistics, you must dislodge these "presumptions" as delusions and work with gathered data. And then there's the Hi-square test you need data for as well..... so if you have the free time for it, go for it.

Programmer me:
But I'll save you a few hours of wasted time and tell you that random number generators are designed to be pseudo-random and usually pass Hi-square tests. You are literally proving a point more pointless than proving that watching paint dry might become boring at one point.

[shark]

another misconception you have is: you keep "expecting" to evade. Thus, you mix probability with statistics in a very rude manner. I'd almost say "marketing-level rude" when they tell you 78% of users don't have dandruff since using this shampoo instead of clearly saying "78% which was 7 people out of 10" or "78% which was 78000 out of a 100000". You realize the difference yourself, the other has substantially more data to back up the claim.

and you have no data really, just mind-generated numbers. your metrics are worthless as they show alot but reveal nothing of value.

Probability:
if a coin is to be tossed a 100 times and 99 times landed heads-up, the probability of the next one being heads-up is 50%.

Statistics:
if a coin is to be tossed a 100 times and 99 times landed heads-up, the statistical expectation of the next one being heads-up is 99%. statistics is observed probability.

So, before you start talking about "getting shot 1000 times", try to get shot a 1000 times. See *how many tries it takes you to get shot 1000 times* and better do a study on that; at least you'll approximate the internal curve used to normalize the numbers. And as we all know, it's probably a normal distribution but you can check

But I understand, it's hard getting shot 1000 times because 30 will kill you. that implies at least 300 replays of the game.

At best, given this enviroment in which you work - to do is to do a Monte-Carlo approximation and refine your calculation. then draw assumptions if 98% is much more OP than 95%.

Because probability wise, 10% is the same as 90% - it happened or it didn't happen. But you cannot work with frequency of happening based on probability alone. But if you're not a math-inclined person, you will probably reach a terrible misshappen conclusion along the lines of "a single d6 die has a 3.5 average roll". when translated to english, that means "you can expect landing 4s most of the time" when that is not true. however, throwing two dice *will* produce a result of 7 most of the time.

This is very shakey ground and it's exactly these caveats marketing and pokerscammers use to "prove" whatever point they wanted you to believe.

Programmer me:
who cares. android was compiling so I took the time to shit all over your "just because 50 people say X doesn't make them right" when the real argument should've been "nobody here knows math so I'll stick with my own theory"

You don't evaluate how good a system is by using it out of it's specs. Main argument against your 98%->99%. neither 98 nor 99 are physically available options; it doesn't go that far. So why extrapolate to infinity? Why be a mathtard about it? To excercise mental gymnastics against other mathstumped people?

Tell you what, next time don't start a statistical/probability discussion *UNTIL* you figure out the math behind the goat game. Only when you really understand why it's not 50-50 but rather a 66-33 can you understand why I wrote all this text to tell you math doesn't work the way you (currently) think it does...

[Harnisfechten]

taken by itself (ignoring the game), yes, each percentage point has the same value. 1/100. Taken in the context of the game, however, each percentage point has a multiplier of importance attached to it.

Maze has it right:

The ships in game have 30hp, and lets assume you're being attacked with 1 damage missiles.
With 0% evasion it takes exactly 30 shots to be destroyed.
With 1% evasion it takes an average of 30.3030... shots to be destroyed.
...
With 50% evasion it takes an average of 60 shots to be destroyed.
With 51% evasion it takes an average of 61.2245... shots to be destroyed.
...
With 80% evasion it takes an average of 150 shots to be destroyed.
With 81% evasion it takes an average of 157.8947... shots to be destroyed.
...
With 98% evasion it takes an average of 1500 shots to be destroyed.
With 99% evasion it takes an average of 3000 shots to be destroyed.
And, of course, with 100% evasion you can't ever be destroyed.

The difference should be very clear at this point. That first 1% protects you from less than a third of a shot, while the 1% from 98%-99% protects you from 1500.

as you can see, each percentage point has a different value in the game. dodging 99% of shots is a huge jump from dodging 98%, which is a slightly less huge jump from 97%. The difference between 50% and 49% is much larger than the difference between 0% and 1%. This concept is why games usually follow an exponential curve when it comes to upgrades and xp and such.

You're thinking of the percentages without looking at them in the context of the game.

[Maze1125]

Stuff

I assume, from context, that your posts were aimed at me.
In which I case I have to say that they were nothing but a whole lot of name-dropping and telling me that "You can't do that." with absolutely nothing to back it up.

You tell me that can't mix probability and statistics (which I never did) and then do exactly that by telling me that I have to use statistical methods but I have to prove myself first by understanding the Monty Hall problem, which is problem of pure probability.

Not a single thing you said had any mathematical substance, while my posts had hard numbers and facts about the game. I have absolutely no need to gather actual data, as statistics is just a poor substitute for probability that we only use because it is impossible to know the underlying structure of the world by theory alone. With this game, however, we can understand it's working completely, because it was a structure programmed by a human, so we can just take what we know about it and apply probability theories directly, producing a far more accurate result than statistics ever could.
Mathematicians didn't make a killing at casinos by studying the statistics of Blackjack, they did it by directly studying the probabilities, because Blackjack is a fixed known system, just like this game.
The only way statistics could be relevant is if you're arguing that there's a programming bug causing a bias in the random number generator, or similar unknown factor, because that's is what statistics is for; finding unknown factors in the first place, not analysing known factors.

Oh, and when discussing averages, it's perfectly appropriate to use decimals, even in a situation where only integers can actually occur, because it's an average, not a prediction.

And if you want numbers that are in the actual game, here you go:
With 0% evasion it takes exactly 30 shots to be destroyed.
With 10% evasion it takes an average of 33.33... shots to be destroyed.
With 20% evasion it takes an average of 37.5 shots to be destroyed.

Those are all numbers that can actually occur in game, and the 10% from 10%-20% gives greater protection from shots than the 10% from 0% to 10%. The difference isn't as exaggerated as when comparing 0%-1% vs. 98%-99% but it is still very clearly there.

[andrewas]

I think the problem here is that some people are looking at the wrong number. Yes, each point of evasion blocks the same number of shots. As a player, thats not a number I particularly care about.

The interesting number is how much better is another five points of evasion. If Im at 50% then a 5% boost would take care of 10% of the incoming shots that would overwise hit me. Depending on how many shields I have and what size of salvo the AI is tending to fire at me, that 10% can be fairly meaningless, if it not enough to keep me alive then my scrap is better spent on increasing my offensive ability to reduce the incoming fire at the source, or on the shields so that I can stand to take more hits. Or it can be the difference between taking a point of damage on almost every salvo, and only taking damage if the enemy get lucky. In that case the evasion is the better buy. Also, if I don't have defence drones then evasion is more attractive since missiles ignore shields.

In short, evasion is not something you can evaluate in isolation. When people talk about the higher points of evasion being worth more than lower points, they are talking about its impact on their ability to survive enemy fire, not about the absolute percentage of shots it will stop.

As for your maths professors, I'd be interested to know how that conversation went, because I suspect you didn't give them anywhere near enough information to solve this problem or even to interpret the point you were failing to grasp. The answer they gave will be technically correct but useless in actual play. The first step in doing math is to ask the correct question.

Oh, and you earlier stated that 0% and 100% were 'off the percentage scale'. Tell *that* to your maths professors. Graph survivability against evasion, and the curve is asymtototic at 100%, theres no discontinuity. 100% isn't a point we can get to in game but it is a valid point on the scale.

To take another example, go play a mage character in angband or any of its variants. Spell failure rates. 5% is pretty good, right? No, it'll get you killed sooner rather than later. One in twenty spells fail, it won't be long till it happens when it really matters. So how low is enough? 4% is 20% better than 5%, in that you have a 20% lower chance of a spell failing at a critical moment. 3% is 25% better than 4%. 2% is 33% better than 3%. 1% is 50% better than 2%. Each percentage point does more for your long term survival prospects than the last. But its not till the magical 0%, garaunteed success at each and every casting, that you can actually depend on magic. The only difference is that, because you can get to the extreme end of the scale, the effect is much more pronounced than with FTLs evasion.

[cicobuff]

@shark

You are correct in the basic principles. But horrible wrong in the evaluation of the value of each percent increase practically.

If you really have professors of mathematics around (or you can look for industrial management professionals), go talk to them about about the Six Sigma as popularized by Jack Welsh.

Ask them why it is increasingly more expensive to achieve higher sigma values. If all points in percentage is the same, why is it much more costly incrementally to achieve say 99.9999% from 99.9998% success rates as opposed to 99.9998% from 99.9997%?

edited: grammar

[BKT]

FTL : Serious Business

... Then again, I might be wrong— I doubt this discussion has anything to do with FTL, so...


Regardless, once the enemy fired their missile, it WILL hit your ship regardless of how much evade you have, while on the other hand, your missile will ALWAYS miss its target when you really need them to hit, so the whole evade thing is kinda mood. This is a scientific fact and is not open for any debate.

[Neverpraying Mantis]

I have a question that I asked somewhere else but no one knew the answer:

Once the RNG determines that the ship will be hit, how is it determined which rooms is hit?
In particular - do 2 square rooms have half the chance of being hit compared with 4 square rooms?


My subjective gaming experience suggests that that is in fact the case but I could be totally wrong. If I have more crew than 4 (needed for systems that can be manned) I tend to send the rest to 2-square rooms to minimize the chance that they are hit by a shot. Does that even make sense?

[BKT]

I don't know the answer to that question. But I do know for a fact that the it has something to do with crew's HP; as crew HP decrease overtime when he's in room X, the probability of enemy shot hitting room X approaches 1.


... On a more serious side though. I believe it's per room and not per tile and is completely random based on my experience. Then again, my experience also told me that the game deliberately and purposefully trying to troll me in any way it possibly can despite its random nature, so...

derp...?

[UltraMantis]

I have a question that I asked somewhere else but no one knew the answer:

Once the RNG determines that the ship will be hit, how is it determined which rooms is hit?
In particular - do 2 square rooms have half the chance of being hit compared with 4 square rooms?

My subjective gaming experience suggests that that is in fact the case but I could be totally wrong. If I have more crew than 4 (needed for systems that can be manned) I tend to send the rest to 2-square rooms to minimize the chance that they are hit by a shot. Does that even make sense?

It has been confirmed that a room is picked randomly. So there is equal chance of differently sized rooms being hit.