I didn't want to pollute the genestealer thread with more stats discussion, but in case anyone wants to exercise their brain I'll put this here. I will put forward the argument that considering variance can give you a modest advantage as a general and is worth considering for list design.


Moving on from genestealers, to address this point in a more general sense as I see it a lot: probability distribution is usually NOT a bell curve. This is only the case for 4+ rolls. That has been the whole point of the genestealer discussion (albeit used to support different and separate assertions), and why looking at the distribution IS a more useful metric than the average.

Take 2x5+ vs 3+. These two rolls have exactly the same average, but the latter has a lower chance of getting 0 hits and a higher chance of getting 1 or more hit. You can ignore that if you like, but it does have a marked effect on how good the unit is at its specific role, and interplays with the formation size to determine how good the formation is as a whole. To whit: if you have a large formation and are going for a strategic win (i.e. the odds are in your favour and you planned on winning) you want 3+. If you are a small formation, are looking to deter an assault, or make a last ditch kamizake attack, you want 2x5+ because in all of those cases you are relying on "getting lucky".

Clearly this has consequences for list designers. Yes statting is an art (if only because we aren't clever enough to conceptualise all the maths), but it can still be guided by the science.

As a more general observation, if your decisions to assault are based on achieving the average, with the greatest respect IMO you are making poor strategic decisions. That is because the chance of getting average hits or better is actually only 50/50. I know that is not how my mind works during a game; I cant'/don't do the required factorials in my head on the spot(!), so I am looking for the average to be "some margin" higher than what I need to compensate for this effect. It is a poor approximation of reality, so it is useful as a general to bear in mind that with lower rolls, this margin actually does not need to be as high.

Anything that adds or removes variance to the result is affected by this. First strike, for instance, raises the variance by magnifying the impact of hit rolls and armour saves. Conversely, macro weapons eliminate the variance introduced by armour saves. It is also why blast markers and inspiring characters are so good - because they have no/minimal variance - it makes your estimations as a general more accurate which gives you a strategic advantage.

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If on the other hand you're bothering about the 2*5+/3+ difference for a single unit in a game of toy soldiers that is published by the users w/ no commercial implications, then you're bothering too much.

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some of us like really detailed painting, some of us like really detailed thinking.

Is this opinion on bothering too much coming from the same man who started the now seven page 'Have had enough' grammer thread? i recon this is as important.

*edit: and interesting read OP, even though i know nothing about maths.

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Your right Apoc. Its a good point. >:D

All good points Kyrt and things to keep in mind.

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List design *is* more art than science. Getting dug into micro stat evaluations doesn't achieve a more balanced, fun list without the guiding hand of an artist.

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Currently doing a plastic scenery kickstarter

I concur Doc...


But I fail to see the big picture here Kryt. Are you saying overall that it's total non-sense to have a unit, or for that matter a army, perform average?

OR

Are you saying army lists shouldn't be balanced?

I appreciate this thread is not for everyone, but some people do like thought experiments and it's in it's own thread so you don't have to read it. I think it's a shame you bothered to post a comment like that, but to each their own I suppose. I won't hold it against you

But you've misread my post (or I've not communicated it clearly enough) if you think this is about a single unit. Yes I gave an example to use as the basis of illustrating the effects of variance, but the post is about how appreciating the finer points of probability can make you a slightly better player/list designer overall.


I agreed with you there, what I would say is that if you have a background appreciation of how variance affects the game, even if it to the detail of the examples I have given, you really don't need to dive into the maths for every unit/formation to be able to design its stats to make them fulfil their role in a list. I would never advocate that, it would be absurd and impossible.

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Neither really.

The point about "aiming for average" was about how you as a general decide what to do in a game itself, using the specific example of an assault. I was putting forward the opinion that when you decide whether to assault something, if you are thinking "if I get average results I will just win this, so I'll go for it", then you are being fairly risky because the chances of you getting average results or better is only, by definition, 50%. I suggested that initiators of assaults usually want to have the odds in their favour so as not to mess up their strategy, and so the way people actually make these decisions is by thinking "on average I should get enough kills plus a bit, so I'll go for it". In my opinion this is our way of subconsciously accounting for the way probability works*. Given that this "plus a bit" is a bit of a guess on our part, I was saying it might be worth knowing that this "plus a bit" does not need to be as much for units with lower hit rolls as it does for higher numbers of dice (because of the different probability distributions they have).

The point about list design is simply that the same thing (variance) makes different stats more suitable for some roles than others even when they average results are the same. It is not usually a large effect for a single unit, but is magnified in larger formations. Whilst it is impossible for a list designer to model probability distributions when designing and balancing a list (!), it might help to generally bear it in mind.

* The way the brain works is quite fascinating in my opinion. It's really good at some things, like predicting outcomes, but IIRC it does it in a very different way to a computer - based on intuition and approximation rather than calculation of probability. Sometimes it gets things really wrong simply because of the kinds of tasks it has evolved to be good at. For example, try to conceptualise 10 things, or a week's time. Now try to conceptualise how many atoms there are on the Earth, or a hundren billion years. It's very difficult to do, because in our daily lives we are built to count things we can see and do things within our own lifespans. That's why we use analogies: "the same size as fifty football pitches laid end to end" etc etc. It might also explain why we have trouble as a species planning effectively beyond what is a relatively short term.

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URGH!

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Gah!

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Heh. At least one of them is right.

If the average gamer had a solid understanding of probability and especially how probability/chance changes then a shift in play would probably be seen. The only probability stuff i can remember from maths at school is enough to remind me that my brain sucks at trying to work that sort of thing out by 'intuition'

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Now I got it!

Interesting points Kyrt, and I think your right.

Funny thing about lifespans. You think about the future and how far along it is, say 20 years. Then you think about where you are right now in life and look back and say, "Yikes! Where the Hell did the last 20 yrs go?"

One point I continually have to make for myself is that if you will, on average, win by four, that is not a safe assault. The odds of losing that is pretty high, guessing something around 30%.



Units usually come in formations. Take 8 of those 2x5+/3+ and you start to see some significant differences.