A game full of averages

[vinush]

Ok, basic idea behind this thread is as follows:

We all discuss this unit or that model, and then math-hammer the crap out of it. Average rolls to hit, to wound, to save, etc. and then base its performance on that, but how many of us have even once had that actual result come out in a game?

Take my Empire Halberdiers, for example. Last game I had a unit that was totally unsupported by characters because of how deployment went, so they were totally outside of the Ld/BSB bubble, no hatred rerolls from WP's, etc. Just a vanilla unit of 25 halberdiers, no shields. They went toe to toe with a unit of Night Runners. Night runners got the charge.

Combat round 1: Night runners have initiative, so go first. 15 attacks, hitting on 4's, he managed a whopping 3 hits (far below average!), wounding on 4's he managed 3 wounds (well above average!) and I saved 1 of them (needing 6's). My return attacks, 11 Halberdier attacks hitting on 4's I got 9 hits, wounding on 3's I managed 3 wounds. When it came to combat resolution, I had 3 ranks, banner, 3 kills for a total of 7, he had 2 kills plus a single rank (I'd softened them up pre-combat through shooting) meaning he lost by 4. He needed a 3 or less to hold, was outside of the general/BSB bubble, and rolled a 2 and a 1, holding. Now, based on averages, I should have wiped the floor with him, even taking any individual incident of rolling any number of dice during that round we didn't get an average set of results once.

Combat round 2: He goes first with his 15 attacks, managed to get 10 hits! Wounding on 4's he got 7 wounds. I managed to save 4 of them on 6's! My return attacks were totally fluffed, hitting twice out of 11 attacks and I managed to kill one! When it came to combat resolution he had 3 kills, no ranks. I had 1 kill, banner and 3 ranks, this time I won by 2, and he was testing against Ld4 effectively. He rolled Boxcars, and fled 11" (bringing him into range of his general's unit for next turn) and I pursued a whopping 5". Once again, none of this was average dice rolling.

He failed to rally, and continued to run off the board in subsequent turns, despite having 2 goes at rallying on Ld7 due to his general (supposedly an average dice roll for 2 dice).

Now, what's the point of this? It's not to brag about how awesome my halberdiers were (well, maybe a little) but more to discuss if anyone has ever had that perfectly average round of dice rolling? And to what extent do we put stock into math-hammering unit/model average rolls?

I do remember once having an average number of hits from 10 crossbowmen at short range (5 hits on 4's!) but then got all of them wounding, so was above average there...

THE \/ince

[theunwantedbeing]

If you expect a unit to do exactly what the mathhammer averages say then you aren't understanding the point of it.

Similarly, denouncing mathhammer as worthless when you don't roll exactly average is again, missing the point entirely.

[vinush]

I never claimed I was expecting a unit to do exactly what the averages suggest, it was more a case of has anyone ever had even a single round of averages?

It was meant to generate discussion on why we use math-hammer, what its purpose is, etc.

I have never denounced it, either, so I wonder if you read the post, or if I didn't quite get my point across?

THE \/ince

[Agoz]

I never claimed I was expecting a unit to do exactly what the averages suggest, it was more a case of has anyone ever had even a single round of averages?

It was meant to generate discussion on why we use math-hammer, what its purpose is, etc.

I have never denounced it, either, so I wonder if you read the post, or if I didn't quite get my point across?

THE \/ince

Yes, I've rolled exactly average before, many times in fact. For example with 4+ to hit and 4+ to wound I often get exactly 1/4 of my attacks wounding.

[vinush]

Yes, I've rolled exactly average before, many times in fact. For example with 4+ to hit and 4+ to wound I often get exactly 1/4 of my attacks wounding.

Did exactly 1/2 of the attacks hit? Did exactly 1/2 of those hits wound? Or was it a case of when all was said and done, 1/4 of the attacks resulted in wounds?

THE \/ince

[theunwantedbeing]

I never claimed I was expecting a unit to do exactly what the averages suggest,

Sadly plenty of people often see/use mathhammer as a prediction rather than a guide.

it was more a case of has anyone ever had even a single round of averages?

Lots of times when there is a whole number average, never when there isn't.

It was meant to generate discussion on why we use math-hammer, what its purpose is, etc.

To know what to expect in various scenarios and to compare units.

[Still Standing]

I never claimed I was expecting a unit to do exactly what the averages suggest, it was more a case of has anyone ever had even a single round of averages?

It was meant to generate discussion on why we use math-hammer, what its purpose is, etc.

I have never denounced it, either, so I wonder if you read the post, or if I didn't quite get my point across?

THE \/ince

No such thing as a single round of averages... A thousand rounds of averages, now that's another matter...

[zoggin-eck]

We all discuss this unit or that model, and then math-hammer the crap out of it.

Well, some of us don't

No, honest! I think it sucks all the fun out of the game, and was a completely alien concept for the guys I play against and myself until this until people started talking about Warhammer on the internet. For me, it should be enough to look at a units stats/point values/rules and decide if it's worth taking, how to use it and so on. I get that some people love that sort of thing, but micro-managing every element of a hobby, something I do for fun and to unwind, seems weird.

Anyway, we all know steeds always perform better than the riders!

[Enigmatik1]

Anyway, we all know steeds always perform better than the riders!

Never have truer words ever been spoken. My Skeletal Steeds are a nightmare (no pun intended) for my opponents while any Skeletons or Charioteers hitching a ride usually can't hit the broad side of a barn (MWBD or no MWBD). LOL!

[sulla]

Never have truer words ever been spoken. My Skeletal Steeds are a nightmare (no pun intended) for my opponents while any Skeletons or Charioteers hitching a ride usually can't hit the broad side of a barn (MWBD or no MWBD). LOL!

I don't think my cold ones have managed a single kill in the last 3 or 4 outings I took knights... Just to be different to everyone elses, I suppose...

[Tarian]

I've had some very average rolls before, and some very not-so average rolls. However, the point of getting the averages is to get a good feel of what your unit should do, on average. Is there times where a unit will severely over or under perform? Yes, it is a game of dice, after all. However, in my opinion, a lot of gamers I play with could definitely use a does of averages, so they don't pull certain moves, like charging 15 Zombies into a 7x2 block of Swordmasters, and expecting them to hold.

[Morkash]

Well, some people need mathhammer to see which unit is best for whichever purpose. But no matter how much you calculate and maximize your chances if the dice go Tzeentch-y, you're ruined.
I think occasional examples prove little, even average performance gathered over several games have little power because the single event where everything/nothing goes off is unaffected. For example my Leadbelchers fired average since the new book arrived. Taking 8 usually gives me 8D6 = 24-32 shots hitting on 4+/5+ and mostly wounding on 3+/4+. On good averages that gives me 10-11 kills per shooting phase, on bad averages only 4. Still there are so many factors to consider that you can rarely predict their performance. One game they shoot a few wounds of a Steamtank, another game they fail to kill a single Gutter Runner in a phase.

Generally, I'm not sure if I understand this thread either. People are mathhammering to gain an advantage, usually in competitive play. Consider it as a form of metatactics trying to tip the odds in your favour.

[Quinzy]

The purpose is, basically, to see what a unit does on average. It's really quite simple, and no different to the role averages play in any other system or in real life. It only makes sense to establish what a unit is most likely to do, most likely to perform. You know what you can then rely upon.

[vinush]

Quinzy, can you rely on them to do that?

As the game uses dice, there is an inherent unreliability in all things that rely on it.

THE \/ince

[Quinzy]

You can rely on usually rolling a 6 one sixth of the time.

There's no guarantee you'll roll one six in six dice. But it's statistically likely. That's something you can factor in when strategising.

[ihavetoomuchminis]

Where would you bet your money on when throwing 6 dice? On rolling 1 six, or on rolling 5 sixes? That's what statistics and averages are for .

[Haravikk]

Mathammering is only really useful for getting an idea of how a unit should perform, and whether or not it's a better or worse choice for a particular role. Still, when planning your army you should always consider the worst case, as while you can be reasonably sure that say… a unit of Hammerers will hold out against nearly any enemy without fleeing, you can't be as certain as you would with a unit of Slayers, so you should choose character placement and placement of other units accordingly, as you never know when you're going to roll all 1's.

[Griefbringer]

Speaking of maths, using the binomial distribution, it is quite easy to actually calculate the probability of the average result. Using a spreadsheet programme to do the calculations can be helpful though, it can get a bit clunky to calculate these by hand.

For example, let's assume a situation where 12 models shoot at a target, and each has a 25% chance of causing a casualty (4+ to hit, 4+ to wound, no save). The average result one could expect from them is to score 3 casualties (though they can potentially cause 0 to 12 casualties).

Doing a quick check with a spreadsheet software at hand, it appears that the unit has around 26% of causing exactly 3 casualties, 39% chance of causing less than 3 casualties, and 35% chance of causing more than 3 casualties.

The amount of dice rolled has an effect on the probability of scoring exactly the average result. While those 12 shooters have 26% probability of scoring average results (3 wounds), a unit of 24 shooters would only have around 19% chance of scoring average result (6 wounds), while a unit of 4 shooters would have around 42% chance of scoring average result (1 wound).

[Brewmaster_D]

Mathammer is a useful tool for determining a baseline for what to expect from your units. If you operate on a "feels like" basis, the game will quite often throw you curveballs which to players who are striving for the top levels of competition simply aren't acceptable.

However, a "hope for the best plan for the worst" policy is really what differentiates the good players from the mediocre players - when you reach a point where you understand what your unit should do on average, but also appreciate that outlying rolls can and will happen, your playing then starts to adapt to this.

"I know my White Lions should statistically win this combat, but it's a bit too close for comfort. If I Timewarp them, the odds of them failing now drops to near 0"

It's a good matchup, and I know this due to mathammer, but I'm also taking measures to compensate for those times where the unexpected happens.

D

[Sir_Turalyon]

Mathhammering illustrates how well a unit (or any experiment) may be expected to perform, and comes closer to truth more times we repeat the same experiment. Take a single coin toss - when we toss a coin over a wager or a prize, each of us has 50% chance of winning it. It does not mean both of us get to win half of the prize every time - or that it's possible to win half the prize alll - when we toss, one is lucky and gets whole wager, one is not. But if we have, say, thousand prizes and toss a coin over each one, we can expect that each of us will get about 500 of them. If one gets substantialy more, either he's lucky - it happens, just less likely -or there's something wrong with the coin.

So, in your example Mathhammer does not mean that Halaberdier units with 12 fighting models, hiting on 4+ and wounding on 3+ will score 6 hits, of which 4 will wound. It does not say these halabardiers will kill about 4 enemy models per round. It does not even say that, if they keep fighting the enemy ad infinitum, the total number of wounds already scored divided by number of turns already fought will be closer and closer to four.

It says that, given the random nature of game, each of these phrases is as close an estimate as we can get.

Also, actual statiscics deals with idea of deviancy (saying not that halaberdiers cause about 4 wounds per turn, but that they cause about 2-8 wounds per turn, 4 being the most likely outcome; it does not say your hallabardiers will cause 4 wounds, either, it says there is nothing special about them killing 4 models, killing 6 models is not unusual, but if they kill 10 models you should gape in awe at your lucky roll). Warsees mathhammer usualy does not bother with that, with much less precise results,