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Why do I see all of these guys pull out their calculators to do mathhammer? Dont you get the same thing from experience? The only problem with mathhammer is that it is like a science experiment under perfect conditions the results do not reflect in game results. I mean you may figure out the chances of certain results but it doesnt take into considerations of certain results at certain times. Such as a glancing hit destroying a battlecannon or immobilized transports.

I know I am about to be bombarded by mathhammer evaluation responses but you should evaluate units when they are on the field, not with a piece of paper and calculator.

If you know the chances, it helps you decide what to do during the game. I hope people aren't bringing calculators to a game, some quick math in your head should be just fine. It allows you to direct the correct amount of firepower/cc power to a situation and have better odds at coming out on top. You don't have to rely as much on luck, and it may save you from doing mistakes.

CKO wrote:
I know I am about to be bombarded by mathhammer evaluation responses but you should evaluate units when they are on the field, not with a piece of paper and calculator.

Why not do both?

In my experience, math-hammering is good for picking the types of units you might want to try on the tabletop or in determining how best to use a unit.
Its an initial guess often. A good player will evaluate the statisticals against their experiences with that unit and others, compare them to their playstyle and determine what works best for them.

Often, I find that doing math-hammering for the sake of math-hammering does yield interesting results that go against your common sense.
Examples are how 1 Flamer shot = 1 Plasma shot if you can hit 3 Marines or how Autocannons usually superior against light armor then the more expensive Lascannon.

"No thanks, no gaming today, I'm staying home doing mathhammer". Not likely :-)

I calculate when I can't play the game due to lack of time or opponents. I also do it because I really like math, and because it gives me interesting insights into mechanics of the game. And I honestly believes it gives me a good foundation for the practical testing of units. In a play situation my subjective view of things and my enthusiasm for the game often gets in the way of analysing. Also, it's hard to get a reliable statistic for an effect unless you do many iterations of it, something that takes a lot more time if you do all the attempts "live" on the table top.

Not this again.

Look, statistics (a.k.a Mathhammer) informs your decision making during the game.

Do I shoot my Lascannons at the Monolith or the Heavy Destroyers? Do I shoot my Autocannons at the Rhino or the Drednaught? Which attack will have the best chance at being successful and not just a wasted shot.

Do you shoot an autocannon at a Land Raider? No, why, because basic addition says str 7 + D6 has no chance against Armor 14. Statistics are a simple extension of this concept. Do I shoot my Missile Launcher at the Land Raider? Basic addition says str 8 + D6 can glance Armor 14, should I take a shot or are my chances so slim that the shot is wasted?

This helps prevent you blaming the "Dice Gods" when you don't get that miracle 6 needed to pen the Land Raider with a Lascannon. Or when your single shot gets cover saved and that was the one thing you needed to win the game and didn't get.

As a simple example. Your opponent moves Nasty Unit A towards you. Logically, on the field, you know you have two possible counters for this that are in range. However, you also know you can only commit one of these, as you need to other for a counter-tactic you have planned. Which do you use? Mathhammer tells you that one of these units has a 60% chance of success; the other 70%. In a situation like this, you would use the 70% unit. Either could potentially win or lose, but you would play the odds to give yourself the best possible chance of success.

cko not only is math hammer boring... the math people are using when they throw out these percentages is wrong. you can't model warhammer with arithematic. you need probability and statistics.


Automatically Appended Next Post:
and yes you can do much better with simple experience. somebody on another thread mashed numbers together to find, amazingly, it takes 20 shots to kill a predator at long range. and we all know from experience that is not true...

And the good thing about being a nice math geek is that I do not make sweeping assumptions on how a loosely defined group such as "math people" do calculations. *looks pointedly at GTT16th* An average number is just an average number, and it is easy to find with arithmetics. The trick is to know what use you can make out of this number, the difference between data and information. One use is that you can apply it into probabilities.

If you want to look at the spread of probabilites you need another set of tools. Questions like: "How many SPM HBs do I need to shoot to have at least a 75% chance of taking out a rhino?". "How many more do I need to have a 90% chance?". "How many more for a 99% chance?" And you need probability, statistics and good knowledge of the rules to realise that you can never up this probability into a theoretical 100%.

And on the subject of statistics: A single result, (not even consider the reliability of the source "somebody on another thread") does not merit any evaluation of the method. This is applicable for how a particular unit/weapon/special rule performs if tried in just a few battles. And it is definitely applicable when evaluating the effectiveness of mathhammer on these forums.

Mathhammer is just a tool. It helps me do clever things.

since you're a nice person i know you won't mind sitting through some remedial grammar with me. watch.

the math... people... are using. subject, object of the subject. verb. as in the math *that* people use.

constantly amazed.... constantly....

no s in arithematic.

anyway yes you can find the average chance of, say, a bolter shot wounding a marine, with arithematic. what you cannot find with arithematic is how many bolters you need to shoot at that marine to be reasonably certain (say 95 times out of 100) of killing him. which is why... math hammer... without the aid of probability and statistics... is nonsense.

GloryToThe16th wrote:anyway yes you can find the average chance of, say, a bolter shot wounding a marine, with arithematic. what you cannot find with arithematic is how many bolters you need to shoot at that marine to be reasonably certain (say 95 times out of 100) of killing him. which is why... math hammer... without the aid of probability and statistics... is nonsense.

Depending, of course, upon what information the user is attempting to glean. Both pieces of information are useful and applicable to the game.

Aha, then I follow you. I blame me being raised speaking swedish, together with a relatively low expectations of people ability to write proper and polite sentences on internet forums. Sorry for my snarky remark on that subject, it was entirely undeserved.

However, my point remains this: I do believe that mathhammer can include the use of statistics and probability, and will benefit from doing so, but it doesn't have to. And, it can still be a useful tool just looking at the simple P(hit)*P(wound)*P(fail save)=P(kill) calculations. For example: "Is it worth the +1p to upgrade my termagants flehsborers to a pair of spinefists?" Simple multiplicative mathhammer says that 100 shots with a fleshborer will on average kill more targets in several important categories such as MEQ, TEQ and ORKs. So the upgrade is definitely not worth the points. For this, I don't need statistics and I don't need to consider the spread of the results. Simple multiplication is "good enough". This is especially true since fleshborers and spinefists are usually fired in huge numbers, so tends to conform better to the average.

However, In situations where a few dice are rolled, statistical spread (that is the proper word in english, right?) becomes more important. It is a lot more timeconsuming to calculate though, so I usually settle for the "good enough". The trick is to know just how good that is, so I don't expect a predator to go down after exactly 20 shots of a HB.

I do agree with you that a lot of people tends to take the multiplicative mathhammer a bit too literal. But that doesn't make the method nonsense.

Is it just me, or is GloryToThe16th presuming to give Mellon lessons on English grammar like a fish trying to teach Lance Armstrong how to ride a bicycle?

x

GloryToThe16th wrote:its you

GloryToThe16th wrote:which is why... math hammer... without the aid of probability and statistics... is nonsense.

I always thought use of the word "Math Hammer" included (or is primarily comprised of) probability and statistics.

Mellon then i apologize too. Please excuse my rudeness.

You can get a basic idea of what's going on with arithematic i agree. I don't know how to model 40k with statistics and probability myself. Wish I did. I'm just starting to study math in college. It's my major.

I'm not sure if statistical spread is the right word. I understand what you're saying. The fewer dice you roll the more likely it is that your actual results will vary from what the math suggests will happen. Conversely the more dice you roll the more closely it will conform.

I agree with the way you're approaching it. I was quick on the trigger. What I mean to say is that when you see tables of percentages showing how likely one unit is to kill another, it's often based on flawed assumptions. For example if I want to kill a terminator 100% of the time I have to make it take 6 armor saves because 1/6 x6 = 1. I would guess that you would have to make it take like 10 or 12 saves to kill it even 95% of the time. Anyway it's bad math, but people talk about their percentages like they're dead certain.

Mathhammer leads to a comfort zone that frustrates people and is unrealistic on the battlefield.

Maybe if you do it badly. You're better off determining the probability of each potentiality rather than determining which potentiality or fraction thereof is most likely, for example.

CKO wrote:Mathhammer leads to a comfort zone that frustrates people and is unrealistic on the battlefield.

Every player know that the game depends on the dice roll , and math hammer just helps tips
over the chances to achieve what they hope to achieve.

As to the average vs probability issue, for most people averages are enough to give you an idea of what to expect. Anything more and it would get too complicated for your typical game and frankly, few people have the energy to be doing calculations (or looking up results of those that they already did) to go for the probability.

A prime example of this is "how many Bolter shots does it take to kill a Marine?"
For me, knowing that it takes roughly 9 shots to kill a Marine is enough. This gives me the information I need to make the assessment on the battlefield that if I rapid fire two 10 man squads into a 5 man combat squad, I stand a reasonable chance of killing off the heavy weapon guy buried inside.

minigun762:

Actually the example that you give is the sort of thing where people get mislead by averages. If it takes 9 shots on average, at minimum it takes 1.

Let's set the problem like this:

You have four Tactical combat squads within 12" of two Tactical Squads. Two of your combat squads have Heavy Bolters, two of your combat squads have Plasma Guns.

Supposing everything else being equal, in what order do you commence shooting to maximize the efficiency of your shooting? Remember to show your work...

Nurglitch wrote:
You have four Tactical combat squads within 12" of two Tactical Squads. Two of your combat squads have Heavy Bolters, two of your combat squads have Plasma Guns.

Supposing everything else being equal, in what order do you commence shooting to maximize the efficiency of your shooting? Remember to show your work...

1) rapid fire the 2x PG squads into 1 Tac squad.
Average result should be:
4 S7 = 2.67 hits = 2.2 dead Marines
16 S4 = 10.67 hits = 5.33 wounds = 1.78 dead Marines
Total = 4 dead Marines

2) rapid fire 2x HB squads into 1 Tac Squad.
Average result should be:
6 S5 = 4 hits = 3.33 wounds = 1.11 dead Marines
16 S4 = 10.67 hits = 5.33 wounds = 1.78 dead Marines
Total = 2.89 dead Marines

End result = 10 Tac squad + 3-4 Tac Marine squad leftover. Considering the amount of wounds placed on the target squad, there is a fair chance you've killed off one of the SW, HW or VS models. This is the reason I fired the PG before the HB. The PG shots will help to reduce the squad to a smaller maximum number meaning that when you start stacking wounds with the Heavy Bolter, you have a better chance of torrenting the important stuff.

EDIT:

Nurglitch wrote:minigun762:
Actually the example that you give is the sort of thing where people get mislead by averages. If it takes 9 shots on average, at minimum it takes 1.

I should have been more clear on my previous example. To be useful, you must understand that the averages are just a best guess. Nothing is stopping you from killing 1 guy or 8 guys even though the average would be 4. For me, the best thing to do is put a +/- on it. If the average says 18 Bolters = 2 guys, I should understand that my expected results will probably be 1-3 guys dead.

Experience is a really unreliable tool for calculating the probability of something happening because experience is clouded by psychological distortions like preconceptions, loss aversion and confirmation bias. Check out the Monty Hall problem or the Gambler's Fallacy for good examples of how people's assessments of odds can't deal with mathematical probabilities that are counter-intuitive.

...or just check out one of the billions of Dakka threads on how assault cannons are more likely to hurt a landraider than a lascannon, or one of the half-billion threads about how lascannons are extremely unlikely to kill a landraider, and you can see for yourself how many people cling to what they remember as their "experience" against what the numbers say.

In general, experience is pretty reliable. But in places where the probabilities aren't intuitive, mathhammer actually gives you the more accurate expectations.

Glory to the 16th, your apology is gladly accepted!

Actually, I'd like to offer you a gift of friendship. I had to dig a bit in my old math knowledge and on the internet to get some tools, and it took a bit of work, but I managed to create a small table that lets you look up what probability you want of hurting your target, and what saves your target has, then it tells you how many saves you must force to get this probability. It's not very useful in a gaming situation, since it doesn't care how many wounds are failed. But it was a fun excercise none the less, and I might be able to rework the formula to work better for hurting bigger units. Anyhow, I named the table after you.

No hard feelings here, I hope that I can gain a lot of 40k related insights out of your math-studies in the future, and a lot of interesting discussions until then.

Here it is, the Gtt16th table:

minigun762:

Sorry, it was a trick question: I left out something of extraordinary relevance: the make-up of the Tactical Squads. That definitely affects the utility of stuff like Plasma Guns when mixed in with weapons with a higher AP value because even if the Plasma Gun hits twice, both hits may be allocated to a single model.

Assume further, then, that the Tactical Squads have a Sergeant, a weapon specialist, and a heavy weapon specialist.

thanks melon. glad to meet you

My statistics professors would probably end themselves if they ever have the misfortune of stumbling upon this thread.

Nurglitch wrote:
Assume further, then, that the Tactical Squads have a Sergeant, a weapon specialist, and a heavy weapon specialist.

I just went ahead and assumed that the Tac squad had the standard loadout of SW, HW and PW/PF Sarge.

flavius everyone agrees math is better than going by experience. but experience is better than going by bad math... and thats what math hammer generally is. you cant model the game with arithematic. you need probability and statistics.

I mean if you take a marine in close combat with another marine then it has a 1/12 chance of killing that marine with each attack. that's true because 1/2 x 1/2 x 1/3 = 1/12. so math hammer-ers go on to say well I need 12 attacks to be reasonably sure of killing that marine because 1/2 x 1/2 x 13 = 1/12 and 1/12 x 12 = 12/12 or 100%. this is bad math. if it were good math the marine would always always always die whenever you roll 12 attacks against it, since 100% means all the time and 12/12 = 100% we all know that isnt how it plays out. when you roll 6 dice you're not going to get 1 2 3 4 5 6 very often... and thats basically what the arithematical approach assumes. you're going to get 1 1 2 3 4 6, 2 2 4 5 5 etc. that's what you need stat and prob to model.

if you just want to take an educated guess with numbers, math hammer without prob and stat is fine. if you want to have mathematical certainty then it is not.

GloryToThe16th wrote:mini each bolter shot has a 1 in 12 chance of killing the marine... but that does *not* mean you're going to kill 1 marine for every 12 bolters you fire. remember?

No, it doesn't mean that it will happen, Thats what I'm saying.
9 Bolter shots = 6 hits (on average) = 3 wounds (on average) = 1 failed save (on average) so (on average) it takes 9 Bolter shots to kill a Marine.
You could shoot 9 shots and kill 0, 2, 3 or 9 Marines but chances are that it will be 1.

My point was that for most people, this is enough "math-hammering" to make an informed decision on the tabletop.