Mathhammer vs TableHammer; Relationship

[Schlitzaf]

So we have had a lot of threads discussing MathHammer and within those threads, folks rebuking Mathhammer (both the formulas and concept) while presenting their own table hammer as evidence. By extension the rebuke of the table hammer has often come as “annodotal evidence” or “good luck”. Now I like my MathHammer, folks who read my posts see I do it a lot.

 

If I said “In my experience Crusader Squads are fine, despite only difference in wargear from 10 Man Chaos Marine Squads is one extra power weapon attack, instead of second special. The addition of Neophytes in Crusader Squads, for some reason makes the squad a lot more efficient than appearances would have you. Despite being only 14 points cheaper (ftr that is another Marine or a Special equivalent of price difference). Regardless of fighting Khorne Zerkers, Genestealers, Hordes of Chaff or otherwise.”

 

Folks can and will say “Lucky or circumstantial,” however what I can then show, is that infact with Math it isn’t lucky. A 14 Man Crusader Squad for whatever reason (170-190ish) will beat 8-9 Zerker Squad (162-180ish). If you spend two points to interrupt or you had charged. Overwatch/shooting Kill 1-2.

 

Simply because while you might 6-8 models depending which model you take save on. The remaining 7-8 if you were charged killed 1. If you charged, Killing 3. (With 0.5 Dead Marines left overh). Meaning only 3-4 Zerkers killing 2-3 Crusaders. Zerkers are then shocking -5 or 6. Meaning 4+ shocks another.

 

In either case none of that goes through my head mentally. But I register it and think about it afterward as I backtrack thinking how the game goes and then during online discussion I explain the MathHammer. And know I now vague MathHammer and Game Results I better prep myself for the reception of Zerker Charge. Both Hammers need to be used together in unison, to some if not equal degree, to be best Warhammer General.

[chapter master 454]

Mathhammer gives you a sense of a units effectiveness. From it you can generate their overall effectiveness and average performance which is an important thing for any player to know as it gives you a sense of where things should go. However a lot of math hammer can get bogged down in academia and vacuums, as nothing within 40k is done on its own. Things like cover play a massive part of this as marines can exchange fire for the whole game because of having a 2+ save. Other factors come into play as well such as synergy with other units coupled with various methods of fighting come into play such as focus fire, having various units benefit from a commander and so on. This means units can be worth more than their points may indicate. People can mathhammer those stats however their effect on the game is far greater than some may consider. In the most basic terms, a standard marine squad benefits greatly from a captain as by stats half their misses get another attempt to hit again where 2/3s of them will hit. This means a captain could be worth several marines worth of shots by himself indirectly.

 

Tablehammer is the practice. Mathhammer is the theory. In Theory, Theory and practice are the same. In Practice, Theory and practice aren't the same. This element has various nebulous variables such as player choices which can be influenced. Terrain is another variance that can not be accounted for accurately. After all, in practice the games most important turns are the first and second but beyond that any mathhammer you have must account for losses and possible loss of best targets. This means units can rapidly reach a point where they waste a turn doing nothing that then influences mathhammer.

A good thing to remember is that in any given game, infantry by themselves without transports can only move 30" in a 5 turn game if they don't advance (and on average, if they advance EVERY turn it is an extra 17.5" which is for even numbers equals 4 feet) which means that as much as horde can 'overwhelm' you gun lines, you only need to kill the ones that matter and there is only so many 20 man blocks that can fit within range of an objective (and for one objective).

 

There is then one other form of hammer, killhammer. A mix of math and table hammer. But that isn't the topic of the thread.

 

The two things we have are the pure logical mathhammer minds of the scientists and desk generals who think certain things should be effective vs. the soldiers and captains who lead their men and see what works and what doesn't.

 

For example: When i first saw Tau's weapon choices and options, I thought that Burst Cannons and ATS would be incredibly powerful and effective. After all, putting 8 str5 ap1 shots down range sounds great for infantry shredding. However what was found that due to poor ballistic skill and the cost of crisis suits these were ineffective where as the flamers are far better. ATS also only works for more expensive weapons as the cheaper weapons benefit more from a third copy (even mathhamer backs this up).

Was I wrong to assume such? No because it sounds like it works, 18" Str5 Ap1 4shot weapon sounds good but the whole doesn't.

Mathhamer is like how science works in reality and should be: Make your theory (hypothesis) and why it should work. Then go and test it. Sadly in 40k we cannot create controls due to RNG but it lets you see how it functions. You may find it works well however you will note that it does struggle in fringe cases and these would need testing or vice versa. 

Don't just throw numbers, throw some dice and see if what you say adds up but remember that is your results for your ecosystem you play in. Some may struggle vs. a guard army due to their meta game being more suited to those armies (possibly those groups can't afford/build enough terrain or there are just so many horde armies). It's all about understanding where each view point comes from.

[Firepower]

Folks can and will say “Lucky or circumstantial,” however what I can then show, is that infact with Math it isn’t lucky. A 14 Man Crusader Squad for whatever reason (170-190ish) will beat 8-9 Zerker Squad (162-180ish). If you spend two points to interrupt or you had charged. Overwatch/shooting Kill 1-2.

 

This is what bothers me about mathhammer.  The tone of certainty.  "Will beat" is inaccurate.  "Should beat" is accurate.  Mathhammer gives you a good idea of how things will stack up, but it's still probability.  You can flip a coin a hundred times and get 100 heads.

[Stormxlr]

Mathammer is only as good as your math is.

Math is perfect, you are not. Humans are flawed, we can forget any number of variables. Trust the math, dont trust yourself.

[Wargamer]

There are no problems with Mathhammer, only with the people who fail to understand what an average is or how probability works.

 

This is well understood by most Blood Bowl players, and while they have their own ideosyncrasies like assuming a last turn GFI always fails, that game is built around risk management and probability manipulation. 40k, not so much, which is why people don't understand that missing 4/5 2+ to hit rolls doesn't change the fact that you'd expect no more than one miss if that.

[Claws and Effect]

I understand that if I have a weapon that wounds on a 2+ that 82.3% of all my rolls should successfully wound. That's what should happen.

 

What frequently DOES happen is I score 4 hits and roll 4 1s multiple times in one game. Seriously, that actually happened to me in the last tournament I played in. I failed so many easy rolls my opponent was starting to feel sorry for me.

 

Mathhammer says I shouldn't fail that many rolls over the course of a single game. But I did.

 

Outlier case? Of course. But I've learned that while mathhammer can be useful, it isn't always going to predict what will actually happen. 4 lascannons should kill at least 3 marines the majority of the time. I failed to even wound one.

[Eddie Orlock]

... Simply because while you might 6-8 models depending which model you take save on. The remaining 7-8 if you were charged killed 1. If you charged, Killing 3. (With 0.5 Dead Marines left overh). Meaning only 3-4 Zerkers killing 2-3 Crusaders. Zerkers are then shocking -5 or 6. Meaning 4+ shocks another. ...

Rigorous mathhammer usually involves graphs that show some manner of probability distribution that better presents the spreads of the curves. I guess you could approach the same information by talking about curve types and raising a discussion of standard deviation but that's considerably more opaque to most of the audience.

 

Simplified analysis akin to the quoted implies that there is a sure and certainty that Hits on a three, wounds on a four, saves on a three means you need Three wounds, thus six hit, thus nine shots with tactical marines with bolters to drop one opposing tactical marine with bolters, but the truth is considerably more complicated. If we start by assessing the odds that one shot makes it through (2/3)*(1/2)*(1/3)=(1/9) = P_​success​ and treating all the conditional rolls as one thing we can slug this through a binomial distribution. Simpler though is to answer the question of how likely is this to fail completely.

 

P_failure = (1 - P_​success) thus P_{complete failure on all nine shots} = P_failure^​(9)​ = (8/9)⁽⁹⁾​ = 134,217,728/387,420,489 ≈ 0.346.

 

This commonly alleged guaranteed kill has a greater than one third failure chance. That's huge.

 

And this impeachment of common mathhammer misconception and statistics abuse totally neglects the geometry concerns that are usually completely overlooked in the analysis. Not every model gets to attack to full effect all the time. Of course this is usually overlooked because it's tough model mathematically.

[toaae]

Mathhammer says I shouldn't fail that many rolls over the course of a single game. But I did.

 

That's not what mathhammer says. It says you shouldn't fail that many rolls over the course of ten thousand games.

 

There is a perception problem with mathhammer; it isn't predictive, but often you'll see posts like the one above used to discredit it. Mathhammer is merely figuring out averages. We all know that we play a dice game, and random results play a monstrous part in the results of whole game, single phases and individual model performances. Nothing short of weighted dice can give you a prediction of the result of any single or set of rolls.

 

Mathhammer is good for an apples-to-apples comparison of things. Is a power klaw better point-for-point than a big choppa against T7/3+? How many more bolters on average does it take to kill a terminator as opposed to an aggressor? And other questions such as these.

 

Nothing can tell me how well my Sanguinary Guard are going to do if they charge berzerkers. But thank's to mathhammer, I know that taking powerfists on my SG is more likely to produce more damage than taking Encarmine Axes. So when I'm building my models, and I'm trying to decide their equipment, I at least have an idea of which weapon I should expect to see perform better. Doesn't mean my results will fall in line with that.

[Beams]

I much prefer if people post probability graphs or tables as opposed to averages. Averages tell very little of the story, but breaking Down individual probabilities of each possible ility is harder, and so it doesn't happen. Which makes units like Repentia look horrible, when. In reality, their output is wider and less accurate, but has a decent chance of being much better than equivalents.

 

I sometimes run simulations and see what happens in each battle, for 1000+ battles, and that I trust better.

Edited January 29, 2018 by Beams

[D3L]

I understand that if I have a weapon that wounds on a 2+ that 82.3% of all my rolls should successfully wound. That's what should happen.

 

What frequently DOES happen is I score 4 hits and roll 4 1s multiple times in one game. Seriously, that actually happened to me in the last tournament I played in. I failed so many easy rolls my opponent was starting to feel sorry for me.

 

Mathhammer says I shouldn't fail that many rolls over the course of a single game. But I did.

 

Outlier case? Of course. But I've learned that while mathhammer can be useful, it isn't always going to predict what will actually happen. 4 lascannons should kill at least 3 marines the majority of the time. I failed to even wound one.

no

 

you misunderstand statistics, or rather you're falling prey to Gambler's Fallacy.

 

For your 2+ weapon example, maths tells you 82.3% of all my rolls should have successfully wounded, at an event number close to infinity, ie: over a very large sample

 

nothing "Should Happen" ,  everything can happen and will in a very large set, in a large enough set you'll also roll 1 million ones, back to back

the example

 

 4 lascannons should kill at least 3 marines the majority of the time. I failed to even wound one.

 

is also wrong

 

4 lascannons will kill 3 marines the majority of the time, at a time near infinity, the anecdotal evidence of rolling and wounding merely one, is nothing unusual or irrational

Edited January 29, 2018 by D3L

[Claws and Effect]

Okay....

 

If mathhammer's averages only prove out over the course of thousands of games, what use is it to someone who plays maybe a dozen games in a year?

 

I'm not being snarky there, it's an honest question. I'm capable of math, but I don't enjoy it. Is there a good reason why I should spend my extremely limited hobby time on graphs and spreadsheets instead of painting or playing? Especially when you consider that winning isn't the be all and end all for me.

Edited January 29, 2018 by Claws and Effect

[totgeboren]

Mathhammer is just a tool available to give people a means of better understanding their game experience.

 

If you play and it feels like a unit never manages to accomplish the task you set out to do, mathhammer can allow you see if it's just your game-play that is bad, or if your unit is doing as well as would be expected given average rolls.

 

For example, waaay back in 4ed, Assault Cannons got the rule "Rending". The rule made it easier to damage stuff on a hit-roll of 6.  Suddenly everyone was using Assault Cannons on everything that could take them, because they killed a lot. So much that it was obvious something was awry.
Running through the mathhammer, it was rather easy to see that with those rules, it was entirely expected that Assault Cannons would be the king of all guns, since they had a slightly better chance of killing vehicles than even multi-meltas within short range, and were massively better anti-infantry weapons compared to heavy bolters and the like. And they were often cheaper than many other heavy weapons too.

If GW had used some mathhammer, they would have easily seen this problem waaay before putting it to print. Because their intent was not that one heavy weapon should be the best anti-tank and anti-infantry and anti-monster and being rather cheap, at the same time.

And on a more personal note. Sometimes you have that one dude with say a meltagun that never manages to kill anything. Doing the maths gives you an approximation of what to expect, and suddenly you might realize that the model isn't cursed or that you just have bad luck. It could be that he should only success like 1 in 10 times or something like that.

 

Also, many people have one or two opponents they face more often than others. Against that opponent, they might have the issue described in the first post. A unit of Berzerkers vs some BT dudes, often getting locked in combat. The CSM player might think that his dudes are much more elite than the BT, and expect them to win most of the time. But his experience shows something else. "Why" he might ask, do some mathhammer, and see that he needs to play differently with his Berzerkers. It turns out that are not all that much more elite than the BT all things considered, and so he might make sure to soften the BT up a bit before committing his Berzerkers against them or something.

[Claws and Effect]

I'm very deliberately NOT going to optimize my list against my wife's army (Nids). I could, but I don't want to ruin her game experience by fielding a list she can't beat. She's a newbie and I want her to enjoy the game. If that means I take some losses I'm good with it, since I'll have fun either way.

 

She likes the idea of lots of little gribblies, so my Fire Raptor is staying on the shelf against her, since I already know it excels at killing the stuff she wants to bring and she doesn't own a counter for it.

Edited January 29, 2018 by Claws and Effect

[D3L]

Okay....

 

If mathhammer's averages only prove out over the course of thousands of games, what use is it to someone who plays maybe a dozen games in a year?

 

I'm not being snarky there, it's an honest question. I'm capable of math, but I don't enjoy it. Is there a good reason why I should spend my extremely limited hobby time on graphs and spreadsheets instead of painting or playing? Especially when you consider that winning isn't the be all and end all for me.

I don't believe anyone has told you, that you had to, in fact in the spirit of hobby things, you probably shouldn't, you may find more pleasure by not engaging the maths 

 

as Frater Totgeboren stated, it's a tool you can use to rationalise performance, and understand the average expectation of how things may go.

 

if you do want to play with maths, you can get a handle on the expected value by using the law of large numbers and frequency distributions to estimate what  you could expect, note, this is not the same as to what you will get.

 

some of us have either learnt it, teach this, taught it or work with these concepts, or all of the above and find it hard to switch off... but is it conducive or necessary to having fun? absolutely not, and giving up your fire raptor is cool! (and sportsman like, fair play to you Frater, and i'm sure your partner appreciates it!)

 

Mathshammer will however, tell you quickly, if you work it out, that although you give up the fire raptor, that deathwatch kill-team with 4 frag cannons, is far more effective at horde trimming, and thus, you might be wrong with your assumptions about what's fun, sportsmanship, or effective (nb: I haven't actually bothered to work out if this example is more effective, it was a domain example as to why you particularly may wish to use maths, but I'll leave it as an exercise to the reader)

 

Edited January 29, 2018 by D3L

[toaae]

Is there a good reason why I should spend my extremely limited hobby time on graphs and spreadsheets instead of painting or playing?

 

Of course not. For some of us, working out the average output of something is fun. For others, it's delving into more complicated math Eddie Orlock alluded to. But by no means should it be considered a necessary part of the hobby experience.

 

It just happens that for online discussions, we don't have much else to compare to. Anecdotal evidence is far, FAR worse than mathhammer when it comes to not understanding the context; what is good for one set of players may not be for another. At least math is universal. It's just often perceived wrong on both fronts, from those that think it's unreliable, to those that don't take into context and believe any scenario can scale to any number of models.

[WarriorFish]

The two types of hammer are tools in your war gaming box to help you inform your decisions. No more, but no less. Even the most devoted of number lords will also work with practical experience and wider game theory as will the veteran gamer also look to maths to support potential moves.

 

TL;DR: it should never be maths vs experience, it should be maths and experience ;)

[ERJAK]

The two types of hammer are tools in your war gaming box to help you inform your decisions. No more, but no less. Even the most devoted of number lords will also work with practical experience and wider game theory as will the veteran gamer also look to maths to support potential moves.

 

TL;DR: it should never be maths vs experience, it should be maths and experience ;)

Yep. There are plenty of people in the hobby who are mathematicians and statisticians. And plenty of said people have done plenty of mathhammering to build perfect army lists that...immediately fall over due to any number of extraneous factors including the 'stupidity' factor that math seems to have problems dealing with.

[totgeboren]

 

Yep. There are plenty of people in the hobby who are mathematicians and statisticians. And plenty of said people have done plenty of mathhammering to build perfect army lists that...immediately fall over due to any number of extraneous factors including the 'stupidity' factor that math seems to have problems dealing with.

 

 

Except the ones who win tournaments consistently because they have stacked the odds in their favour time and time again?

Edited January 29, 2018 by totgeboren

[Atrus]

I've never put any stock in mathhammer.  Laws of averages etc, I know from personal experience are a fickle and cannot account for the dice gods or luck.  From a mathhammer point of view, I know by all rights that a wraith knight should go down to 42 S8 -4 D6 melta shots in melta range.  Dice gods and my notorious dice rolls tell me that I never had a chance of doing more than 6 damage to it.

 

"The mathhammer be more guidlines, yarr."

[Wargamer]

I understand that if I have a weapon that wounds on a 2+ that 82.3% of all my rolls should successfully wound. That's what should happen.

 

What frequently DOES happen is I score 4 hits and roll 4 1s multiple times in one game. Seriously, that actually happened to me in the last tournament I played in. I failed so many easy rolls my opponent was starting to feel sorry for me.

 

Mathhammer says I shouldn't fail that many rolls over the course of a single game. But I did.

 

Outlier case? Of course. But I've learned that while mathhammer can be useful, it isn't always going to predict what will actually happen. 4 lascannons should kill at least 3 marines the majority of the time. I failed to even wound one.

4 Lascannons should not kill 3 Marines.

 

Each shot has a 67% chance to hit. That's 2.4 hits. So let's call that 3 and assume you did reasonably well.

 

Each shot has an 83% chance of wounding. Again, from our three hits you expect 2.4 wounds from 3 hits, or 1.6 from 2. So I think it's fair to call that 2 wounds.

 

So even before factoring in saves, it's clear you are overestimating your odds because you assume that a 2+ is an auto success.

 

Or to do this another way, there are 1,296 possible combinations of rolls for your four Lascannon shots.

16/1296 results are 0 hits.

128/1296 results are 1 hit.

384/1296 results are 2 hits.

512/1296 results are 3 hits.

256/1296 results are 4 hits.

 

Add up those totals, and you can expect to get 3 or 4 hits only about 59% of the time.

 

Like I said. Mathhammer is fine, it's people not understanding it that's the issue.

Edited January 29, 2018 by Wargamer

[Sloeberjong]

Mathhammer helps you gain small advantages for it makes it obvious what weapons perform best against specific targets. It helps building lists. It'll help me when deploying so I can get to the best targets for my units. It doesn't consider things like terrain, movement, weapon ranges, character effects, psychic powers, strategems (yours and opponents) and, to some extent, taking casualties. In that sense it's quite relative.

 

I'm an engineer so I use mathhammer automatically in my head. I use it to decide what units are best used against what other units (if I get to shoot unit x against unit y what would be a reasonable outcome?). It's not set in stone, you can get lucky or unlucky so you still need some common sense. You'll need a backupplan if it falls apart. 

 

An extreme example is anti tank units. We all know that using bolters as AT weapons is a bad idea even though they CAN damage tanks. Mathhammer teaches us that a lascannon, on average, will be a better weapon against tanks for the points than a squad of bolters. You don't need to calculate anything to realise this, but for some things it might be a bit more nuanced and so you can calculate some probabilities. It can help you outweigh the choice of Dakka or flamer Aggressors. I haven't done the math on those, but I think they might have subtle differences.

 

Basically it's not the end all be all, you need some common sense about how you want to use the units you've calculated. Because you can't calculate movement and stuff.

[chapter master 454]

 

I understand that if I have a weapon that wounds on a 2+ that 82.3% of all my rolls should successfully wound. That's what should happen.

 

What frequently DOES happen is I score 4 hits and roll 4 1s multiple times in one game. Seriously, that actually happened to me in the last tournament I played in. I failed so many easy rolls my opponent was starting to feel sorry for me.

 

Mathhammer says I shouldn't fail that many rolls over the course of a single game. But I did.

 

Outlier case? Of course. But I've learned that while mathhammer can be useful, it isn't always going to predict what will actually happen. 4 lascannons should kill at least 3 marines the majority of the time. I failed to even wound one.

4 Lascannons should not kill 3 Marines.

 

Each shot has a 67% chance to hit. That's 2.4 hits. So let's call that 3 and assume you did reasonably well.

 

Each shot has an 83% chance of wounding. Again, from our three hits you expect 2.4 wounds from 3 hits, or 1.6 from 2. So I think it's fair to call that 2 wounds.

 

So even before factoring in saves, it's clear you are overestimating your odds because you assume that a 2+ is an auto success.

 

Or to do this another way, there are 1,296 possible combinations of rolls for your four Lascannon shots.

16/1296 results are 0 hits.

128/1296 results are 1 hit.

384/1296 results are 2 hits.

512/1296 results are 3 hits.

256/1296 results are 4 hits.

 

Add up those totals, and you can expect to get 3 or 4 hits only about 59% of the time.

 

Like I said. Mathhammer is fine, it's people not understanding it that's the issue.

 

 

Should not vs. what happens is a huge difference. Anyone who plays tabletop will look at four lascannons opening up on marines in the open and think in general "well that's 3 marines dead" in general as the two following saves that matter are both 16.67% rates against the lascannons (fired by marines). Yes there is math saying 2 survive but with experience on the table it wouldn't be unfair to EXPECT 3 to die from that salvo as it is highly likely.

Like I said with Tablehammer vs. Mathhammer, one gives you understanding of the unit in theory, the other in practice and sadly one is from experience while the other is easily done (and likely done incorrectly as I have done...must of rolled a 2 on my math check XD) by anyone.

[NatBrannigan]

I don't mind a bit of math, it can tell you what you "should" expect in some circumstances. I do think some of the math is used to prove particularly stupid points though. The example's above are nice and sensible for example whereas other examples, not so much!

 

Such as someone in the "Are Guard OP" thread comparing 10 Terminators and a special character's damage output to the equivalent points of Guard Infantry squads. That was 160 infantry, then they all magically were issued the first rank fire second rank fire order and were also all within rapid fire range... Low and behold their damage was higher so Guard Infantry are too good.

 

How did all those Guardsman get their orders?

Why wasn't the points cost of the officers required taken into account?

How did those Guardsman all get within rapid fire range? They don't physically fit!

How did they get there without taking any casualties?

 

That's where it falls down and tablehammer comes into it a bit. Cover was a good example. Try getting 160 Guardsman into cover. I suspect it's easier to get 11 Terminators into cover.

 

Still nothing wrong with a bit of math!

[Mileposter]

I posted it once before... "Should" is such a dangerous concept. It's my opinion that "should" has no business in the hobby, on any topic, on any level, at any point in the game. You're far healthier thinking without that concept. It's hard, though - and even I've fallen prey to using the term a few times.

 

But Mathammer doesn't tell you what SHOULD happen. It can't. It can only tell you what's LIKELY.

 

That part's already been covered a dozen times above. I only repeat it to lead into this: Some say that it's just semantics. 'Should' and 'likely' are close enough, it doesn't matter. But that little difference makes a huge impact on how you treat it.

Change the way you think about it, and you'll change the way you treat it. If you change the way you treat it, you'll change how you feel about it. But you'll never be able to change how you feel about it unless you change how you think about it.

Change the way you think about it, and you change the world.

 

And for the semantic naysayers:

http://i.imgur.com/t9kd3pw.jpg

Try that little exercise and then say semantics aren't important.

[NatBrannigan]

Well...

 

If we really want semantics I give you this from the Oxford English dictionary.

 

Should: Used to indicate what is probable.

 

So Mathhammer does in fact tell you what should happen. It does not tell you exactly what will happen.