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My Mathhammer Page, Clever People Required


kiblams

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Last night I started a page to do my mathhammer on after spending a while creating a spreadsheet for me and my friends to use.

This is the URL:

Kiblams AoS Mathhammer Page

The page is very basic with pretty much no styling at all, but I wanted to get it working correctly before tackling how pretty it looks. That's were you guys come in; I wanted to see if some clever people could double check the numbers for me?

I'm also looking for a little feedback on if you think it will be useful to you personally and if there is anything glaringly obvious missing from the way that it functions?

Thanks for your help guys!

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Doesn't seem to work O.o I'm testing the Tzeentchian Spears of a unit of 6 Enlightened: 13 attacks, hit on 4+, wound on 3+, rend -1, damage 2. The average damage output of these attacks is 13*1/2*2/3*2=8.67 against a target with no save or a 6+ save. If I put rend=1 into the calculator, I get the correct result against a target with 6+ save - however, if I give the target no save, I instead get a 10.10 damage result. If I set rend=-1, I instead get 5.77 damage. It seems that I need to set the rend characteristic to positive numbers, and that the calculator bugs out if the save becomes worse than no save.

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9 minutes ago, Solaris said:

Doesn't seem to work O.o I'm testing the Tzeentchian Spears of a unit of 6 Enlightened: 13 attacks, hit on 4+, wound on 3+, rend -1, damage 2. The average damage output of these attacks is 13*1/2*2/3*2=8.67 against a target with no save or a 6+ save. If I put rend=1 into the calculator, I get the correct result against a target with 6+ save - however, if I give the target no save, I instead get a 10.10 damage result. If I set rend=-1, I instead get 5.77 damage. It seems that I need to set the rend characteristic to positive numbers, and that the calculator bugs out if the save becomes worse than no save.

Great catch! Thanks for finding the negative save bug! (that's fixed now)

Yeah.. I kinda made rend a positive number... I will look to reverse that!

Thanks again!

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18 minutes ago, Auticus said:

For me the reason I'd not use it is simply because I don't want to have to input the same data over and over again.  The data I compiled takes all of the units in the game and comes up with their averages and stores it in a SQL table so you just reference the unit.  

Wow, that must have taken a while, and be a pain to keep updated. I really didn't fancy the hassle and to be honest wasn't sure where I would stand with GW and IP on that front.

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No problem! There seems to be some numerical errors as well. If I give the attacks reroll 1s to hit I get a slightly different result compared to if I give them reroll 1s to wound - in reality, these two bonuses yield the exact same damage since they are multiplicative and simply applied at different stages of the attack chain.

13*(1+1/6)*1/2*2/3*2 = 13*1/2*(1+1/6)*2/3*2

One functionality I would like is to be able to enter in several attacks together, and get the total result. For the enlightened in question, it would be nice to enter the spears, beaks and discs and get the total damage against all saves instantly, instead of having to do them all separately and recording all 6 values each time.

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27 minutes ago, Solaris said:

No problem! There seems to be some numerical errors as well. If I give the attacks reroll 1s to hit I get a slightly different result compared to if I give them reroll 1s to wound - in reality, these two bonuses yield the exact same damage since they are multiplicative and simply applied at different stages of the attack chain.

13*(1+1/6)*1/2*2/3*2 = 13*1/2*(1+1/6)*2/3*2

One functionality I would like is to be able to enter in several attacks together, and get the total result. For the enlightened in question, it would be nice to enter the spears, beaks and discs and get the total damage against all saves instantly, instead of having to do them all separately and recording all 6 values each time.

Are you sure? I would think that is only the case if you have either hits or wounds set to 'auto'. I just tried hits on 'auto' with wounds 4+ rerolling 1s, and then hits 4+ rerolling 1s and wounds on 'auto' and they returned the same numbers. 

I do have multiple attached on my 'to do list' but as a short term workaround I have added the history so you can compare and add two different weapons easily. 

Thanks for your continued feedback! :)

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4 hours ago, hot_boy_ronald said:

I just had more damage dealt when someone had rerolls on failed saves. Should be less damage dealt. 

 

EDIT: All rerolls, whether on failed saves or save rolls of 1 result in more damage dealt to the target. 

I fixed rend yesterday from a positive to a negative number, I must have broken the tells in the process ? thanks for the heads up!

Fixed that now :)

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does this stuff even actually work?

often seeing people go on about math hammer and using the most efficient points for damage. then surely everyone would be using the same army if you wanted to win....

yet squiggs won the last heat didnt they & Seraphon almost won the one before. 

 

almost as if 2>1 therefore 2= better doesnt quite work. 

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First off, I'd state that player ability is by far the most important. Then there is also the fact that point efficiency is not the be all end all in list design. While math hammered point efficiency is important to keep in mind, making a strong list is about combining the tools you need to win the game. While Brimstone Horrors, for example, may be very point efficient, having 400 of them will not help you win any games, because you lack the tools to do the job. However, bringing 60 of them and using them to their strengths could be a very good idea.

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I personally find mathhammer more intriguing than anything. I am by no means a power gamer, but I like to know roughly what my units are likely to do against different saves and rerolls.

It's not going to win you games, and I don't think anyone is under that illusion; model placement and decisions in game are what wins games, but it should at least arm you with an understanding of what a unit is capable of.

It also helps to put my mind at ease when I see 10 Sisters of the Watch wipe out 13 of my Plague monks in one round of shooting, as I know it's about statistical xD

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2 hours ago, tolstedt said:

I find the percentages used in the AoS combat calculator to be more useful than a straight damage characteristic.

What does damage dealt mean here?  Average?  Expectation?  I like to see the curve as well.

The damage means that if all dice rolled perfectly statistically; that's how much damage would be dealt,

I find it gives a good idea of what I can expect from a unit provided I'm not rolling terribly or above average in terms of luck.

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I did some of these sort of calculations when I was trying to find an excuse to build and paint some Black Guard models instead of another unit of Executioners..

Unfortunately the statistics said  No, there really is no reason to build that kit as black guard.

The more relevant part of this story is that I also rolled a hell of a lot of dice to test the statistics (yes it was a slow evening that day!) dice average usually turns out 1 or 2 Lower per 20 dice than the stats would suggest...

I guess this is because a dice roll is not only an excercise in random number statistics - there are a bunch of random physical influences contributing to the result too. But its interesting that it would consistently be LESS than stat average!? I have no idea how that works.

I agree its quite fascinating and hats off to you guys who take the time to make it into a big excercise - working it out for a couple of models was enough for me I think! 

 

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Funny,  I started doing a similar project a few weeks ago and have it up online as well!  Good to see I wasnt the only one doing so, I just need to actually get to work on making mine prettier haha.

 

Edit:  Nice to see we get the same results, at least so far as i've tried.  Means my math hasnt completely failed me over the years!  I like that you list damage vs all saves as well as the one entered by the user, that could be nice for figuring out what unit is the best target for another.  

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3 hours ago, Drofnum said:

Funny,  I started doing a similar project a few weeks ago and have it up online as well!  Good to see I wasnt the only one doing so, I just need to actually get to work on making mine prettier haha.

 

Edit:  Nice to see we get the same results, at least so far as i've tried.  Means my math hasnt completely failed me over the years!  I like that you list damage vs all saves as well as the one entered by the user, that could be nice for figuring out what unit is the best target for another.  

Thanks! Mine is also seriously lacking in styling! ?

Ok to seeing yours if you go 'public' with it ?

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20 hours ago, Twitch of Izalith said:

I guess this is because a dice roll is not only an excercise in random number statistics - there are a bunch of random physical influences contributing to the result too. But its interesting that it would consistently be LESS than stat average!? I have no idea how that works.

Either you haven't rolled enough dice or the dice have a bias. There is literally no reason for a fair D6 not to average out at 3.5.

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On 9/23/2017 at 12:04 PM, Gilby said:

Either you haven't rolled enough dice or the dice have a bias. There is literally no reason for a fair D6 not to average out at 3.5.

I rolled 60 dice 30 times figuring that would represent an average game. They are just standard 12mm dice.

There is reason and its that when you roll a dice you not not only generating a random number between 1 and 6 you are Primarily deciding which side of a cube will land facing upwards - which has 6 results but ones determined by physical variables not numerical ones. you determine which face lands upright by its starting facing, the angle and force its thrown at, the air it moves through and the surfaces it contacts with. 

All the factors are completely random so dice are a great way of determining random results but with the number of dice rolled in an average game, the physical method of generation is likely to produce other than statistically average results. If you roll 60 dice you never get 10 of each number. In fact another anomaly I noticed is that you very often get 1 particular number with far less results than you would expect out of the 6. Again statistics does not have an answer for this - a dice roll is a physical probability not a pure mathematical one.

I don't mean to sound like i'm making a big deal out of it or saying you are totally wrong but there is some sense to what I am saying too. 

 

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On 9/24/2017 at 3:13 PM, Twitch of Izalith said:

you determine which face lands upright by its starting facing,

As this is random all other variables that have any sort of non-random effect will simply maintain this original randomness, unless you're using non-fair dice. Trust me on this, the result of a fair dice is random and over the long run will average out at 3.5. Humans have evolved to notice patterns and are notoriously bad at judging probabilities as we have an innate desire for things like this to seem random. Which usually means us looking for patterns, i.e. if I just rolled 10 sixes in a row the probability of another 6 feels like it should be less than 1/6, but it is just as likely as it was for the first roll.

On 9/24/2017 at 3:13 PM, Twitch of Izalith said:

If you roll 60 dice you never get 10 of each number. In fact another anomaly I noticed is that you very often get 1 particular number with far less results than you would expect out of the 6. Again statistics does not have an answer for this -

60 dice isn't that many. The explanation for this is the law of large numbers. The 'particular number with far less results' will be random, so roll those 60 dice 1000 times and every number will have had the opportunity to be the 'particular number' and the difference you're seeing will average out.

Result of a typical roll of 60 dice:

Result Count
1 13
2 7
3 15
4 8
5 13
6 4

Results of typical roll of 60,000 dice:

Result Count
1 10129
2 10035
3 9945
4 9879
5 9994
6 10018

 

The result of a  dice roll is a discrete uniform distribution. 

 

On the original topic. I started to make a tool for calculating wounds etc. but never got around to finishing it after messing up when modifiers were applied with regards to re-rolls. Will get back to it when I have more free time, but tried to include as many abilities and modifiers etc. as I could think of. Any obvious ones I missed?

1.jpg.3839465c0131c3319a12f7642907c0f1.jpg

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20 hours ago, Gilby said:

On the original topic. I started to make a tool for calculating wounds etc. but never got around to finishing it after messing up when modifiers were applied with regards to re-rolls. Will get back to it when I have more free time, but tried to include as many abilities and modifiers etc. as I could think of. Any obvious ones I missed?

It looks fairly comprehensive, It's annoying how the abilities in AoS are so nuanced and specific for saves vs damage and mortal wounds. I made the same page now but for 40k and the extra saves in that game system are very generic, so I have been able to account for them using 2 drop down boxes, one for invulnerable saves and one for saves vs damage (which includes mortal wounds)

As it stands I have no idea where to begin with adding the crazy extra saves that can be used in AoS, could be at it for weeks and the page would become very cluttered and confusing.

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38 minutes ago, kiblams said:

As it stands I have no idea where to begin with adding the crazy extra saves that can be used in AoS, could be at it for weeks and the page would become very cluttered and confusing.

No idea about making websites but my plan in excel was to make all the parameters lookup from a table on another page. So I'd enter the data for the unit regarding it's abilities and stats into the table with the units name at the top and then have a drop down box at the top of the tool limited to the row of unit names. Once I had it all working I'd be able to just choose a unit I've put the values in for already and then only three boxes would be worth looking at; wounds to save, mortal wounds to save and total damage done. It would need a second drop down for the unit doing the saves too. Then I'd look at adding in things like damned terrain, etc. Could just hide most of the clutter then. Probably easier to show than explain it if I ever finish it! :D

 

38 minutes ago, kiblams said:

@Gilby I hope you rolled all 60,000 of those dice :D

You are right of course but it doesn't play out over the course of an average game - you don't roll that many dice. Good theoryhammer chat though B|

Haha! Even I'm not that mad xD

GHB1 Kunnin Ruck came close! But yeah, it'd be boring if it did, has to be some luck involved. :P 

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