unded
Junior Strategist
Posts: 760
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Post by unded on Dec 17, 2017 15:10:52 GMT
It won't really matter, Mac.
Each attack is an independant event, so as long as you aren't averaging the main-hand and off-hand damage, then you're simply going to multiply the expected damage outcome by the number of attacks, which will come to the same conclusions. The X% to hit in his calculations are all you really need.
Regarding the buffs, you're going to have to somehow price in spell-avoidance and shooting-avoidance to your comparison if you're comparing their effectiveness for their points (I know this started out by comparing damage output, but the points you pay are for both offensive and defensive capabilities).
-und_ed
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Post by macdaddy on Dec 17, 2017 15:28:36 GMT
undedWell the issue is if you treat each attack as it’s own isolated probability function you are losing a large part of what happens when you roll a series of dice the math changes. Rolling 4 6’s in a row on 2D6 is less likely than if you take each roll in its own little sphere of probability. In other words, The more you roll, the more you increase the probability of rolling a result less than 6. When you do the math in a series it changes how many attacks hit. I’m going off this from a limited Education in statistics and to probability. So I’m more than happy to be shown wrong , I am honestly too lazy right now to go through all the math for that haha. I think saying “the crusader is better at cracking arm than the juggernaught” is Incredibly desengeneous. If crusaders were better in that regard you would see them everywhere. Instead you see a lot of mixed protectorate jack builds (or dervish Spam...*sigh*) Granted, you could take the whole argument that protectorate has a better balanced jack stable, which has merit. But that’s a whole mother discussion
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Post by droopingpuppy on Dec 17, 2017 15:40:43 GMT
droopingpuppy +1 Mat is way more relevant than +1 Pow.. IME rolling hard sixes is some of the diciest moments in my gaming. This is for my opponents too. It for certain matters more against Def13 or 14. Needing 7’s to Hit is the boost threshold and the crusader is really gonna struggle to kill anything Def 13-14. Also, in your math are you including bought attacks? Because that’s a big deal. What makes Mat relevant IS WHEN YOU USE A LARGER VOLUME OF ATTACKS. (Sorry for caps bold doesn’t work on my phone) When you only give each model 2 attacks, it skews the math to make Mat look less relevant. You honestly need to go back and redo all of that math assuming each jack buys 3 extra attacks (or 2 extra assuming charge) to give us better and more precise results. No the math says opposite, and you guys don't give me something to turn it other than your personal taste. Personal taste doesn't prove the model's real strength and possibility. And that's more meaningful because warjacks and warbeasts can make the additional attacks. If you really want to hit only one attack then accuracy is quite important, really(such as want to trigger a chain attack or making a power attack). But for armor cracking the targets are generally have lower DEF so most hits are quite accurate already, and you can bought many attacks(usually at least 4 attacks consider focus spent) so average expected damage per one attack is actually important thing. For the clarify, the math shows you the expected average damage per an attack; average damage divide hit rate. So if an attack hits by 50% and cause 10 average damage on a hit, then the result is 10÷2=5 average damage. In this case, if you make two attacks then probably only one attack hits(50% of two attacks) and one hit causes 10 damage, so you cause 10 damage by two attacks and the result is 5 damage per one attack.
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unded
Junior Strategist
Posts: 760
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Post by unded on Dec 17, 2017 16:07:50 GMT
I'll illustrate it for you, Mac. Puppy's math are sound, so I'll use the Hammersmith and the Stormclad for a springboard.
For the Hammersmith (11/19), an individual attack from a Juggernaut gives an expected damage of 6.41. If you load up on FOC, you simply have 4 attack * the expected damage, which is 25.67. The crusader has an expected damage of 6.667 per attack. Again, loading up on FOC just gives you 4 * 6.6667 = 26.67, still outperforming (by a small margin) the Juggernaut.
For the stormclad (12/19), an individual attack from a Juggernaut gives an expected damage of 5.83. Loading up on FOC, expected damage output is 4 * 5.83 = 23.33 The Crusader has an expected damage of 5.77. Loading up on FOC gives 4 * 5.77 = 23.11.
As you can see from the above examples, it's just a simple multiplier, which means whatever results you garner from the first individual attack analysis will carry through to the full focus spend analysis.
Where this becomes a lot (one hell of a lot) trickier is when analysing variance (which is essentially a measure of reliability), but I think that's more stats than anyone really wants to dive into here.
-und_ed
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Post by macdaddy on Dec 17, 2017 16:50:04 GMT
Ok I think I understand where you guys are coming from now. Thanks for taking the time to clarify.
I’ll have to take some time and play around with this. It seems like a fairly interesting little excessise and may be worth going into variance for a more refined result (mostly for my own development as I play 2 factions with lots of Mat 6)
It’s for sure interesting to see the averages played out. Most games a heavy kills what it touches short of bad dice, but maybe it’s my perspective on what “bad dice” is that makes that more skewed.
I’m still more convinced that Mat7 has a bigger impact than the math shows, mostly because of my experience with Mat6 and Mat7 in game. But the hard math seems to point differently. Hmmmmm
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unded
Junior Strategist
Posts: 760
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Post by unded on Dec 17, 2017 19:10:49 GMT
For me I swing in favour of the MAT 7, but that's mostly because my most loathed opponents are Cygnar, who sport DEF 12 jacks (2 of my factions have easy access to wraithbane, so I don't factor in Arcane Shield much). I also face a lot of Trollbloods, who again are sporting DEF 12 beasts who are effectively ARM 20 the whole time. More of a local meta thing really, but with a tiny meta like my own that's all that really matters (to me).
One of these days I'll get around to writing an article on Variance and bore everyone on here to tears. Luckily for everyone, today is not that day.
-und_ed
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Post by droopingpuppy on Dec 17, 2017 19:26:52 GMT
Anyway it is sure that score a miss on a melee attack is very, very annoying to see, because making melee attack also means you are enter the enemy's melee threat range as well. Probability gives us the expected value, but it does not give a proof for the result of the next roll we made.
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Post by wolfchild on Dec 19, 2017 11:51:29 GMT
Factoring in a boost to hit, or the fact these jacks usually have 2 melee weapons means your primary damage per hit (with hit ratio factored) isn’t going to be the same multiplier for the rest of that jack’s attacks. Eg. A jack w a POW 14 and a POW 18 weapon is going to have lower damage output on average over initials than its bought attacks, as it will only use POW 18 on bought attacks. Also, as has been noted by others, shifting from a 7s to hit on 2d to 7s on 3d massively shifts the odds compared to 6s on 2d to 6s on 3d, because of the skew on the bell curve. A player WILL boost to make sure they hit rather than just keep rolling. There variables are almost too massive to compare without a huge algorithm. The model must take into account when it’s better to boost damage too. If a jack/beast IS ‘pillowfisted’, then it will likely need to boost damage over bought attacks, but you’d hope it could hit more reliably.
I doubt anyone without use of a computer and a host of algorithms to calculate all the jacks and beasts’ potentials can truly establish a factor for raw ability to cause damage in game. Is that what u truly mean when ur trying to quantify pillow-fisted”?
Maybe u need to revise what you’re defining as “pillow-fisted”. Literal ‘pillow-fisted’ conjures an image of a boxer wearing the padded gloves. Suggesting the boxer would hit much harder they u took the gloves off. The accuracy of the boxer is not reduced noticeably, yet his/her damage output is artificially reduced. Using that definition, none of our jacks / beasts are pillow-fisted unless they have a debuff spell or effect on them.
Sorry semantics ......
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Post by droopingpuppy on Dec 19, 2017 18:03:52 GMT
Remember that if a heavy warjack/warbeast needs to boost either attack or damage roll, it is not a good situation already.
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Post by welshhoppo on Dec 19, 2017 18:18:40 GMT
Remember that if a heavy warjack/warbeast needs to boost either attack or damage roll, it is not a good situation already. I knew warp wolves needed a nerf..... say, someone who is better at doing Mathy things than me, what are the odds of the Crusader and Huggernaut of one-rounding the basic hordes heavies? Because I always feel that due to the lower chance of crippling them, they can often wait out the 2 turns needed to smash a warmachine heavy.
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Post by chillychinaman on Dec 19, 2017 21:35:43 GMT
Can't take credit for the calculations, but buyorboost.com says:
Dire Trolls and Legion Sharks are about 12/18 with 30boxes. Assuming full focus and a charge, a Juggernaut has about 37% while the Crusader sits at 12%.
For an Angelius at 14/16/25 it's 45%/17% and for a Warpwolf it's 14/16/29 32%/9%.
For reference the numbers for a Crusader are 10/19/32 20%/4% and a Juggernaut 10/20/34 2%/0.2%
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princeraven
Junior Strategist
Shredder spam is best spam
Posts: 256
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Post by princeraven on Dec 20, 2017 1:46:00 GMT
That's an unbuffed Crusader I'm guessing since I'm getting 36% with Hymn of Battle included against 12/18/30.
Also your Legion stats are slightly inaccurate, Carnivean chassis beasts are 11/18/30, Angelii are 14/17/25, S/Neraphs are 14/16/27.
To compare, a Carnivean has a 35% chance of killing a Crusader and a 5.7% chance of killing a Juggernaut. A Strength warped Feral Warpwolf with/without Primal has a 28%/88% chance to kill a Crusader and a 3.3%/50.6% chance to kill a Juggernaut.
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