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Post by thorpyuk on Mar 8, 2024 16:42:41 GMT
Hi All, As some of you may know, i'm a real fan of mathhammer, and having started a TK army recently (despite the fact everyone says they're crap, I like theme & style!) I decided i'd take a closer look at the maths behind their most basic of troops... the humble Skeleton Warrior. I think what attracts me most about them is the points cost... 4 points/man is very cheap, and they even come with a shield!! Unbreakable & Fear also adds to the attraction, despite the drawbacks of no march & the crumble (unstable). I decided to first of all double-check what 90% of TK players are saying - take them neat, with no upgrades. Is that correct? To test the theory i've pitted a unit of 40 with full command (190 points, 10 x 4) against a unit of 20 naked dwarf Longbeards coming in at 270 points (5 x 4). (Ok not physically naked, but naked in a points-sense - absolutely no upgrades, not even a shield!) I did this on purpose - i wanted a comparison whereby the light armour had an effect, so it had to be str 4 or lower.. HW&S - 22 attacks, 7.33 hits, 2.44 wounds, 1.63 kills, 4.07 losses, differential +2.6 (the difference between points lost/round and points killed/round. Positive means that the unit is more effective on a point-for-point basis. Ok, so not a bad start, they seem to be worth their points at least! Although they'll eventually lose, they're value-for-money on a per point for point basis. HW&S + LA - 22 attacks, 7.33 hits, 2.44 wounds, 1.63 kills, 3.40 losses, differential +2.5. Virtually identical.. S&S - 29 attacks, 9.67 hits, 3.22 wounds, 2.15 kills, 4.89 losses, +0.9 differential. Ok so giving them spears and the extra rank of attacks does give them a pinch more hitting power, but the loss of the parry costs more than it gains. S&S + LA - 29 attacks, 9.67 hits, 3.22 wounds, 2.15 kills, 4.07 losses, differential +1.5. Slight improvement on naked spearskellies, but then we're at a whopping 6 points a man! And i'm cheap!! (Just ask the Mrs!) SO virtually no difference across all 4 readouts, but I bet when I give the dwarfs great weapons, that massively skews in favour of just the basic 4-point model: HW&S - 22 attacks, 7.33 hits, 2.44 wounds, 1.63 kills, 5.09 losses, differential +1.1 so not as good against the higher strength attacks as the number of wounds increases, but overall not too terrible still naked. HW&S + LA - 22 attacks, 7.33 hits, 2.44 wounds, 1.63 kills, 5.09 losses, differential -4.0 - now it's a clear win without the upgrade. S&S - 29 attacks, 9.67 hits, 3.22 wounds, 2.15 kills, 6.11 losses, -1.8 differential. S&S + LA - 29 attacks, 9.67 hits, 3.22 wounds, 2.15 kills, 6.11 losses, differential -8.0... totally not worth it against higher-strength attacks. So the conclusion of this very basic look at skeleton warriors are that light armour probably is only worth it against mass missile troops like elves, and spears are definitely not worth it. This is just the very start of my deep-dive into skellies - i'm fully aware that my analysis is super-basic and doesn't look at the crumble rule, buffs, other opponents etc etc so stay tuned it's coming!  |
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Post by thorpyuk on Mar 15, 2024 8:41:49 GMT
Ok, not lets add the results of unstable into the mix & see how they stack up. Note that of course this assumes that it's a one-on-one situation, with no other supporting units or flank/rear charges etc, no BSB or anything else influencing combat - it's the basic results of the combat resolution. I'll then include another additional unit, in another formation, to see if the results are consistently in favour of the 'best value' configuration.
Lets use our initial 'naked longbeards, 5 x 4' scenario, with full command again. If I include the additional losses from unstable, lets see what that does to the differentials (remember we're 10 x 4 with full command):
HW&S: previous +2.6, new -1.4
HW&S+LA: previous +2.5, new +2.5 (combat is drawn)
S&S: previous +0.9, new -9.1... losses increase significantly here with loss of parry
S&S+LA: previous +1.5, new -4.5
So on first glance, both 'spear' and 'sword & board' configurations are actually improved by light armour being included. However, my suspicions are that when higher strength attacks hit & wipe out the benefit of the save altogether, this will go in the opposite direction, so lets include the results of the 'great weapon' longbeards before we move onto... a hoard of HE Swordmasters!
HW&S: previous +1.1, new -9.6
HW&S+LA: previous -4.0, new -14.0
S&S: previous -1.8, new -21.8
S&S+LA: previous -8.0, new -32.0
Now all of a sudden, the tables are turned - the additional point spent on light armour is completely wasted due to the higher-strength attack & just erodes the points differential further.
Ok, lets see how our el-cheapo skellies fare against the elite high-elf swordmasters! Now clearly this is a very unfair matchup... the swordmasters (despite being massively undercosted) are worth more than double the cost of our humble unit & aren't ever going to be a matchup we want. This time, i'm increasing the number of ranks to 6, giving us 60 skellies - it doesn't affect the math, but due to the high number of wounds received, it seems sensible. Lets take a look at the results:
HW&S: before unstable -58.9, after unstable -142.9
HW&S+LA: before unstable -82.5, after unstable -187.5
S&S: before unstable -93.2, after unstable -213.2
S&S+LA: previous -121.5, after unstable -265.5
Some horrendous numbers in there (why oh why did they feel the need to make swordmasters 2 points cheaper?!), but they support the conclusions above. Essentially, against massed high-strength attacks (ogres, WoC etc), just take naked skellies for the parry save. Against lower-strength attacks like empire, goblins, most elves (inc massed str 3 bow-fire) - light armour is a worthwhile upgrade! Lets prove it by switching that Swordmaster hoard for a hoard of empire spearmen hitting at strength 3:
HW&S: before unstable -5.7, after unstable -17.7
HW&S+LA: before unstable -5.7, after unstable -15.7
S&S: before unstable -14.2, after unstable -24.2
S&S+LA: previous -12.0, after unstable -12.0
So there we have it... a definitive answer as to what is the best way to configure our skeleton warriors. Against most enemies naked is fine, but the light-armour upgrade is likely worth it if you know you're likely to see a lot of strength 3/4 attacks including massed missile fire. Spears are almost never worth it - leave them at home!
Stay tuned for a deeper dive into the math behind the skeleton elites... Tomb Guard!
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Post by thorpyuk on Mar 28, 2024 15:56:11 GMT
Alright... as promised, lets take a closer look at Tomb Guard. On the face of it, their stats aren't particularly amazing... WS3, S4, T4, 1A is pretty average for an 'elite-level' troop... but they do have the addition of - killing blow! They are also able to purchase halberds, giving them a base S5 which is nice, albeit at a high cost of +2pts / man.
First off, lets see how the basic hand weapon & shield in horde formation (10 x 4) fare against that unit of 20 longbeards (both with full command, longbeards hand weapon only):
TG + HW&S = 22 attacks, 3.67 killing blow hits, 7.33 standard hits, 6.72 wounds caused, 2.55 wounds received. Differential +52.7 - so first off, they are definitely worth their points & perform well against the small longbeard unit - although they are a 470pt unit vs a 270pt unit. In this scenario, they would win combat by an average 6 points & kill the unit in 3 turns if it didn't break.
TG + Halberd = 22 attacks, 3.67 killing blow hits, 7.33 standard hits, 8.56 wounds caused, 3.67 wounds received. Differential +55.0 - this seems to suggest that the 2pt upgrade to halberds is probably worth it, given it's extra armour-piercing capabilities. In this scenario, they win combat by an average 7 points & kill the longbeards in 2.3 turns if they don't break.
Note that i've been a bit unfair on the poor longbeards. I've assumed nobody charges, and if they did get a charge off, they'd get +1S on the charge.
Lets add-in longbeard reinforcements & see how the math stacks up again. This time it's horde vs horde & i'm giving the longbeards a shield too - now it should be interesting because on paper both units cost exactly the same points (550) - at least when the tomb guard are upgraded to have halberds:
TG + HW&S = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 7.18 wounds caused, 7.18 wounds received. Differential +14.4 (+14.4 including unstable) - now combat is tied because both units are causing the same number of wounds each. Positive differential because with the HW&S option (11pts / man), the TG unit is cheaper. Lets see how they get on with halberds:
TG + Halberd = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 9.09 wounds caused, 10.33 wounds received. Differential -16.2 (-29.2 including unstable). Now, they lose combat & the differential begins to turn negative - interesting how picking the matchups can be crucial!
So what have we learned so far about tomb guard? Firstly that they're a very good unit & definitely worth their points cost. Secondly, that the halberd upgrade is worth it & makes sense in some situations.
As a last analysis, lets pit them against... that High Elf Swordmaster horde!
TG + HW&S = 31 attacks, 10.33 hits, 5.17 killing blow hits, 10.91 wounds caused, 18.89 wounds received. Differential -66.0 (including unstable -165.0) - the ludicrously undercosted elves murder the TG unit. Including the results of unstable, an average 28 models would be lost in a single round - ouch! Lets see how the halberds get on:
TG + Halberd = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 13.78 wounds caused, 22.67 wounds received. Differential -115.6 (-245.6 incluidng unstable). In a single round, 33 TG would be slaughtered - thats almost the entire unit to a man! The only consolation would be the 14 kills in return. I think it's worth pointing out that both these units cost EXACTLY THE SAME... it really does show how badly-balanced the elf books are...
Ok, hope that helps someone! In a nutshell, Tomb Guard are a great unit, the halberd upgrade can be useful in the right matchups but the standard HW&S versions are also effective, but whatever you do, don't match them up against a swordmaster hoard!
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Post by grandmasterwang on Mar 30, 2024 5:55:20 GMT
I am loving this mathhammer.
I'd like to go back to the original example of pleb skeletons.
Tomb Kings are a unique case in that they have 2 easy ways to buff themselves without magic with a Necrotect and a Tomb Prince/King.
While no doubt the spear upgrade cost is still too much, with rerolls to hit in that first turn, the spear skeletons may get a significant benefit over the hw/shield skeletons.
This goes beyond the realm of mathhammer but it's worth mentioning that the Spear/LA skeletons benefit the most from the Lore of Nehekhara bringing them back due to the higher cost.
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Post by grandmasterwang on Mar 30, 2024 6:04:45 GMT
Alright... as promised, lets take a closer look at Tomb Guard. On the face of it, their stats aren't particularly amazing... WS3, S4, T4, 1A is pretty average for an 'elite-level' troop... but they do have the addition of - killing blow! They are also able to purchase halberds, giving them a base S5 which is nice, albeit at a high cost of +2pts / man. First off, lets see how the basic hand weapon & shield in horde formation (10 x 4) fare against that unit of 20 longbeards (both with full command, longbeards hand weapon only): TG + HW&S = 22 attacks, 3.67 killing blow hits, 7.33 standard hits, 6.72 wounds caused, 2.55 wounds received. Differential +52.7 - so first off, they are definitely worth their points & perform well against the small longbeard unit - although they are a 470pt unit vs a 270pt unit. In this scenario, they would win combat by an average 6 points & kill the unit in 3 turns if it didn't break. TG + Halberd = 22 attacks, 3.67 killing blow hits, 7.33 standard hits, 8.56 wounds caused, 3.67 wounds received. Differential +55.0 - this seems to suggest that the 2pt upgrade to halberds is probably worth it, given it's extra armour-piercing capabilities. In this scenario, they win combat by an average 7 points & kill the longbeards in 2.3 turns if they don't break. Note that i've been a bit unfair on the poor longbeards. I've assumed nobody charges, and if they did get a charge off, they'd get +1S on the charge. Lets add-in longbeard reinforcements & see how the math stacks up again. This time it's horde vs horde & i'm giving the longbeards a shield too - now it should be interesting because on paper both units cost exactly the same points (550) - at least when the tomb guard are upgraded to have halberds: TG + HW&S = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 7.18 wounds caused, 7.18 wounds received. Differential +14.4 (+14.4 including unstable) - now combat is tied because both units are causing the same number of wounds each. Positive differential because with the HW&S option (11pts / man), the TG unit is cheaper. Lets see how they get on with halberds: TG + Halberd = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 9.09 wounds caused, 10.33 wounds received. Differential -16.2 (-29.2 including unstable). Now, they lose combat & the differential begins to turn negative - interesting how picking the matchups can be crucial! So what have we learned so far about tomb guard? Firstly that they're a very good unit & definitely worth their points cost. Secondly, that the halberd upgrade is worth it & makes sense in some situations. As a last analysis, lets pit them against... that High Elf Swordmaster horde! TG + HW&S = 31 attacks, 10.33 hits, 5.17 killing blow hits, 10.91 wounds caused, 18.89 wounds received. Differential -66.0 (including unstable -165.0) - the ludicrously undercosted elves murder the TG unit. Including the results of unstable, an average 28 models would be lost in a single round - ouch! Lets see how the halberds get on: TG + Halberd = 31 attacks, 5.17 killing blow hits, 10.33 standard hits, 13.78 wounds caused, 22.67 wounds received. Differential -115.6 (-245.6 incluidng unstable). In a single round, 33 TG would be slaughtered - thats almost the entire unit to a man! The only consolation would be the 14 kills in return. I think it's worth pointing out that both these units cost EXACTLY THE SAME... it really does show how badly-balanced the elf books are... Ok, hope that helps someone! In a nutshell, Tomb Guard are a great unit, the halberd upgrade can be useful in the right matchups but the standard HW&S versions are also effective, but whatever you do, don't match them up against a swordmaster hoard! Fascinating wounds in the Longbeard matchup vs TG HW/shield being identical. I personally don't think Swordmasters are broken purely (only!!) because you can shoot the squishy t3 pansies. Against a Rock lobber or impact hit they die just as easily as a measly light armor/shield skeleton. Hth they mathhammer advantage almost everyone with the WS6 and 2 attacks but against shooting the T4 Tomb Guard fare far better. I didn't realise they pulped Halberd Tomb Guard quite so badly however. It's worth noting that in the mathhammer matchup a Tomb Prince with WS5 doesn't help TG at all vs Swordmasters which is noteworthy. Alas Halberd Tomb Guard killing blow is completely wasted against Swordmasters. I appreciate your calculations and thorough posts. I think the Halberd upgrade at 2 points is well pointed for consideration where it is neither a 'do not take' or a 'no brainer' which I like to see. Spears at 1 point are unfortunately a 'very rarely take' option. I take them because they look better imo and are iconic, but the VC book where they are a free option is better internal balance wise. |
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Post by thorpyuk on Mar 30, 2024 11:28:41 GMT
I am loving this mathhammer. I'd like to go back to the original example of pleb skeletons. Tomb Kings are a unique case in that they have 2 easy ways to buff themselves without magic with a Necrotect and a Tomb Prince/King. While no doubt the spear upgrade cost is still too much, with rerolls to hit in that first turn, the spear skeletons may get a significant benefit over the hw/shield skeletons. This goes beyond the realm of mathhammer but it's worth mentioning that the Spear/LA skeletons benefit the most from the Lore of Nehekhara bringing them back due to the higher cost. Thanks Grandmaster, I completely agree with you on halberd TG.. they definitely have their uses! Having that S5 attacks really helps an army with not much armour-piercing ability. On basic skellies & hatred- I'm going to do some more analysis soon... the aim? Turning basic 4-pt skellies into killers!! |
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Post by thorpyuk on Mar 31, 2024 18:48:49 GMT
Alright, new update.. the aim? Turning a 190-pt horde of 40 skeleton warriors into a unit-killer! I want to see if I can get a unit of the 4-pt HW&S skellies to win combat against a hoard of swordmasters!
Assuming a full command each, and no charging bonus, the skeletons lose combat by a massive 23 on average, meaning that when you factor in standard wounds dealt, the skeletons will be wiped out in a single round of combat.
First, lets remind ourselves of the basic results with no other modifiers:
Skellies HW&S - 31 attacks, 10.33 hits, 3.44 kills, 23.61 wounds received. Lost combat by 23.
Now, lets add hatred to the unit (achievable through the use of a Necrotect or Rhamotep:
Skellies HW&S + Hatred - 31 attacks, 17.22 hits, 5.74 kills, 23.61 wounds received, lost combat by 19.
Ok, now lets try including Frenzy (Rhamotep):
Skellies HW&S + Hatred + Frenzy - 41 attacks, 22.78 hits, 7.59 kills, 23.61 wounds received, lost combat by 17.
Hmm... combining Hatred & Frenzy does help a bit, but we're nowhere near winning combat... but we have improved our result by 6 resolutions points. Lets assume we now manage to successfully cast 'Nerus incantation of protection' into the mix & see how that helps the combat!
Skellies HW&S + Hatred + Frenzy + 5+ ward - 41 attacks, 22.78 hits, 7.59 kills, 18.89 wounds received, lost combat by 12.
Alright... with Hatred, Frenzy and a 5+ ward save, we're now 11 points better-off than our starting point, but we're still losing combat heavily! Our problem is that we're just not hitting hard enough, and killing enough elves! I know what we can do to turn the tide of this combat.... 'Usekhps Incantation of Desiccation'! Lets see if that finally tips the scales:
Skellies HW&S + Hatred + Frenzy + 5+ ward + Usekhps hex - 41 attacks, 22.78 hits, 10.12 kills, 15.11 wounds received, lost combat by 5. Argh! So close! Now we're within touching distance of beating those pointy-ears, but not quite!
Another assumption thrown into the mix... we manage a successful cast of Ptras incantation of righteous smiting onto the unit too! At this point. our humble skellies have hatred, frenzy, a 5+ ward save & an extra attack from Ptras, while the swordmasters have had 1 point of S and T lowered.... can we finally win the day? Lets see:
Skellies HW&S + Hatred + Frenzy + 5+ +extra attack, + Usekhps hex = 51 attacks, 28.33 hits, 12.59 kills, 15.11 wounds received, lose combat by 2.
Noooooo we still cant beat them with all that! How about I pop a tomb prince into the unit giving them WS5? Will that finally turn the tables?
Skellies + everything - 51 attacks, 38.25 hits, 17.0 kills, 15.11 wounds received, win combat by 3.
YEAH!!! Our 'humble' unit of skeletons managed to finally beat the swordmasters! And all it took was the additions of a tomb prince, hatred, frenzy, and the successful casting of 3 combat-orientated spells and we have our victory at last! Note that if we had a Tomb King in the unit instead of a tomb prince, that would have turned the average combat resolution from +3 to a whopping +7!
So to summarize, yes it is possible to turn a humble unit of 4-point skeleton warriors into killers... but in all honesty, you'd be better off just avoiding the combat altogether!
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