Skill Ratings & Point Value - Feedback Wanted

[Joel47]

How much of a difference is there in a Skill 4 vs Skill 3 matchup as opposed to a Skill 1 vs Skill 0. I predict the # of victories or ratio to be much closer and thus negligible on the Skill 1vs Skill 0 while skill 4 vs skill 3 to show a much larger margin of victories to the Skill 3 unit.

because now we are not so much looking at PV values for TMMs, but an All Things being equal what value is SKILL in  match-up.

That's easy enough to do. I suspect the way this simulator works (no tactics in play, just some simple range manipulation) anything more than one point of difference will create a landslide. Let's see if I'm correct...

Attacker \ Defender	Hunchback IIC (IV) (Skill 4)	Hunchback IIC (III) (Skill 3)	Hunchback IIC (II) (Skill 2)	Hunchback IIC (I) (Skill 1)	Hunchback IIC (Skill 0)
Hunchback IIC (IV) (Skill 4)	-----	Hunchback IIC (III): 475/263/262(4.4)	Hunchback IIC (II): 593/162/245(4.2)	Hunchback IIC (I): 634/82/284(4.1)	Hunchback IIC: 640/36/324(4.0)
Hunchback IIC (III) (Skill 3)	Hunchback IIC (III): 480/265/255(4.4)	-----	Hunchback IIC (II): 437/208/355(4.1)	Hunchback IIC (I): 453/117/430(4.0)	Hunchback IIC: 468/65/467(4.0)
Hunchback IIC (II) (Skill 2)	Hunchback IIC (II): 580/134/286(4.2)	Hunchback IIC (II): 387/223/390(4.1)	-----	Hunchback IIC (I): 311/156/533(4.0)	Hunchback IIC: 314/80/606(4.0)
Hunchback IIC (I) (Skill 1)	Hunchback IIC (I): 627/74/299(4.1)	Hunchback IIC (I): 441/137/422(4.0)	Hunchback IIC (I): 301/163/536(4.0)	-----	Hunchback IIC: 191/99/710(4.0)
Hunchback IIC (Skill 0)	Hunchback IIC: 679/24/297(4.0)	Hunchback IIC: 482/61/457(4.0)	Hunchback IIC: 332/74/594(4.0)	Hunchback IIC: 178/88/734(4.0)	-----

Glass cannons that they are, there are a lot of draws, especially once the skill improves. If we drop the draws and add the two sets (yes, the top-right and bottom-left sections of the table are independent -- there's a TODO item about that I have yet to bother tracking down) we get:
Skill 4 vs 3: 955 to 528 - 64%
Skill 3 vs 2: 824 to 431 - 66%
Skill 2 vs 1: 612 to 319 - 66%
Skill 1 vs 0: 369 to 187 - 66%
So a one point skill differential will result in winning 66% of the time, regardless of the actual skills.

[Joel47]

True, but sometimes a Unit is just better ;)

Hopefully we got most of those taken care of with the last PV revision. (This script helped show that jump wasn't worth nearly the original points.) But that's why I'm hoping to crowdsource some lists with as few independent variables as possible -- if we're going to base skill costs on something other than straight PV, it would be good to know what to base it on. We want to determine what type of unit (fast? well-armed? tough?) scales best with improved skill, and what scales worst.

[Joel47]

Here's a run with some heavier units, PV 46. I've been reminded of a petty annoyance with the current system: Because of the way skill points are added, it's literally impossible to make certain skill/PV combos. In this case, you cannot make a 46 PV unit that has a skill of 2.

Code: [Select]

[
  {"name":"Black Hawk-KU BHKU-O", "points":46, "skill":4, "type":0, "armor":7, "structure":3, "weapons":[6, 5, 0], "move":10, "special":["ENE"]},
  {"name":"Thor II C", "points":46, "skill":4, "type":0, "armor":6, "structure":4, "weapons":[5, 5, 3], "move":10, "special":["CASE"]},
  {"name":"Banshee BNC-3E", "points":46, "skill":3, "type":0, "armor":8, "structure":8, "weapons":[2, 2, 2], "move":8},
  {"name":"Lynx LNX-9Q", "points":46, "skill":3, "type":0, "armor":6, "structure":3, "weapons":[4, 4, 1], "move":10, "special":["ENE"]},
  {"name":"Hammerhands HMH-4D", "points":47, "skill":2, "type":0, "armor":6, "structure":6, "weapons":[3, 3, 1], "move":6},
  {"name":"Battle Cobra A", "points":47, "skill":2, "type":0, "armor":4, "structure":3, "weapons":[4, 4, 0], "move":12, "special":["ENE"]},
  {"name":"Rifleman RFL-3C", "points":46, "skill":1, "type":0, "armor":5, "structure":5, "weapons":[3, 3, 0], "move":8},
  {"name":"Peregrine (Horned Owl)", "points":46, "skill":1, "type":0, "armor":3, "structure":3, "weapons":[3, 3, 2], "move":12, "special":["ENE"]},
  {"name":"Hunchback IIC", "points":46, "skill":0, "type":0, "armor":3, "structure":3, "weapons":[4, 4, 0], "move":8, "special":["CASE"]},
  {"name":"Sentinel STN-3Lb", "points":46, "skill":0, "type":0, "armor":4, "structure":2, "weapons":[3, 2, 2], "move":12}
]


Attacker \ Defender	Black Hawk-KU BHKU-O (Skill 4)	Thor II C (Skill 4)	Banshee BNC-3E (Skill 3)	Lynx LNX-9Q (Skill 3)	Hammerhands HMH-4D (Skill 2)	Battle Cobra A (Skill 2)	Rifleman RFL-3C (Skill 1)	Peregrine (Horned Owl) (Skill 1)	Hunchback IIC (Skill 0)	Sentinel STN-3Lb (Skill 0)
Black Hawk-KU BHKU-O (Skill 4)	-----	Thor II C: 457/424/119(5.5)	Black Hawk-KU BHKU-O: 803/150/47(6.0)	Black Hawk-KU BHKU-O: 456/435/109(5.7)	Black Hawk-KU BHKU-O: 533/327/140(4.4)	Battle Cobra A: 459/407/134(3.5)	Black Hawk-KU BHKU-O: 714/209/77(3.2)	Peregrine (Horned Owl): 531/328/141(5.1)	Black Hawk-KU BHKU-O: 442/335/223(2.7)	Sentinel STN-3Lb: 457/447/96(5.4)
Thor II C (Skill 4)	Thor II C: 450/428/122(5.4)	-----	Thor II C: 711/230/59(7.8)	Thor II C: 537/373/90(5.5)	Thor II C: 623/291/86(7.9)	Thor II C: 484/396/120(3.5)	Thor II C: 798/136/66(5.9)	Peregrine (Horned Owl): 466/427/107(4.7)	Thor II C: 765/132/103(4.6)	Thor II C: 573/336/91(4.8)
Banshee BNC-3E (Skill 3)	Black Hawk-KU BHKU-O: 815/136/49(6.1)	Thor II C: 726/226/48(7.9)	-----	Lynx LNX-9Q: 714/231/55(8.2)	Banshee BNC-3E: 505/455/40(9.8)	Battle Cobra A: 739/161/100(4.6)	Banshee BNC-3E: 554/399/47(7.4)	Banshee BNC-3E: 522/427/51(6.3)	Banshee BNC-3E: 772/156/72(4.8)	Banshee BNC-3E: 578/367/55(6.5)
Lynx LNX-9Q (Skill 3)	Black Hawk-KU BHKU-O: 459/433/108(5.8)	Thor II C: 500/396/104(5.6)	Lynx LNX-9Q: 687/251/62(8.2)	-----	Lynx LNX-9Q: 418/417/165(8.3)	Lynx LNX-9Q: 552/295/153(3.0)	Lynx LNX-9Q: 555/285/160(6.2)	Lynx LNX-9Q: 441/404/155(4.6)	Lynx LNX-9Q: 788/102/110(5.1)	Lynx LNX-9Q: 588/306/106(4.9)
Hammerhands HMH-4D (Skill 2)	Black Hawk-KU BHKU-O: 539/342/119(4.3)	Thor II C: 598/285/117(8.1)	Banshee BNC-3E: 507/454/39(9.7)	Hammerhands HMH-4D: 438/393/169(8.4)	-----	Battle Cobra A: 489/283/228(3.3)	Hammerhands HMH-4D: 584/282/134(4.5)	Peregrine (Horned Owl): 589/275/136(6.8)	Hammerhands HMH-4D: 674/154/172(2.3)	Sentinel STN-3Lb: 705/191/104(6.5)
Battle Cobra A (Skill 2)	Black Hawk-KU BHKU-O: 439/429/132(3.3)	Battle Cobra A: 443/426/131(3.5)	Battle Cobra A: 738/179/83(4.7)	Lynx LNX-9Q: 554/275/171(2.9)	Battle Cobra A: 454/317/229(3.3)	-----	Battle Cobra A: 327/319/354(3.1)	Peregrine (Horned Owl): 573/207/220(3.9)	Hunchback IIC: 265/166/569(2.0)	Sentinel STN-3Lb: 414/306/280(4.3)
Rifleman RFL-3C (Skill 1)	Black Hawk-KU BHKU-O: 725/199/76(3.2)	Thor II C: 808/123/69(6.0)	Banshee BNC-3E: 526/434/40(7.7)	Lynx LNX-9Q: 549/303/148(6.3)	Hammerhands HMH-4D: 589/257/154(4.7)	Battle Cobra A: 334/311/355(3.1)	-----	Peregrine (Horned Owl): 639/193/168(5.2)	Rifleman RFL-3C: 809/66/125(4.2)	Sentinel STN-3Lb: 722/167/111(5.2)
Peregrine (Horned Owl) (Skill 1)	Peregrine (Horned Owl): 530/341/129(5.0)	Peregrine (Horned Owl): 451/440/109(4.7)	Banshee BNC-3E: 503/445/52(6.4)	Lynx LNX-9Q: 422/402/176(4.7)	Peregrine (Horned Owl): 580/287/133(6.8)	Peregrine (Horned Owl): 559/238/203(3.9)	Peregrine (Horned Owl): 630/178/192(5.2)	-----	Peregrine (Horned Owl): 844/34/122(3.8)	Sentinel STN-3Lb: 486/242/272(3.4)
Hunchback IIC (Skill 0)	Black Hawk-KU BHKU-O: 465/308/227(2.7)	Thor II C: 743/156/101(4.7)	Banshee BNC-3E: 789/136/75(4.8)	Lynx LNX-9Q: 784/102/114(5.1)	Hammerhands HMH-4D: 685/149/166(2.3)	Hunchback IIC: 253/177/570(2.0)	Rifleman RFL-3C: 819/52/129(4.2)	Peregrine (Horned Owl): 845/38/117(3.8)	-----	Sentinel STN-3Lb: 939/6/55(3.5)
Sentinel STN-3Lb (Skill 0)	Sentinel STN-3Lb: 469/439/92(5.4)	Thor II C: 516/370/114(5.0)	Banshee BNC-3E: 556/398/46(6.6)	Lynx LNX-9Q: 571/275/154(4.8)	Sentinel STN-3Lb: 725/178/97(6.5)	Sentinel STN-3Lb: 380/356/264(4.3)	Sentinel STN-3Lb: 676/200/124(5.2)	Sentinel STN-3Lb: 474/261/265(3.4)	Sentinel STN-3Lb: 948/3/49(3.5)	-----

1. The Thor IIC is a beast at this level, losing only to the Peregrine and drawing with the Battle Cobra.
2. The BH KU (the other skill 4 unit) also does very well.
3. The Hunchback does poorly once it's facing things that can take more than one hit.

[sadlerbw]

Oh, and since I totally ignored Xotl's original question, if I am min-maxing a force, I don't often go below Skill 2 unless it is a unit I plan to use for indirect or artillery fire. Then I will consider Skill 1. However, I don't generally use Skill 1 or 0 as they tend to be a bit unfair without further restrictions on how many units can have that skill. That said, I prefer Skill 2 if I can afford it on my biggest hitters. Skill 2 is usually cheap enough that I can get it on more than one unit, and isn't quite as tempting for the enemy to gang up on as Skill 0 or 1. If I'm paying for a skill upgrade, I'd rather go all the way to 2 on a smaller number of units than 3 on a larger number. So, for me 2 is the magic number.

I will also voluntarily de-skill units that i plan to use as spotters, as their skill is irrelevant to that job. De-skilling fast light units, stealth BA, or infantry to use as spotters is a bit cheesy, but I will absolutely do it if I'm playing a zero-theme, kill-at-all-costs type of game. Other than that, I do not lower skill values below 4 for any reason other than theme.

All that said, I generally try to assign skills in a thematic way, rather than for pure min-maxed performance. If I am playing a 'run whatever you want' game, I don't generally allow more than a single Skill 0 for any reason, and any Skill 1's need a good reason to be there. For the most part, I prefer not to have anything better than Skill 2 or worse than Skill 5 in any great numbers. Some hero's and complete failures can be fun to throw in occasionally, but playing a force made entirely of either one is too far from the median. Strange things start happening to gameplay when you are almost guaranteed to hit at medium range on the majority of the units in the game, or when you are so bad that nothing but short range matters.

[Joel47]

Hopefully we can include something that reduces the PV recovery for putting terrible pilots in C3 spotters.

[Xotl]

nckestrel did suggest the idea of giving diminishing returns on Sill Rating penalties, and with the testimony here I'm inclined to follow that.

The idea of creating a C3 exception is interesting and may be easily workable (either no discount, or a further reduced discount).

Joel47: Can you tell me what you feel you're learning from the data you're crunching?  There's a lot of info, but what do you think it means for the broader game and the issue we're wrestling with?

[Descronan]

Glass cannons that they are, there are a lot of draws, especially once the skill improves. If we drop the draws and add the two sets (yes, the top-right and bottom-left sections of the table are independent -- there's a TODO item about that I have yet to bother tracking down) we get:
Skill 4 vs 3: 955 to 528 - 64%
Skill 3 vs 2: 824 to 431 - 66%
Skill 2 vs 1: 612 to 319 - 66%
Skill 1 vs 0: 369 to 187 - 66%
So a one point skill differential will result in winning 66% of the time, regardless of the actual skills.

I'm curious how the percentages stack up after you compare skill 4 vs. bigger skill differences. Otherwise, it comes out to about a 30% difference. The question is if that should reflect a 30% PV cost difference.

[Elmoth]

Ouch. C3 point calculation is already a nightmare. Please, no more messing with that.

[Tai Dai Cultist]

nckestrel did suggest the idea of giving diminishing returns on Sill Rating penalties, and with the testimony here I'm inclined to follow that.

The idea of creating a C3 exception is interesting and may be easily workable (either no discount, or a further reduced discount).

Joel47: Can you tell me what you feel you're learning from the data you're crunching?  There's a lot of info, but what do you think it means for the broader game and the issue we're wrestling with?

Do these models use varying to-hit penalties?

High skill when everyone is at +3 is entering diminishing returns on PV investment.  OTOH High Skill when everyone is at +7 is OP rather than diminishing returns.

The inability to factor number of units in this model may be an issue if Unit A with skill 0 is the same PV as 2 of Unit Bs at skill 4, and A reliably loses at low penalties to hit but reliably wins at high penalties to hit.

[NeonKnight]

Glass cannons that they are, there are a lot of draws, especially once the skill improves. If we drop the draws and add the two sets (yes, the top-right and bottom-left sections of the table are independent -- there's a TODO item about that I have yet to bother tracking down) we get:
Skill 4 vs 3: 955 to 528 - 64%
Skill 3 vs 2: 824 to 431 - 66%
Skill 2 vs 1: 612 to 319 - 66%
Skill 1 vs 0: 369 to 187 - 66%
So a one point skill differential will result in winning 66% of the time, regardless of the actual skills.

Just to help my understanding of the end numbers

Skill 4 vs 3: 955 to 528 - 64%

What exactly is the 955 to 528? Is that number of Wins? or number of losses? And 955 out of what exactly?

Right now I see this (First Column after the -----):

Hunchback IIC (III): 480/265/255(4.4) Which I think is Win/Loss/Draw, and if I add those numbers together I get 1000

If I look to 2nd column 1st row I see:

Hunchback IIC (III): 475/263/262(4.4)

So, adding the first set of numbers (480 & 475) I do get 955, and the second set I get 528, so that matches up.

That said, taking those two number then

955 Wins, 528 Losses means, out of 1483 matches, Skill 3 won 64.3%

Correct?

If so, the rest of your numbers should be put into the same categories, and comparing the same amounts, because otherwise:

Skill 4 vs 3: 955 to 528 - 64% (only accounts for 1483 matches)
Skill 3 vs 2: 824 to 431 - 66% (only accounts for 1255 matches)
Skill 2 vs 1: 612 to 319 - 66% (only accounts for 931 matches)
Skill 1 vs 0: 369 to 187 - 66% (only accounts for 556 matches)

If we include all the numbers (to bring back to the full 2000 matches), we instead see:

Skill 4 vs 3: 955 out of 2000* - 48%
Skill 3 vs 2: 824 out of 2000* - 41%
Skill 2 vs 1: 612 out of 2000* - 31%
Skill 1 vs 0: 369 out of 2000* - 18%

*The rest being either a Loss or a Draw.

And that is a little more telling.

[Xotl]

Ouch. C3 point calculation is already a nightmare. Please, no more messing with that.

There is no separate C3 point calculation in Alpha Strike (beyond costing the unit itself).

[Elmoth]

I know. What I mean is that the system to cost the units in the network is way less elegant than other parts of the AS system.

[NeonKnight]

Skill 4 vs 3: 955 out of 2000 - 48%
Skill 3 vs 2: 824 out of 2000 - 41%
Skill 2 vs 1: 612 out of 2000 - 31%
Skill 1 vs 0: 369 out of 2000 - 18%

To further expand on these calculations.

SKILL 4 v 3 (Favor to Skill 3)

48% Wins, 26% Losses, 26% Draws

SKILL 3 v 2 (Favor to Skill 2)

41% wins, 22% Losses, 37% Draws

SKILL 2 v 1 (Favor to Skill 1)

31% Wins, 16% Losses, 53% draws

SKILL 1 v 0 (favor to Skill 0)

18% Wins, 9% Losses, 72% Draws

So, as the Skill gets higher the 1 point shift results in more draws, less losses and conversely, less wins as well.

[Joel47]

I was ignoring draws because of the particular mech being used -- glass cannons like the Hunchback IIC generate a lot of draws. Because of that, NeonKnight, I think you're pulling more from that data than can be easily supported. If we use tough, low-damage units instead...

Attacker \ Defender	Charger CGR-1L IV (Skill 4)	Charger CGR-1L III (Skill 3)	Charger CGR-1L II (Skill 2)	Charger CGR-1L I (Skill 1)	Charger CGR-1L 0 (Skill 0)
Charger CGR-1L IV (Skill 4)	-----	Charger CGR-1L III: 707/267/26(10.7)	Charger CGR-1L II: 847/142/11(9.1)	Charger CGR-1L I: 906/80/14(8.3)	Charger CGR-1L 0: 927/61/12(7.7)
Charger CGR-1L III (Skill 3)	Charger CGR-1L III: 682/299/19(10.2)	-----	Charger CGR-1L II: 668/311/21(9.4)	Charger CGR-1L I: 772/191/37(8.5)	Charger CGR-1L 0: 831/145/24(7.8)
Charger CGR-1L II (Skill 2)	Charger CGR-1L II: 821/161/18(9.1)	Charger CGR-1L II: 636/336/28(9.5)	-----	Charger CGR-1L I: 619/332/49(8.5)	Charger CGR-1L 0: 727/215/58(8.9)
Charger CGR-1L I (Skill 1)	Charger CGR-1L I: 901/90/9(8.1)	Charger CGR-1L I: 784/188/28(8.4)	Charger CGR-1L I: 608/342/50(9.3)	-----	Charger CGR-1L 0: 576/348/76(8.4)
Charger CGR-1L 0 (Skill 0)	Charger CGR-1L 0: 933/54/13(7.5)	Charger CGR-1L 0: 825/151/24(8.5)	Charger CGR-1L 0: 699/245/56(8.6)	Charger CGR-1L 0: 562/358/80(8.8)	-----

That's probably more useful. It does show diminishing returns, especially between 1 and 0.

[Tai Dai Cultist]

Joel47 are you able to change the to-hit penalties under the hood?  I'm sure high skill units will perform at more significantly better rates than lower skills if higher-to hits are assumed in the calculations.

[NeonKnight]

I was ignoring draws because of the particular mech being used -- glass cannons like the Hunchback IIC generate a lot of draws. Because of that, NeonKnight, I think you're pulling more from that data than can be easily supported. If we use tough, low-damage units instead... {SNIP BIG TABLE}

That's probably more useful. It does show diminishing returns, especially between 1 and 0.

Sorry, I just used waaaaaaaaay above the Hunchback as an example just cause it was first on your original example.

So, if I understand the data correctly, my original hypothesis of there is more advantage to go from a Skill 4 to a Skill 3 than from a Skill 1 to Skill 0, is correct/supported by the initial data?

[Tai Dai Cultist]

Sorry, I just used waaaaaaaaay above the Hunchback as an example just cause it was first on your original example.

So, if I understand the data correctly, my original hypothesis of there is more advantage to go from a Skill 4 to a Skill 3 than from a Skill 1 to Skill 0, is correct/supported by the initial data?

That's pretty mathematically obvious. So long as the game only ever revolves around +3s to hit.  Obviously it doesn't.  While that was an acceptable presumption for the unit-to-unit comparison, I don't feel it's also fine in comparing skill-to-skill.  Differing modifiers puts Skill values at different places on the bell curve.  With a +7 modifier, 1 to 0 is the same mathematical advantage as 4 to 3 is at +3 to-hits.

[sadlerbw]

Cheap spotters are...well, they are cheap. Whether it is C3, Indirect Fire, or Artillery, low-skill spotters are just going to be inexpensive. Why? because anyone can be a spotter. There is no unit type or special required (ok, there is for C3, but not for the others.) Everything is a spotter if it wants to be. However, most of the time it doesn't matter that much because anyone you are going to dedicate to being a spotter is probably dirt cheap anyway.

A true spotter, in my mind, is a unit that does little to no damage, and can be de-skilled without loosing much performance in any other aspect of attacking. In this case, the majority of a units PV is going to come from defensive stats, and almost nothing will be from attack stats. In this case, de-skilling a unit saves you more on lowering your overall PV than you loose by being useless at any sort of attack other than spotting. So, units with 1/0/0 damage or less, and lots of defensive PV: buckets of armor, high TMM, or specials like STL and MAS. The thing is, these units are already really cheap. De-skilling them does still offer some benefit, but it really isn't all that much. This is especially true for C3 spotters, as they don't have the luxury of trying to hang out at long range. They need to be in medium, or even short range, to do any good, and at those ranges their defensive bonuses which make up most of their PV help the least. Plus all you need to screw up a C3 spotters day is ECM. You don't even need line of sight, just get within a foot and they are busted.

Anything that does real damage, even at short range, you wouldn't want to de-skill because then you really are giving up any chance at using that traditional attack damage. Even something like a Charger might not want to because Skill still matters for physical attacks, and a 4 damage physical is nothing to sneeze at. I used a Kuma 3 as a spotter once, and I didn't de-skill it because I wanted the option to charge or punch, and that was much more of a gamble at Skill 6 or 7. I have de-skilled infantry and BA before, and it really doesn't save you that much. I still did it, but it wasn't a big deal.

Honestly, that is the most important factor. These defense-only units that we would consider using as dedicated spotters with terrible Skill ratings just don't cost that much in the first place. So, when you lower their skills, you don't get all that much back.

Looking at a few examples:
Savannah master (Interdictor): TMM4, 1A/1S, 0/0/0 damage. Going from Skill 4 to Skill 7 saves you 3PV.
Charger 1A1: TMM 2, 5A/6S, 2/0/0 damage. 4 to 7 saves 6PV.
Rogue Bear (Hybrid): TMM1 (plus LMAS and STL), 2A/2S, 2/0/0 damage, 4 to 7 saves 3PV.
Ostscout 7K: TMM 3, 2A/3S, 0/0/0 damage, 4 to 7 saves 6PV.

So, if I take my do-nothing spotter and de-skill it from 4 down to 7, it saves me enough PV to raise the skill of a mediocre unit by one level. I could take something like a Shadow Hawk 2H at 30PV, and raise it from Skill 4 to Skill 3 for 6PV. Well, assuming I used the Charger or the Ostscout. The other two, I would need to de-skill two units to pay for a single one-skill upgrade on the Shadow hawk. I guess my point is that cheap spotters are already so cheap that de-skilling them doesn't save you enough to be game breaking.

[Tai Dai Cultist]

To illustrate the point in my above post:

...
Assuming Medium Range and a +1 def modifier (29% of all units in the game have this), the to-hit chance associated with these Ratings are:
4: 58.33%
3: 72.22%
2: 83.33%
1: 91.66%
0: 97.22%

Assuming Medium Range and a +3 def modifier (16.5% of all units in the game have this), the to-hit chance associated with these Ratings are:
4: 27.77%
3: 41.66%
2: 58.33%
1: 72.22%
0: 83.33%
...

Assuming +7 to hits (Medium range, cover, and a +3 def mod) the to-hit chance associated with these ratings are:

4: 8.32%
3: 16.65%
2: 27.76%
1: 41.64%
0: 58.3%

So in this case, the 4 to 3 Skill upgrade gives +8.33% odds of success whereas the 1 to 0 upgrade gives 16.66% improvement.  Which upgrade is most valuable depends entirely on the specific context of where the numbers lie on the bell curve.

[Joel47]

:)Joel47: Can you tell me what you feel you're learning from the data you're crunching?  There's a lot of info, but what do you think it means for the broader game and the issue we're wrestling with?

My initial runs have appeared pretty random, as I was just grabbing units with the same adjusted PV and tossing them into the ring. As I see it, there are three independent variables this script would be useful in checking: Firepower, Durability, and Maneuveratility. Since it may have gotten lost in the noise, I'd like for someone to put together lists of 5-6 units that hold two of those constant, varying the third and correcting the PVs using the existing skill chart. That should give us some insight.

Joel47 are you able to change the to-hit penalties under the hood?  I'm sure high skill units will perform at more significantly better rates than lower skills if higher-to hits are assumed in the calculations.

Working on it. Well, working on actual paying work, after which I was going to toss in a cover chance and a woods chance -- essentially a percent chance each round that the initiative winner/loser would get cover, and a chance that both are affected by woods. It'll be configurable, but I'm thinking 25%/5% for cover and 30% for woods as starting points. I could just toss a flat modifier in as well, but that seems like you could do that just by adjusting the skill values.
One thing I'm not simulating is jump -- without an actual battle with terrain, jump just hurts you, applying more of a modifier to you than it does your opponent. Now with wildly differing skills that might not be the case, but let's save that for later.

And yes, NeonKnight, if there's no cover and most combat happens at medium range (anecdotally, the latter is usually the case in my real games; the former at least a third of the time), you're going to run into greatly diminishing returns from your skill below 2 where the bell curve flattens out. But Tai Dai Cultist is correct in calling that mathematically obvious. If I put a flat modifier in, you'd see the inflection point shift; with a high enough mod ("it's night in the forest and everyone has cover") you'd see the 4-to-3 jump become worth much less than the 1-to-0 jump. That's why I'd really rather focus my efforts not on the relative values of different levels of skill (as I suspect that with real-world cover it's all in the fat part of the curve) but on seeing if units with the same PV but greatly different stats respond differently to skill.

[NeonKnight]

To Tai Dai Cultist...No, no it most certainly is not.



A Skill 4, at +2 (medium Range) no cover against a TMM of 1 requires a roll of 7+.

As we can see on the chart above that means 7 is rolled 16.67% of the time, 8 is rolled 13.89, and on an on.

Reducing the Skill by 1 to Skill 3 means that now we only need a 6+ to hit, or a 13.89% increase to the to hit chance.

Skill 2 is 5+ (an additional 11.11% chance), Skill 1 is 4+ (an additional 8.33%), and Skill 0 is 3+ (an additional 5.56%)

Or in Other words:

SKILL 4 rolls the needed 7+ 58.34%

SKILL 3 rolls the needed 6+ 72.23%

SKILL 2 rolls the needed 5+ 83.34%

SKILL 1 rolls the needed 4+ 91.67%

SKILL 0 rolls the needed 3+ 97.23%

As you can see, all things equal as the SKILL gets lower, the % chance gap does not get larger on each step, but rather gets smaller.

And right now, arguing to make a skill lower than the skill immediately before it more expensive, means paying more PV costs for a lower return. In other words, charging someone 10 PV to improve a skill from 1 to 0 means paying 1.8 PV per percentage point increase (5.56% better chance to hit) versus the SKILL 3 person paying 2 PV to increase their skill from 4 to 3 or, 0.14 PV per percentage point increase (13.89% better chance to hit).

[NeonKnight]

And yes, NeonKnight, if there's no cover and most combat happens at medium range (anecdotally, the latter is usually the case in my real games; the former at least a third of the time), you're going to run into greatly diminishing returns from your skill below 2 where the bell curve flattens out. But Tai Dai Cultist is correct in calling that mathematically obvious. If I put a flat modifier in, you'd see the inflection point shift; with a high enough mod ("it's night in the forest and everyone has cover") you'd see the 4-to-3 jump become worth much less than the 1-to-0 jump. That's why I'd really rather focus my efforts not on the relative values of different levels of skill (as I suspect that with real-world cover it's all in the fat part of the curve) but on seeing if units with the same PV but greatly different stats respond differently to skill.

And that is the point I seem to not be making or some people not want to see.

YES, I think the SKILL 0 person should need to pay to get there, its the scale that I think, In My Opinion, should be different from what it has traditionally been.

I think going from SKILL 4 to SKILL 3 should cost, say 5 points, going from SKILL 3 to SKILL 2 should cost 4 points, SKILL 2 to 1 should be 3 points and SKILL 1 to 0 should be 2 points. But each step must pay the step before, so at the end, a SKILL 0 pays, 5+4+3+2 or 14 points.

If you still hold to the theory that 4 to 3 should be cheapest, and get more expensive as one goes down the scale, Then the odds favor the lower skills sure, but a savvy player can save a butt load on points and get more bang-for-their-buck.

And we are back to folks kvetching about losing a 100 point unit a couple lucky rolls

[Tai Dai Cultist]

To Tai Dai Cultist...No, no it most certainly is not....

Now re-do your own math for needing skill+7s to hit.  Spoiler alert: You need 11s at skill 4, 10s at 3, and ultimately 7s at 0.  The same %s apply to different skill values because their location on the bell curve has moved.  You'll see that needing 10s instead of 11s is a 8.33% jump (skill 3 instead of 4) whereas needing 7s instead of 8s is a 16.66% jump (skill 0 instead of 1).  At this place on the bell curve, 4 to 3 is not the most mathematically meaningful advancement; 1 to 0 is.

So again my point is that (what I take to be you saying) "4 to 3 is the most meaningful skill improvement because it gives the biggest improvement when 3 is at the top of the bell curve" is actually meaningless, because whichever advance puts you at the top of the bell curve is the most meaningful.  It could be 4 to 3 in one situation just as easily as it could be 1 to 0 in the next circumstance.

[Joel47]

What's interesting to me here is that, given that the difference of opinion is based on the "average" to-hit number, that the relative worth of the first skill improvement vs the worth of the last depends in part on the target -- if you're shooting slow units, jumping from 4 to 3 is a very much worth the points, but going all the way down to 0 a total waste of points; however, if you're shooting TMM 6 VTOLs that never come closer than medium range, going from 4 to 3 might not even get you to where you can hit.

It's times like this where I really wish we had a corpus of data the way computer games do. If I'm ever evil overlord talked into helping with a BV revision, the first thing I'd do is ask the Megamek folks if they're keeping logs. If they are, I guarantee I could improve BV using a million game results that include anonymized user ID, unit list, map list, and the final tally (won/loss, destroyed/crippled/damaged/untouched). But there's no such database for AS.  :P

[Scotty]

But the number of things in the game that generate Skill+7 to hit is negligible.  We can't use terrain while making these considerations, because there is no "correct" terrain configuration.

Therefore it is imperative to focus our efforts to the most common and therefore most universally applicable situations - that being a TMM between +1 and +3, with no terrain modifiers.

You can't balance around outliers.

[Tai Dai Cultist]

But the number of things in the game that generate Skill+7 to hit is negligible.  We can't use terrain while making these considerations, because there is no "correct" terrain configuration.

Therefore it is imperative to focus our efforts to the most common and therefore most universally applicable situations - that being a TMM between +1 and +3, with no terrain modifiers.

You can't balance around outliers.

I agreed with that for unit vs unit comparison.

I don't agree that +7 "all in" as a to-hit penalty for a shot in game is an outlier circumstance.  Yes it's easier to ignore modifiers to hit for "mathing it up" but (imo) you can't ignore realistic to-hits like that when evaluating skills.  If all you're ever theorizing is that skill 0 only ever takes you from needing 4s to 3s to hit, then you're not fully considering the advantage of having skill 0.  And that's inherently flawed for assessing the true value of having skill 0.

[nckestrel]

But the number of things in the game that generate Skill+7 to hit is negligible.  We can't use terrain while making these considerations, because there is no "correct" terrain configuration.

Therefore it is imperative to focus our efforts to the most common and therefore most universally applicable situations - that being a TMM between +1 and +3, with no terrain modifiers.

You can't balance around outliers.

My very first game of Alpha Strike outside my small group was a game at Gencon, where a company of heavies (half clan) couldn’t hit my Spider at medium range in water.

There is a point when you ignore outliers and outliers become the way to play because you didn’t balance for them.

[Tai Dai Cultist]

My very first game of Alpha Strike outside my small group was a game at Gencon, where a company of heavies (half clan) couldn’t hit my Spider at medium range in water.

There is a point when you ignore outliers and outliers become the way to play because you didn’t balance for them.

Maybe we play with WAY more terrain than you guys do, but skill+6 is pretty well the norm in my games (Med range, TMM, and you virtually never get a shot on a target not benefitting from cover).  Skill+7 (i.e needing 11s @ skill 4/7s @ skill 0) is absolutely plausibe as your best shot with a given unit for the round.

[NeonKnight]

Now re-do your own math for needing skill+7s to hit.  Spoiler alert: You need 11s at skill 4, 10s at 3, and ultimately 7s at 0.  The same %s apply to different skill values because their location on the bell curve has moved.  You'll see that needing 10s instead of 11s is a 8.33% jump (skill 3 instead of 4) whereas needing 7s instead of 8s is a 16.66% jump (skill 0 instead of 1).  At this place on the bell curve, 4 to 3 is not the most mathematically meaningful advancement; 1 to 0 is.

SO, what you are saying there is, all calculation should then be assumed to be taking place at long range (+4) against TMMs of 3. If only the MUL would let me search based on that kind of criteria.

I have the old excel sheet, and I can say of all the AS units (all 6436) on the excel sheet, only 3015 do damage of 1+ at long range but at least 5242 do damage at medium range. And I know in almost all my AS games, the majority of the fight takes place at medium range, and even based on the (albiet old PV calculation from AS Companion), the very first step puts the emphasis on medium range damage:

Page 138 AS Companion

Step 1: Determine Unit’s Offensive Value
To find a ground unit’s Offensive Value, add together the following Offensive Factors:

Attack Damage Factor: Combine the unit’s standard weapon attack values at each range bracket (Short, Medium, and Long) with the unit’s Medium range attack value. For example, a unit with a standard attack of 3/2/1 would begin calculating its Offensive Value with an Attack Damage Factor of 8 (3 + 2 + 1 + 2 =8).

I am assuming this step has not changed in the new PV calculations.

Again, for my calculations I am assuming a game at medium range (the go-to combat range).

We can if you want, look at comparing attacker jumping SKILLs at long range against targets with TMMs of 3 in woods (+2 for both parties) and behind cover (for another +2) if you really want.
 That would mean a +2 for woods, +3 TMM, +2 Jump, +2 Partial cover and +4 Long Range for a total of SKILL +13 to hit, thus even the much feared and needs to be avoided SKILL 0 needs a 13 or better on 2d6 ;)

[Tai Dai Cultist]

SO, what you are saying there is, all calculation should then be assumed to be taking place at long range (+4) against TMMs of 3. If only the MUL would let me search based on that kind of criteria....

No what I'm saying is there should theorizing where the skill+Xs end up all over the bell curve, rather than 3+X always being in or near the 7 slot.  Always having 3+X at/near 7 on 2d6 is artificially inflating the value of skill 3 because in play, 3+X will not always be at/near 7.  0+X is very plausibly at 7, for example, even without needing to go into Long Range shot modifiers.