Smotherman Formula Discussion

[RCgothic]

As the other thread is getting a little bit jammed with discussions of the Smotherman Formula and how well it does/doesn't work.

I believe we were currently on whether a 6+ prow was worth 35pts.

[Eldanesh]

It does NOT work: the whole formula isn't based on any mathematical basis they just work from the end to the beginning: they took the given pointcosts (doesn't matter if a ship is over- or undervalued) and than they searched some "fitting" cost for the hardpoints.

There is no reason why they priced a specific item. for example: you can decrease the price of the basic cruiser hull by 50 Points and increase the price for the first shield by 50 points an get the same results.
Or give all 30cm weapons a "value" of 0 (as there is no IN ship with less range you can set it to 0) and increase the initial costs of ships and it will still work (meaning you can reproduce the existing ship classes). But I think that everybody will agree that there is a difference in the value of ships with 30cm weapons compared to one with no weapons at all....

More general spoken: they worked on the basis of induction. They saw only white swans (the given ship classes) and concluded "all swans are white" (the formula). But you simply can't work this way.

[Valhallan]

yeah the forumla is broken.

the prow is not worth 35... more like 25. NC are obviously overpriced (though was the formula made when they were guess range?)

we've read over and over that lances are more like 3.5WB = 1 lance, not 1:3. and as pointed out in the FS thread, long range batteries do not scale up with range by integers, but by fractions because of the column shift. however, in the forumula, lances scale up with range by fractions, but we all know they hit just the same at 30cm or 60cm, so they should have a harsher cost increase (with range increase) to reflect this.

we all agree 5cm speed is not worth 1pnt. i mean in the friggin refit table +5cm speed is there and costs +10%! for the cheapest IN escort in the game thats still 3pnts...and rounded up to 5.

shields are obviously way better the more you have. this is not reflected in smotherman either.

it appears the only thing they have about right is 10 points per hull point, 5 points per turret.

[Admiral_d_Artagnan]

We all know Smotherman isn't perfect. Even the author said its not a perfect system. It's probably the closest he got to making a mathematical formula for the game. Could there be other better formulas? Yes. RCG has stated he made one and it works for IN. Good. Now here's to hoping it can work for the other races as well. There were other formulas before and it usually only fit one race and didn't work for the other races.

But as noted also in the other threads, it will be hard to make a formula because the ship costs in the game were mainly reached at by "feel". Hence there will be discrepancies, even within a faction. The Vengeance and Avenger is a perfect example in IN for the Smotherman that shows its imperfection. But I'm all for getting a better formula.

[RCgothic]

Ok, well here's the debut of a revised formula.    
   
This revised formula is based on the principle that weapons that can fire in more than one arc are worth more than those that can't. This has been priced at a 10% increase per arc. In addition, speed, launch bays and turrets are not worth a linear number of points. I've tried to take some account of this.   
   
This Revised Formula also asserts that 1 lance is worth 3WBs at 30cm and 4WBs at 45cm+ (I tried 4.5x but the price disparity was just slightly too much to balance - however it's still much better than at present [6x@30cm, 3.66x@45cm, 2.8x@60cm].   
   
Ok, so here's how it works.   
   
#1. It is assumed that the ship under creation has armour 5+ all round built into the 'hits' value. Deviation from this commands a premium or a refund.   
#2. Escorts have 90' turns built in, but can be downgraded for a refund. Cruisers have 45'.   
#3. Apart from that, simply pick your weapons, speed and other upgrades from the list. The NC has been listed at what I think its true value is = 6 torps.   
#4. This has currently been tested for IN and Chaos vessels, Ork Escorts and System Defences, and I think the results have been pretty good.   
   
Ok, so here goes:   
   

Code: [Select]


Hits:    4pts each.
Shields: 10pts each

Speed     Defence 5cm 10cm 15cm 20cm 25cm 30cm 35cm
Escort      -20   -10  -5   0    2    5    10   15   
Cruiser     -35   -15   0   10  15   22   30   n/a
Battleship  -35   -15   0   10   22   30   40   n/a
+D6 on AAF: 5pts

Turns:
Cruiser 90' Turns: 10pts up to 6 hits.
Escort 45' Turns:  5pt Refund

Armour (pick 1):
6+ all round: 5pts per hit
6+ Prow:      3pts per hit
6+/5+/4+:     Free
6+/4+:        2pt refund per hit.
5+ all round: Free
4+ all round: 3pt refund per hit.

Turrets:
1 Turret:  1pt
2 Turrets: 5pts
3 Turrets: 9pts
4 Turrets: 16pts
5 Turrets: 21pts
6 Turrets: 25pts
Subsequent Turrets: 1pt per turret

Weapons     1arc   2arcs   3arcs   all round
WBs@30cm     2.5   2.75    3       3.3
WBs@45cm     3    3.3    3.6     3.9
WBs@60cm     3.6   4       4.3     4.7

Lances@30cm  7.5   8.25    9       9.8
Lances@45cm  12    13.2    14.4    15.6
Lances@60cm  14.4  15.8    17.3    18.7

Torps        3.75  4.1     4.5     4.9
Nova Cannon  22.5

             1   2     4   6     8
Launch Bays  9   18.7  56  93.3  132.2

An example: Lunar Class

Hits: = 4*8 = 32
Shields = 2*10 = 20
20cm Speed = 15
6+ Prow = 8*3 = 24
2 Turrets = 5
12 WBs@30cm in one arc = 12*2.5 = 30
4 Lances@30cm in one arc = 4*7.5 = 30
6 Torps in one arc = 6*3.75 = 22.5
Total: 178.5
Smotherman Total: 191.5
Game Value: 180pts

Some other values:
Gothic Class. Game: 180, Smotherman 209.5, Revised: 178.5 (identical to Lunar)
Armageddon. Game: 235pts, Smotherman 243.5 , Revised: 237
Acheron. Game: 190pts, Smotherman 177, Revised 187pts
Apocalypse. Game: 265, Smotherman 400.5, Revised 369.2
Repulsive. Game: 230, Smotherman 241, 236.5

The worst deviation I've covered so far is the Slaughter, at 211pts, which is a large amount to be sure. A large of that is a discount for not having any synergy with the rest of the chaos fleet, but not the whole difference by any account. The next largest are the Mars, at 245, and the Dominator at 178.5. Then again, the game puts a premium on NCs, and adding 10pts to these brings them back within tolerance.

[Sigoroth]

You said the Apocalypse in game is 265, obviously a typo. However, you also said that your formula gave 369.2 but I keep coming up with 371.1. I assume you're simply using 60cm lances for your calculations and giving no consideration to the special rule. For which I get:

Hits + armour = 7 x 12 = 84
12L@60cm 1 arc = 12 x 14.4 = 172.8
6WB@60cm 3 arcs = 6 x 4.3 = 25.8
4 shields + 4 turrets = 40 + 16 = 56
NC + 15cm speed = 22.5 + 10 = 32.5

Total = 371.1

[RCgothic]

Ah, sorry. I should have specified that I'm working off the fixed ships version, listed at 365pts with FP9 Dorsals and the new special rule.

That means most of your assessment is correct.

Hits + armour = 7 x 12 = 84
9WB@60cm 3arcs = 9*4.3 = 38.9
12L@60cm 1 arc = 12 x 14.4 = 172.8
4 shields + 4 turrets = 40 + 16 = 56
NC + 15cm speed = 22.5 + 10 = 32.5
Total = 384.2
This was then adjusted down by 15pts for the special rule to 369.2

Possibly that may have been a bit much. You lose 10pts of speed and 10pts of shield, but only when firing over 30cm, which will probably be between 1/2 and 3/4 of the time - an adjustment of 10-15pts. 10pts actually fits better, being only .8 off target!

[horizon]

Heya,

from the smotherman thread:

Hits + armour = 7 x 12 = 84
6WB@90cm 3arcs = 9*4.3 = 38.9
12L@60cm 1 arc = 12 x 14.4 = 172.8
4 shields + 4 turrets = 40 + 16 = 56
NC + 15cm speed = 22.5 + 10 = 32.5
Total = 384.2

Eh, where did we or others agree on 90cm weapon batteries? Or did RcG mean 9@60?

[RCgothic]

Heya,

from the smotherman thread:

Hits + armour = 7 x 12 = 84
6WB@90cm 3arcs = 9*4.3 = 38.9
12L@60cm 1 arc = 12 x 14.4 = 172.8
4 shields + 4 turrets = 40 + 16 = 56
NC + 15cm speed = 22.5 + 10 = 32.5
Total = 384.2

Eh, where did we or others agree on 90cm weapon batteries? Or did RcG mean 9@60?

*face palm*

fixed.

[Gron]

This is a cut and paste from a formula by Shamen Riel Krall posted at portmaw when it was operational:
(Maybe something is of interest)

Hi everybody,

I found the smotherman formula, but some things annoyed me. The first one is that any weapon (weapon batery, lance etc) was the same price firing only one arc or three...

The second was the standard deviation* of this formula, and errors that can occurs (around 30 points on a cruiser for devastation, styx and gothic...).

So I tried to put my mathematical abilities on it, and, with an excell sheet, I worked on an amelioration of the well-known smothemran formula.

I made it for light cruisers, cruisers and heavy cruisers/battlecruisers of the imperial and chaos fleets (rules book and armada), and so I can't say anything for battleships and grand cruisers, excepts that it worked for the despoiler class and the emperor** class when I wanted to verify it (I had less than one point of error).

The formula that I will propose you has a maximal error of 8 points, is sometimes less effective than the smotherman formula (on 19 ships, the smotherman formula is better on 6 ships, 12 for my variation, and one ship is equall for the two).

Firstly the arcs modifiers:

For weapons batteries:
30 cm times 1+0,1 by fire arc after the first.
45 cm times 1+0,25 by fire arc after the first.
60 cm times 1+0,4 by fire arc after the first.

For lances:
30 cm times 1+0,25 by fire arc after the first.
45 cm times 1+0,35 by fire arc after the first.
60 cm times 1+0,45 by fire arc after the first.

Costs:

For weapons batteries:
30 cm 1,875 pts per point of firepower. (22,5/12)
45 cm 3,0729 pts per points of firepower. (36,875/12)
60 cm 3,58 pts per point of firepower. (43/12)

For lances batteries:
30 cm 5,625 pts per point of strength (22,5/4)
45 cm 9,21875 pts per point of strength (36,875/4)
60 cm 10,3021 pts per point of strength (123,625/12)

For launch bays:
without assalt boats 12,375 pts per point of strength.
with assault boats 12, 875 pts per point of strength.
(I tried to fit with the fact tha t an emperor or an oberon will pay 5 pts to switch the kind)
Special: The 5th and the 6th launch bays counts as two, it works with it, maybe it's besause of the fact that with only one reload special order we have more effect...

For torpedoes:
2,8125 pts per point of strength. (22,5/8)

For Nova-canon:
384,38 pts. (275/8)
(I tried to fit with the extra cost of +20 pts when a lunar or a tyrant switches its 6 strength torpedoes by a Nova-canon for +20 pts. But the mars and the dominator would have liked to have it cheaper.)

Hull:

Hit points: 2,5 points each.
Shields: 10 pts each.
Turrets: 10 pts each.
5 armor: 10 pts.
6+ prow: 38 pts.
Virage: 5 pts for 45°, 10 pts for 90° (I think this one should be light cruisers only).
Speed: 1 pt per 5 cm.
+1D6 cm AAF: 18 pts.
+1 on boarding actions: 18,75 pts.
(It was made to represent the endeavour, endurance and defiant classes, on the other hand, to fit with my method, I was forced to estimate it at 20 pts in the smotherman formula, to minimize the quadratic average error and avoid that this error had a big impact on the result. CHAOS CRUISERS DON'T PAY FOR IT, it represents the corridor of these three ships, not a fleet special rule)

As you can see I also tried to fit with options, as the +1 turret for +10 pts of tre overlord, th +20 pts for switching stength 6 torpedoes by a Nova-canon etc... (And the Despoiler with its torpedoes option will not fit, making me think that maybe having torpedoes AND launch bays was payable, as the fact of having "too many" launch bays).

And, in order to be very impressive, the "standard deviation" with the smotherman formula is around 12,79 pts, for my version only 3,89 pts, I only have 4 ships with an error worst than 5 pts, against 10 for the smotherman formula (and I repeat that it was only on 19 ships) and no ship worst than a 10 points error with my variation.

I Think I've not forgotten anything, so if you wnat to comment it I'll be glad.

Thank's for reading me.

* Trully it's not exactly the standard deviation, but the quadratic average error, but with an error on average equal to 0 it become a good estimator of it. If you don't know, the standard deviation gives an idea of how the repartition is made. A little standard deviation means that all the ships have an error really comparable to the average error, meanning that there is a constant error easily repaired; but a high standard deviation means generally that there is a lot of variation on this error. For example, with marks between 0 and 20, the highest standard deviation will be 10, meaning that half the marks are 0 and the other half 20; the lowest, 0, means that all the marks are equall.
The quadratic average error has two intersts, as I said it can easily become a good estimator of the standard deviation, but it also include the average error, meaning that I just had to minimize it.

** In this two cases the formula I propose you was better; I'm just disturbed by the fact that the emperor don't have to pay for his +1Ld. The same way the chaos ships don't pay for their +1 bonus against boarding actions...
(end of quote)

[Valhallan]

nice gron. interesting for comparision, but i like that RcG's doesn't scale turrets, etc. linearly.

[Admiral_d_Artagnan]

RCG's formula seems ok but I still don't think the 6+ prow is that much their weight in gold nor do I just think it's a simple 20% increase in both bands of the WB table. There's other stuff at play which I think should be discussed so that it can be introduced in the system which can tweak it to be better.

[lastspartacus]

6+ prows are not to be overestimated.  Its making your prow, essentially, abeam.  Thats golden for ships that need to close, I've been frustrated by imperial prows many a time.

[horizon]

Untill all those ships with lances pop up and make the prow 4+ toilet paper.

[Sigoroth]

6+ prows are even good against an all lance fleet. This is because it forces your opponent to use an all all lance fleet. The bulk of game-changing, ship-annihilating, spank-you-hard, firepower comes from WBs. Typically when you manage to manoeuvre into 15cm range while on LO. For a good deal of the time WBs may slightly under perform compared to lance alternatives, particularly at range, but when you get them in the right position on the right target at the right time they greatly out perform their lance equivalents.

I certainly believe that 6+ prows are worth 35 pts on BBs. It's also fairly obvious that their value scales to hits, and that they're not worth this value to cruisers. I like 3 pts per hit, seems to fit and brings the cost on cruisers down to 25 pts. Hell, we pay 35 pts for CSM crew, and I wish that this was an option for Chaos too! Despoilers with 7 prow lances and the ability to actually close and use them? Slaughters not being obliterated on the way in? Hades being less of the autokill targets they are now? Executors being a very viable Chaos line-breaker with Apocalypse level broadsides? Repulsives also line breaking for that matter. Hell, at 25-30 pts per ship it makes elements of the Chaos fleet quite plausible as line breakers, despite the paucity of prow torps.

Of course I'm not advocating that Chaos should get this option. Just that a 240 pt Executor with 6+ prow armour would be fine. A 190 pt Slaughter with 6+ armour would also be fine. Hell, Chaos may still be under-priced with this upgrade. Given this, and the attractiveness of the option at this price to Chaos ships, I don't think that 25 pts is too much for 6+ prow armour.