SciFi Saturday – Point-Buy System

The Star Frontiers: Knight Hawks game comes with a small number (4) of pre-designed scenarios, but no guidelines for constructing or balancing your own games after that. While this was common for the era (it's the same approach as in Doug Niles' other TSR wargame of the era, Battlesystem for D&D), I now think it's a serious oversight. I wanted to create a point-buy system to make pickup games of SFKH a snap, and my first thought was to use the spaceship pricing from the Campaign Book for that purpose (see last week). It became pretty obvious that was a total failure -- the small ships just always wreck the large ships at the prices indicated. But if we massage the prices a bit we can get something more reasonable -- namely compress the prices closer together (increase cost for the small ships, decrease cost for the big ships). Here's what I've come up with (edited costs in "mega-credits"):
Ship Cost
Scout 2
Frigate 3
Destroyer 4
Light Cruiser 5
Heavy Cruiser 6
Battleship 8
Assault Carrier * 10

* Assault Carriers include 6 Fighters each.

As always, my doctrine is that "The acid test is gameplay". You just can't balance this stuff by looking at any a priori formula on the statistics, as the interactions are complex enough that you simply have to see how they actually fight against each other. And frankly that's hard. What I used to assess this is to take the earlier price-balancing simulator for my Book of War game, rip out the guts and rebuild it to handle SFKH spaceship combat, and then run a few tens of millions of mock combats to see what happens. The result is that the best combination of prices (keeping it near the campaign book pricing) is what I came up with above. Here's some analysis as spit out by the simulator:

Assessed win percents (budget 10-30):

VS -- 55 88 77 82 67 -- 5 67
FF -- -- 95 88 90 79 59 5 76
DD -- -- -- 51 58 -- -- 2 30
CL -- -- -- -- 72 -- -- 1 38
CA -- -- -- -- -- -- -- 0 24
BB -- -- 63 58 78 -- -- 3 49
CV 66 -- 82 66 74 56 -- 5 64

What this shows is, for the same total budget, the percentage of time that a fleet of one type of ship beats another type of ship. For example: Assault Scouts (VS) beat Frigates (FF) 55% of the time in a straight-up fight with the same cost on both sides. Assault Scouts are favored against 5 opposing types (under "W" for wins), and their average win percentage is 67% across all possible enemies.

So the resulting game isn't perfect by any means. There are clearly 3 preferred types, namely Assault Scouts, Frigates, and Carriers (VS, FF, CV). The other large capital ships are pretty much also-rans. But after trying many combinations it's the best I could come up with, and there's really isn't any wiggle room left in the prices to massage it any further (notice the sequential prices 2, 3, 4, 5, 6 all used above). This assumes that we keep the ship statistics as shown in the book (although scouts get 25 hull points), and we keep the costs simple with small integer values (and near to the book pricing results).

There is the nice fact the there isn't any single best type, and we have at least one rock-scissors-paper cycle to keep the game from being totally solved. Notice that Scouts usually beat Frigates (55%), Frigates beat Carriers (59%), and Carriers beat Scouts (66%). That itself was not easy to make happen. Battleships aren't terrible, either (arguably their price could be 9, but then you get a pattern where every ship beats everything bigger than itself, and battleships lose to everyone).

The simulator is fairly crude, but based on the tightness of the price-points available, I don't see changes making much difference to the ultimate result. Here are some assumptions built into the simulator: (1) It only handles the Basic Game (not the Advanced Game with hit-location, damaged systems, etc.). (2) It doesn't deal with any movement -- ships are simply set up 3 spaces away and blast away at each other. (3) Faster-moving ships are given first offensive attacks (what I see effectively happening in table play). (4) Forward-firing weapons don't get defensive shots (as I see in table play; change that and capital ships fare better, esp. frigates). (5) As soon as an enemy ship blows up, the attacker can switch shots to another (technically not the game rule, but it approximates some intelligent prior shot selection by the attacker). (6) As noted above, Assault Carriers carry 6 Fighters into the game with them (same as what we see in the published scenarios and campaign order of battle).

The combat simulation runs on a random budget of 10-30 mega-credits (again, about what we see for the published scenarios in the Tactical Book). Any remainder is spent on a pro-rated "partial" ship (damaged?) so we don't get weird artifacts like Carriers losing out just because the budget was 28 (and thus simply flushing the last 8 points of value down the drain). Interestingly, the results change for different budget levels. Like, at 10 mega-credits, Frigates beat everything (while Battleships beat everything else); but at 15+ mega-credits, Carriers beat everything (and Assault Scouts win out over everything else). I might recommend a game at 12 mega-credits, where the matchups seem to be as shown in the table and graphic above. Future research: Combinations of ships, tactical movement, and use by intelligent players may modify any of these observations, but I think the point-values given are a solid basis.

If you did use these as the revised prices for warships (in mega-credits), then you have to think about where the Campaign Book system gets tweaked. Maybe engine costs go up for the small types (add a separate expense for hyperspace drives?), while reducing number of engines for the bigger types or something. While the cost for the Heavy Cruiser and Battleship went down (reflecting their relatively low utility, hit points, etc. for their price), we note that the Assault Carrier price is actually pretty much what we computed last week from the Campaign Book (7 for the CV + 2 for the VF at cost 1/3 each). This reinforces a place where I think the rules have a big gap -- there's no line-item or expense for the fighter hangar/launchpad/recovery system on the Carrier. Perhaps if such a system had a cost on the order 3 million credits, and the total was rebated as per the Battleship type, then that would explain things.

Minelayers don't fit into the simulator at all (nor can I see how to use them in my tabletop miniature games), but by interpolation we can guess they would cost 3 mega-credits (same as the Frigates). If you'd like a convenient index-card sized handout to pass around your table, then that's linked below.

Okay, so there's some of the things I was thinking about on this exploration. Finally, if you want to see the Java code yourself and tinker with the settings and prices, then that's the last link underneath here. (Note: Work in progress; next code release due next week.)


SciFi Saturday – Spaceship Costs

The first and largest section of the Star Frontiers Knight Hawks Campaign Book (about a third of the whole) features rules on designing and purchasing spaceships for use in the game. What's not ever included are complete construction-profiles for the stock ships in the game, or how much a "normal" one would cost. Out of curiosity, I've priced up the standard military ships in the game, and the results are below (costs generally rounded to the nearest million credits):

Ship Type M-Credit Cost Computer Level
Fighter 0.35 3
Scout 1 3
Frigate 2 4
Minelayer 2 4
Destroyer 3 4
Lt. Cruiser 5 4
Carrier 7 5
Hvy. Cruiser 9 5
Battleship 12 5

So the standard military ships in the game range between about 1 and 12 million credits. This brings to mind the possibility of a fairly simple point-buy mechanism for opposing fleets, where each player is granted a certain number of mega-credits with which to buy ships (with fighters at 3 per point). I'll discuss that a bit more at the end. A side note from this project is the observation that all computer systems aboard spaceships, as per the SF Alpha Dawn rules, are in the range of levels 3-5 (coincidentally following the engine size: A-type engines connect to level 3 computers, B to 4, and C to 5). Also, the spreadsheets in the zip file above (ODS format) can be used as templates to quickly stat up other ships, if you like.

Well, that's what the pricing rules say; now here's some analysis of those costs. The pricing system given is not very realistic in physical terms. For example, consider last week's discussion about the dimensions of ships. Again: Since cost increase is linear, but given surface area increases as a cube, by paying 20 times more money you get over 3,000 more material in your hull (comparing fighter to battleship). So from that real-world perspective, the costs ought to be higher -- or else the ships should be smaller.

Alternatively, we might compare to real-life warship costs. For example, consider some costs circa WWII, on which our boardgame is thematically based, and for which information is fairly easy to come by. Fighter planes in the 1940's cost some $50-100 thousand to produce (link); whereas a battleship might cost $80 million (link). So while the price difference ratio between the two in our SFKH game is only 1:36, in real life we see it's more like 1:800. This once again indicates that the large ships are too cheap (the battleship could be 20 or even 100 times more expensive than indicated to be realistic) -- or from the opposing perspective, it's a signal that the SFKH capital ships are much smaller, relatively speaking, than WWII naval combat vessels. Take your pick.

Another problem is that there's just not a whole lot of headroom for upwards advancement in the system. For example, if your PCs can afford a size 10 freighter, then as soon as they double their money they have the means to trade up to something like a battleship or similar maxi-sized vessel. (Of course, in real life a shipping vessel is not remotely as expensive as a military warship.)

So in summary, compared to real-world examples, the big ships in SFKH are too cheap. But let's return to the question of using the prices, computed from the construction rules, as the basis for a balanced point-buy game. Well, unfortunately in my limited experience that seems not to work for exactly the opposite reason: the prices for the big ships are too expensive! Every time I game-test this, the big ships get beaten by a price-equivalent batch of smaller ships. It's not too difficult to say why, as the reasons are multitudinous:
  1. First you've got the standard "damage spillover" problem, common to this or almost any other game (it had to be a key part of my Book of War analysis). Having to shoot down a bunch of small targets is likely to "waste" some damage with each kill, whereas a single big target suffers the full amount from every hit (and thus taking fewer hits for the same total damage).
  2. Exacerbating that further, in SFKH, the hull points don't scale with physical size; they actually trend downwards on a pro-rated basis for larger ships (see here). This is totally opposite to real life, where the whole point of a bigger ship is to load it up with thicker and more durable armor. But in SFKH you're getting less defense for the credit, almost as if the hull armor is getting thinner the larger you make the ship.
  3. In addition, your mobility is getting worse. While the single biggest expense in the SFKH construction rules is the payment for the engines (number goes up, and size also goes up, so geometrically increasing), what you're getting for that increased payment is of course worse and worse acceleration and maneuverability. The opponent is running rings around you, lining up shots better, and likely getting off the first attacks (which is a huge advantage: it's the very first thing in my strategy tips). While this might make sense if the ship was carrying heavier armor, as we see above, in SFKH it's actually the reverse.
To repeat: In game-balance terms, the computed prices for big ships are too high, in the sense that big ships are getting demolished in the game by an equivalent value of smaller ships. Which is exactly the opposite of the problem looked at it terms of realism from real-world examples, or even just plain geometry (up above).

What to do? Well, I guess if I was rebuilding the game totally from scratch, I'd bump up the Hull Points for the bigger ships by fairly significant amounts. This would synch up with the stated dimensions, better match real-world battleship characteristics, and make the higher prices worthwhile in-game. But the problem with that is that the tactical game statistics (like Hull Points) are clearly more fundamental to the product, and the prices we're getting here are second-order effects that weren't actually computed or utilized in the original game. So because of that I'll recommend instead lowering the prices to something that game balances the combat statistics, stipulate that the SFKH capital ships are somewhat physically smaller than initially expected (actually matching our WWII comparison and even the official miniature figures), and basically hand-wave away the details of exactly where the pricing gets reduced.

In fact, there's some precedent for exactly that hand-waving of the pricing. In the SFKH Campaign Book there's an explicit gray zone marked out around whether the construction system shown is at all valid for military vessels (even though that's the whole thrust of the boardgame); the rules for ship weapons say:
The procedure above applies to civilian ships only. Most players will observe that military ships carry more weapons and defenses than civilian ships, with fewer penalties. This is possible due to small but significant technological refinements in military designs... [SFKH CB p. 19]
So in the final perspective we're clearly given the authority to make up whatever prices we want for the SFKH tactical game military vessels and call it a day. More on that next time.

Edit (9/23/13): I should note that the prices computed above don't include expendables such as fuel, ammunition, spacesuits, or the recruitment & training of officers and crew. That latter item might outweigh all the other expenses, but it would have similar problems in that the book specifies a geometric increase for less-than-linear game benefit (e.g., 1 fighter pilot versus 400 crew on a battleship).


SciFi Saturday – Hull Specifications

Recall that the first third of the Star Frontiers: Knight Hawks Campaign Book concerns specifying, constructing, and expensing spaceships; so today let's look at the initial point of that process, the "Hull Specification Chart" on p. 11:


The dimensions given for each hull type (length/diameter) are actually quite problematic. While the cost for an initial, empty ship hull is simply linear (50,000 credits times the hull size at a Class I center, etc.), what you're getting in terms of space and material is much greater than a linear progression. Noting that the dimensions themselves are increasing faster than linear (length 30, 50, 75, 100, 130, etc.), then the increase in surface area works out to be about a cube, while the increase in volume is actually a 4th-degree polynomial. (Least-squares power regression is about 70×h^2.7 for surface area, or 30×h^4.0 for volume.)

What this means is: While you're paying 20 times the cost for a battleship hull over a fighter, you're actually getting over 3,000 times as much material for that payment. That just doesn't seem remotely right. (Fighter hull size 1, surface order 10×2 = 20 m^2; versus battleship hull size 20, surface order 600×100 = 60,000 m^2.) And that's not even considering the possibility of thicker hull-armor for the battleship.

In the past, I made an attempt to rectify this by basing the cost for an empty hull on the surface area from that chart, instead of simply a multiplier times hull size. But other considerations argue against that idea: (1) it's just really complicated and winds up outstripping all other costs in the ship construction; (2) the value you get per hull size in the boardgame is pretty close to linear in terms of weapons capacity (CB p. 18), defensive hull points (see here), etc.; (3) the Campaign Book pictorial schematics actually show a linear increase in dimensions, contradicting this table (exactly 2 boxes length per hull size; see p. 6-7); and (4) the official Star Frontiers miniatures show an even smaller difference in dimensions (for example, the UPF battleship miniature is only about twice as long as a frigate, not 4 times by hull size, nor 6 times by the table above, etc.; see here).

So I would want to fix the length/diameter dimensions given in that table above to better synch up with the cost, hull points, weapons systems, miniature designs, etc., found elsewhere in the Star Frontiers: Knight Hawks game. Something like a linear increase in surface area or thereabouts (finding this is left as an exercise to the reader). This would affect the space used on deck layout maps, especially for the larger ship sizes (no more battleships with onboard malls, parks, zoos, Olympic-sized swimming pools, etc.)


Note that the number of engines given in the "Hull Specification Chart" vary both up and down as hull size goes up (they do not, as might be expected, monotonically increase). This might make sense when you consider that there are 3 engine size categories in the game (A, B, C); it would be reasonable for the number of engines to possibly go down at the point where you bump up to a larger engine size category. Except: They don't actually do that; the points where the engine number goes down don't synch up with the engine size class switchovers. Possibly this was some kind of typo or holdover from an early draft of the game before engine sizes were finalized?

Below I've presented an annotated table with  the engine numbers associated with what size the engines are (see Campaign Book p. 12), example of vessel in that category, and a recommendation for adjusting a few values so the table makes more sense. For example, for hull size 5 and 6 -- frigates and destroyers -- the number of engines could be reduced from 3 (as shown in deck schematics p. 23) to 2, or even 1 (as shown in SFKH official UPF miniatures). Here I've chosen to split the difference and set those numbers at 2 engines apiece -- you have to be careful here, because engine expense is actually the greatest single cost in the spaceship construction rules (e.g., reducing destroyer engines from 3 to 2 likewise reduces overall cost from approximately 3 million to 2 million credits). Consider also that at hull size 4, the text for the pirate Corvette stipulates that it indeed has 2 atomic engines for maneuvering (SFKH0, Warriors of White Light, p. 13). For ship abbreviation codes, see here. You could edit some other places in that chart to taste, but I think this is the bare minimum to rationalize things.


SciFi Saturday – Forging Fighters, Pt. 3

Today I'm completing the project of making UPF fighter-squadron miniatures for the Star Frontiers: Knight Hawks game. Previously I sculpted and duplicated a single fighters, put together a trio formation, and made a mold for that. So now I'll be casting from that mold and painting and finishing the miniatures themselves.

Workday 9 -- Setting up in the kitchen for possibly a few hours of pouring metal. I've got tools, talcum powder, lots of rubber bands, work surfaces, and the fighter squadron mold. I've also got the mold for the miniature bases which I'll be casting at the same time. 

First pour seems to be working fine -- no drips or leaks or anything.

Now here I'll point out that the first few pours are basically experimental, and usually some small adjustments are necessary. In this case, the first pour filled the pour hole and actually didn't get any metal at all down into the fighter shapes. As always, the critical bottleneck is that connection between the pour hole and the mold shape itself. At this point I'll take the exacto knife and tweezers and widen that connection point just a tiny bit. I'd really rather have this happen the first time, rather than have the connection be too wide initially and have it impossible to disconnect miniature from sprue, because that problem is basically unfixable. So I'll widen it just a little bit and try again.

Second try: Better, the metal flowed from the pour hole into the central fighter, but froze at that point and didn't get into the shapes on the sides. This is actually a fairly difficult shape I'm trying to cast here, and in retrospect I was cheating quite a bit by having negative space between the fighters running horizontally through the mold. Really, I shouldn't have any expectation for that to work at all. Anyway, I'll go in again and widen the pour hole connection just a bit and try again.

Third time's the charm: with my next pour, all of the space fills in perfectly, and the pour hole connection is still so small that the miniature just falls off by itself without me applying any pressure at all. I even got the horizontal open spaces between the fighter winds to come out. It pretty much doesn't get any better than that. (A few of my subsequent pours don't work as well, and they go back in the ladle -- after enough attempts I'll get the quantity of good casts I was looking for today.)

Near the end of the afternoon, I've got three good fighter-squadron casts, and three base structures to go with them. I've cleaned them all up with a file and used a pin vise to drill holes through the bases where the wires will go.

Close-up of the UPF fighter squadron miniature, showing how small the darn thing is in my fingers. I wish the photo was just a bit crisper, but I'm immensely happy with how much detail I got in the miniature itself. Particular given I did a double-copy operation on this project, I'm really super pleased with it. (The detail this rubber product gets is nothing short of remarkable.)

Workday 10 -- The last step is to prime, paint, and assemble my three miniature squadrons. In the afternoon I've taken time to prime the miniatures flat gray, and paint the bases a glossy black. (This also involves cutting 2" lengths of wire, rolling them flat, cleaning, and gluing them into the bases carefully.) As I've said before, I actually rather dislike painting miniatures, and I'm very happy for these machines to just have a two-step painting job. For my UPF ships, the first step is a base coat in ultramarine (navy blue).

Here I'm done with the blue base coat, and I've also touched up the black bases in a few places.

The second step is to dry-brush the UPF ships with metallic silver. For larger ships, I let more of the blue undercoat show (highlighting the extra detail, and looking a bit like scarred battle damage) -- but for smaller ships like these fighters, I want them looking more fast and sleek, and therefore I'm willing to more fully cover them in the silver paint. It's a bit of a balancing act, so I may got at them with the dry-brush silver as many as three times before I'm happy.

Super-gluing the fighters onto their bases and letting them sit for a bit. This is pretty easy, because the wire fits snugly into the post-hole I made with the pin vise on the bottom.

Last step: I take a white ink pen and note Roman numerals on the base of each miniature to distinguish them during game play. Looks pretty good by my standards, I'm exceedingly pleased with my first ever miniature-from-scratch project!