## Saturday, October 5, 2013

### SciFi Saturday – Point-Buy Combinations

Last time, I presented a fairly simple point-buy system for setting up games in Star Frontiers: Knight Hawks. This was established as the best we could do with a fairly crude battle-simulator program (no movement; faster ship fires first and then each side blasts away). And happens next once I get one of these wargame balance-simulators going is that I get a little addicted to seeing what questions I can get it to answer for me.

### 6-Point Combos

While simulator runs uniform (homogenous) groups of a single ship type at each other to see which is best, obviously in reality the game is played with combinations of whatever ships a player think work well together. And I wanted to find out which combinations would have an advantage, and extended the simulator a bit to handle that. For starters, what if we give each player 6 points (mega-credits) to play with under that system? There are only 4 combinations possible, actually:

 Index Ships 0 Heavy Cruiser 1 Destroyer & Scout 2 2 Frigates 3 3 Scouts

(These are indexed starting from zero to match up with the internal simulator program code.) Here are the results from these matchups:

 Assessed win percents (6-point combo squads): . .0 .1 .2 .3 Wins AvgPct ----------------------- 0 -- 54 -- -- 1 45 1 -- -- -- -- 0 45 2 64 53 -- -- 2 55 3 52 56 50 -- 3 52 

So what this shows is that combo #0 (the lone Heavy Cruiser) is favored to win 54% of its fights against combo #1 (the Destroyer & Scout), but not against any other combination. In summary: As we observed when we first started gaming with the SFKH ship prices, the smaller ships tend to beat the big ones. The all-Assault-Scout combination seems to be the best here, favored over the other combinations. But under our point-buy system, the advantage is quite small: all of the combinations are close to 50% win percents across all the other types (within +/-5% in each case). The Scouts are only a 52% favorite over the Heavy Cruiser, basically a coin-flip. Almost surely the victory will be decided by the better player's tactical movement and decision-making, or simple luck of the dice, regardless of which combination they play with. (Side note: I also considered these with 5-point combos of a Light Cruiser, or Frigate & Scout, but the 5-point combos were roundly beaten by all the others, with average win percents only in the 30% range.)

### 12-Point Combos

As considered above, 6-points are not a bad entry point to the game for possibly brand-new players, but it's a very small engagement compared to those seen in the SFKH rulebooks. (The small scenarios have about 10 points to a side by this measure, with the large ones around 30 points.) In the last post, we had some evidence that the 12-point level might be an interesting threshold. So I also mapped out all the combinations at this level and ran them against each other (ships listed in abbreviated format; see here for key):

 Index Ships 0 CV, VS 1 BB, DD 2 BB, VS×2 3 CA×2 4 CA, DD, VS 5 CA, FF×2 6 CA, VS×3 7 CL×2, VS 8 CL, DD, FF 9 CL, FF, VS×2 10 DD×3 11 DD×2, VS×2 12 DD, FF×2, VS 13 DD, VS×4 14 FF×4 15 FFx2, VS×3 16 VS×6

And below are the results of 10,000 combats each between each possible matchup of these 17 different combinations of ships:

Assessed win percents (12-point combo squads): .. 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 Wins AvgPct -------------------------------------------------------------- 00 -- 67 68 68 74 59 75 68 68 66 82 82 66 78 -- 65 70 15 69 01 -- -- -- 72 -- -- -- -- -- -- 70 -- -- -- -- -- -- 02 36 02 -- 73 -- 74 61 67 55 58 75 53 88 70 58 63 65 53 52 15 62 03 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- 00 31 04 -- 60 -- 63 -- 54 -- -- 63 -- 78 60 -- 55 -- -- -- 07 50 05 -- 77 -- 79 -- -- -- -- 58 -- 90 54 -- -- -- -- -- 05 49 06 -- 67 -- 68 54 61 -- 50 69 -- 84 63 -- 56 56 -- -- 10 55 07 -- 64 -- 66 55 58 50 -- 67 -- 80 61 -- 57 50 -- 50 11 54 08 -- 67 -- 71 -- -- -- -- -- -- 85 -- -- -- -- -- -- 03 39 09 -- 72 -- 76 60 67 55 58 77 -- 88 68 55 61 63 -- 53 13 61 10 -- -- -- 52 -- -- -- -- -- -- -- -- -- -- -- -- -- 01 19 11 -- 51 -- 55 -- -- -- -- 57 -- 74 -- -- -- -- -- -- 04 41 12 -- 68 -- 70 56 60 52 53 71 -- 86 64 -- 61 56 -- 55 12 57 13 -- 60 -- 60 -- 54 -- -- 65 -- 79 55 -- -- -- -- -- 06 47 14 51 80 -- 84 54 56 -- 50 63 -- 94 58 -- 52 -- -- -- 10 55 15 -- 72 -- 74 58 67 55 56 78 -- 89 68 55 63 64 -- 56 13 61 16 -- 72 -- 70 55 66 55 51 73 -- 83 62 -- 57 53 -- -- 11 56 

Obviously, that's a lot of data there (I had to shrink the font to fit on the page, sorry), so let's analyze. Here's the Top 5 best-performing combinations in this batch:

 Index Ships Wins AvgPct 0 CV, VS 15 69% 2 BB, VS×2 15 62% 9 CL, FF, VS×2 13 61% 15 FFx2, VS×3 13 61% 12 DD, FF×2, VS 12 57%

What we see here is that there are some clear favorites among the choices (as opposed to the 6-point level, where everyone hovered around 50% average win rates). The favorites again have a tendency towards the smaller ships: every one of the top 5 includes one or more Assault Scouts, and the very best performer -- a Carrier and one Scout escort -- is really attacking by way of 6 Fighters and the fast Assault Scout. However, the big ships are not totally useless, either: Note that the 2nd best combo features a Battleship with two Scout escorts (and I'm quite pleased to have the BB be a legitimately strong option here). The all-Scout combination, #16, does not appear in the Top 5 (although it is actually 6th-best, with an average win percent of 56% against all other types). But note that none of the Top 5 can be fielded by the Sathar (since they don't have Assault Scouts).

On the other hand, note that none of the combinations beat all of the others. Intriguingly, the #1 combo (Carrier with Fighters & Assault Scout) is actually usually beat by combo #14, which is just a squad of 4 Frigates (with no scouts involved). It's a narrow advantage (51% to the Frigates), but there it is. We did note last time that the Frigates are a strong choice in this point-buy system, and it appears that their many beam weapons do a good job of shooting down a squadron of incoming Fighters. So if you know for a fact that your opponent was always playing Carrier & Scout, then your response should be to bring a squadron of all-Frigates to the table.

For comparison sake, here are the bottom 5 in this matchup:

 Index Ships Wins AvgPct 3 CA×2 0 31% 10 DD×3 1 19% 1 BB, DD 2 36% 8 CL, DD, FF 3 39% 11 DD×2, VS×2 4 41%

The lesson here is that what you don't want to do is bring a fleet of only-large-capital-ships to the fight without any speedier escorts. A pair of Heavy Cruisers alone, or three Destroyers, are simply awful. So is a Battleship with one Destroyer. Generally speaking, the Destroyer suffers a bit in this point-buy scheme compared to the Frigate (it has only 2 extra rocket battery shots, and 10 more hull points, in exchange for slower maneuvering and +33% cost), but as we noted before, there simply isn't any wiggle room available in the numbers we used to modify that at all. Thus it's not too surprising that it shows up a lot in the Bottom 5 here. But it did show up in the lead of one of the Top 5 combos, too, so it's not a total lost cause.

So in summary, it seems like this point-buy scheme is pretty robust, especially taking the 12-point-buy level as an exemplary example. No combination of ships completely dominates all of the others, and the best results come from mixed combinations of different ships. That should provide a lot of space for players to play with, both in the meta-game (of determing which group of ships to bring to the table), and the tactical game itself (maneuvering and shot selection to make the best of the fairly narrow advantages between each combination of ships).

### Java Code

You can see the revised Java code to this simulator program below (version 1.03). If you make any interesting extensions or come up with what you think is a better point-buy regime, please let me know about it!