Bismarck Tactical Values

Avalon Hill's Bismarck (1979) has always been one of my favorite games. However, it's a bit long, and my close friends aren't intense wargamers, so it's hard to find fellow players for a game. So recently Isabelle and I started playing some tactical pick-up games -- cut out the whole strategic search aspect, and just run a straight-up firefight on the battleboard. Not how the game was designed, but it's palatable for both of us, and provides a bit of entertainment.

Of course, the problem is that since the game wasn't designed for this, there aren't any guidelines for setting up or balancing such games. We could use the "victory points" for sinking each ship, or some calculation on each ship's statistics, but I found that none of those seemed terribly consistent. You may be able to guess what the solution was: My customary response of simulating a version of the game in code, running it a few tens of million times in a Monte Carlo simulation, and seeing what balance of objects give a 50% chance of winning against each other. (Prior examples of this were done for: D&D Arena, Monster Metrics, Book of War, Star Frontiers.) Results in this case are shown in the table below (plus PDF, ODS versions):

Methods

• We used the Bismarck itself as the "basis" ship worth 30 points (the same as its victory point value in the game as written). Every other ship in the game was run through a loop of creating N = 1, 2, 3... sister clones and battling each group in 10,000 repeated firefights against the Bismarck. Once we found a number N that beat the Bismarck over 50% of the time, we did a linear interpolation for that type of ship's real value (shown under "Points" above).
• For simplicity, the simplified simulation was always run assuming: Basic combat rules only, a fight at long range, firing at broadsides, with no movement, and port sides facing. The fact that it was at long "B" range implied that only main guns could fire, at half salvoes; and also no torpedoes could be used (which are not in use for Basic game combat anyway).
• Aircraft carriers (CV's) were skipped -- Their power is not in ship-to-ship combat; they are usually allowed to avoid such combat; and they have no main guns usable at long range, so their effectiveness here would be automatically zero. 
• I batched up ships into real-world classes to make the table a bit shorter. "Game #" shows the number of ships of that class included in the game; "Real #" shows the number of real-world ships so constructed. Bismarck and Tirpitz (really sister ships) are separated because the game gives the Tirpitz reduced-fire penalties for not finishing sea trials in its alternative scenario.
• The AI of either side is set to shoot all its guns at the one target on the other side with the biggest guns. When that target is sunk or degraded to zero firepower, the AI switches to the next highest-gunned target, and so forth. This was my attempt to split the difference between real-world action and optimal in-game tactics.
• Code & data archive is made available, as usual (Java ZIP).

Observations

• Compared to the table above, the official game victory points seem to greatly undervalue British battleships (BB, BC). The rules-as-written only award 12, 14, or 16 points for those types (versus 20 or 21 points above).
• Likewise, cruisers of all types seem undervalued in the game. The official rules assign only 6 points for any heavy cruiser (CA; usually 8 points above), and 4 points for any light cruiser (CL; again usually 7 or 8 points above with some exceptions). In particular, the game assigns almost indistinguishable stats for most CA's and CL's, so the difference in victory points is rather hard to justify. The assessed valued of most CL's is exactly double that given for them in the game.
• The French battlecruisers (BC) seem probably the most undervalued. The game only gives them 8 victory points value (assessed above at 19 points; note that victory points as shown assume British control, i.e., the special rule for possible surrender is not in effect).
• The US BB North Carolina is also undervalued at 20 points in the rules (versus 29 above). Note that the rules don't give it special combat advantages like resistance to special damage, reduced evasion damage, etc., that the Bismarck does, so at least a 1-point disadvantage seems reasonable. 
• Ships suffering from the "reduced fire" rule (new ships with a history of gunnery problems, 50% to reduce bow or stern main guns by half in any turn; i.e., King George V, Prince of Wales, Tirpitz) really take a big hit in their value in the simulator. Prime example: The Bismarck is identical to the Tirpitz except for reduced-fire, and the assessed point values come out to 30 versus 24 (i.e., a 6-point difference just for the reduced fire effect). The Intermediate game rules assign 28 victory points to the Tirpitz, which probably should have been lower.
• The Prinz Eugen and her sister ships are best assessed here at 9 points. Note that the game rules vacillate on this datum -- she is assigned 10 victory points in the Basic game, and 8 points in the Intermediate game. The best value is apparently the midpoint of those numbers. 
• We might interpret the fact that all non-German ships are apparently undervalued in terms of game victory points as this: The German player is very much incited to avoid ship-to-ship combat, and truly must focus (as was the goal of the real operation) on evading British combat ships and catching convoys instead. Even if the German player were to exchange exact-same-stats warship for warship, they would then lose on victory points. This could be intentionally modeling why Admiral Lütjens was almost neurotically opposed to engaging in combat, even when his ship was being actively shelled.
  
• The point-values in the table above can be used to set up reasonably-balanced firefights. For example, a 40-point game would simulate the classic Bismarck & Prinz Eugen vs. Hood & Prince of Wales face-off. A 100-point game would make for an epic fleet battle.

Open Questions

• Considering the critique of undervalued game victory point values above, a number of factors not simulated in the program might conceivably make a difference, such as -- Speed, search values, fuel consumption, torpedoes, overall prestige, etc. While I think that most of these would be fairly minimal (depending on ruleset in use), note that most of these factors would if anything further advantage the cruisers -- which are already seen as worthy of improved point valuations above (i.e., if anything, perhaps they should be even higher).
• The battleship-vs-battleship valuations should be the most dependable; they generally have similar values for any factors not handled in the simulation. Speed (evasion) is usually in the range of 28-32 knots, effectively equal for game purposes. A notable exception would be for the older, slow British battleships -- the Revenge & Nelson classes at only 20 and 21 knots. Possibly the high valuations for those classes above should be adjusted downward because of speed.
• I didn't code special handling for the ships with all-front main guns (Nelson, Dunkerque classes). It wouldn't make any effective difference in this all-broadsides scenario, anyway. 
• Point of rules debate: The game Hit Record Pad gives all cruisers a 0-point box for secondary guns on each side. Obviously that provides no fire value (no secondaries are usable at "B" range here anyway). But there is a bit of a dilemma on whether that box should be crossed out for damage purposes or not. If so, it would provide an additional 1-point defensive buffer before cruisers start taking midships damage (which ultimately culminates in sinking). The simulator here assumes we do not spend a damage point marking those zero-boxes. If we adjudicated that the other way, then that would increase the assessed value of cruisers even more.
• The game rules officially allow ships to split their salvoes among multiple targets (whereas my simulator directs all fire from a task force at one target). Perhaps if we had a more sophisticated AI that could split up targets, the big ships with many guns would claw back some advantage when fighting many smaller ships (i.e., lowering the value of cruisers down a bit). One could debate philosophy of whether we should pursue pure in-game advantage, or instead try to simulate real-world fire control tactics of the WWII era.
• In the table above, the "Real #" column is intended if anyone wants to expand the ships in use beyond those included in the boxed game. In addition, many of these classes had even more such ships planned for construction, many of which were scrapped at the outbreak of WWII; players should of course feel free to further expand the fleets in any "What If?" scenarios. Wikipedia is has very well-organized overviews of each class of ships referenced above.

 Thoughts? Anyone still play tabletop Bismarck?