Statistical Study - Tone vs Boise/Atlanta

[Jaels]

I just whipped a little program to simulate an engagement between the Tone, the Boise and the Atlanta.

The parameters were as follow:

- Round 1 is at range 3, round 2 and on are at range 2;
- Tone will fire at the Boise until she destroys it, then switch to the Atlanta;
- Boise will use its Rapid Fire ability on Round 1;
- Tone will use its Scout Cruiser ability on the first ship targetted in the Round.

This resulted in a little function simulating the battle between the ships. Running this engagement ten million times gives the following results:

Tone destroyed, Boise intact, Atlanta intact: 376490 3.8%
Tone destroyed, Boise damaged, Atlanta intact: 1219739 12.2%
Tone destroyed, Boise crippled, Atlanta intact: 986576 9.9%
Tone destroyed, Boise destroyed, Atlanta intact: 2670161 26.7%
Tone destroyed, Boise destroyed, Atlanta damaged: 1091421 10.9%
Tone destroyed, Boise destroyed, Atlanta crippled: 473730 4.7%
Tone destroyed, Boise destroyed, Atlanta destroyed: 1151868 11.5%
Tone intact, Boise destroyed, Atlanta destroyed: 496434 5.0%
Tone damaged, Boise destroyed, Atlanta destroyed: 648580 6.5%
Tone crippled, Boise destroyed, Atlanta destroyed: 885001 8.9%

As we can see, the odds are against the Tone surviving the two cruisers, but it is quite possible to see it happen (around once every 5 fights). In exchange, the Tone should be destroyed without causing casualties once every 4 engagements. The usual result should see the destruction of both the Tone and the Boise, but you have to take in account this is done with dumb targetting.

Shooting at the Atlanta with the main guns and at the Boise with the Torpedo gives this:

Tone destroyed, Boise intact, Atlanta intact: 375617 3.8%
Tone destroyed, Boise intact, Atlanta damaged: 1153520 11.5%
Tone destroyed, Boise intact, Atlanta crippled: 838229 8.4%
Tone destroyed, Boise intact, Atlanta destroyed: 2014186 20.1%
Tone destroyed, Boise damaged, Atlanta destroyed: 958280 9.6%
Tone destroyed, Boise crippled, Atlanta destroyed: 330096 3.3%
Tone destroyed, Boise destroyed, Atlanta destroyed: 1478426 14.8%
Tone intact, Boise destroyed, Atlanta destroyed: 610351 6.1%
Tone damaged, Boise destroyed, Atlanta destroyed: 567371 5.7%
Tone crippled, Boise destroyed, Atlanta destroyed: 952022 9.5%

Doesn't really improve your chance of surviving, and but now it is the Atlanta who bears the brunt of the damage.

And shooting at the Boise with the main guns and the Atlanta with the Torpedo is a losing proposition, as while it raises the odds of sinking both ships, it does so at the expense of the Tone surviving:

Tone destroyed, Boise intact, Atlanta intact: 376321 3.8%
Tone destroyed, Boise damaged, Atlanta intact: 1218421 12.2%
Tone destroyed, Boise crippled, Atlanta intact: 987129 9.9%
Tone destroyed, Boise destroyed, Atlanta intact: 2099620 21.0%
Tone destroyed, Boise destroyed, Atlanta damaged: 626112 6.3%
Tone destroyed, Boise destroyed, Atlanta crippled: 173278 1.7%
Tone destroyed, Boise destroyed, Atlanta destroyed: 1938317 19.4%
Tone intact, Boise destroyed, Atlanta destroyed: 146704 1.5%
Tone damaged, Boise destroyed, Atlanta destroyed: 488081 4.9%
Tone crippled, Boise destroyed, Atlanta destroyed: 875301 8.8%

Hope you find this interesting. I could run a similar test with the Myoko to see if one more torpedo make a big difference (I have a feeling it doesn't, as you'll lose it as soon as you are crippled, and there is a good chance you'll be crippled before the Torpedo phase of round 2).

JL

[Jaels]

The Myoko fare about the same against the two cruisers, which was to be expected:

Myoko destroyed, Boise intact, Atlanta intact: 372645 3.7%
Myoko destroyed, Boise damaged, Atlanta intact: 1203565 12.0%
Myoko destroyed, Boise crippled, Atlanta intact: 955594 9.6%
Myoko destroyed, Boise destroyed, Atlanta intact: 2647700 26.5%
Myoko destroyed, Boise destroyed, Atlanta damaged: 1038501 10.4%
Myoko destroyed, Boise destroyed, Atlanta crippled: 476571 4.8%
Myoko destroyed, Boise destroyed, Atlanta destroyed: 1132192 11.3%
Myoko intact, Boise destroyed, Atlanta destroyed: 631472 6.3%
Myoko damaged, Boise destroyed, Atlanta destroyed: 728291 7.3%
Myoko crippled, Boise destroyed, Atlanta destroyed: 813469 8.1%

JL

[polar]

can you take the two japans cruisers against one of the battleships?

see units stats thread for stats for an american battlesips?

[Jaels]

can you take the two japans cruisers against one of the battleships?

see units stats thread for stats for an american battlesips?

I could, but I don't believe we'll learn much from it. Cruisers are simply not made to go a target as big as the Iowa without something else to distract it.

The Iowa would be able to get free shots at range 5 and 4 with enough firepower to sink either cruiser in one shot, then use its secondary battery against both cruisers at the same time once the range closes. On the other side, the cruisers have guns barely big enough to dent the Armor (and we won't even mention touching the Vital Armor) at long range, and their torpedoes are diminished due to Torpedo defense, so they would need 3 hits to sink the Iowa.

Until we learn more about terrain (which would allow the Cruisers to potentially close the range without getting shot at and use their torpedoes and gun to maximum effect), this would be a turkey shoot. I'd prefer to go with a flotilla of destroyers to sink the Iowa, providing they are cheap enough. You'll lose some closing in, but they should be speedy enough to get to close range and have good torpedo attack that give them a chance for some lucky shots.

JL

[Remember-OWS-]

Now I see the CIHB in your brain J.-L.! :D

[polar]

I generally agree.

However looking at the point cost you can actually send 2 Myoko and 1 Tone
against one IOWA. That improves the odds. If you start at range 3 (somehow imangen that no firing acures before this range)

If IOWA does NOT kill any cruiser outright the first round (with 15 dice attack the average number of hits is 10 so this is not unthinkable). Then the cruisers have a nice ability to kill IOWA I think. (AFTER ROUND 2:atleast 5 torpedos dices, two attacks at 11 dices, one at 10 dices, two at 9 dices and one at 8 dices and most proable two cruisers still reamining on the battlefield ready to close in at range 1.)

However, a better test could be 'bismark' versus 'Tone+myoko'.
Bismark is weaker and cost less points. And should be less extrme battle.

[Autarch]

It just occured to me while reading those results: are torpedo attacks executable every round?

[dictator_wanna_be]

Interesting... I am not sure if I will get into WaS yet... I am woundering about the carrier and aircraft mechanic. How many air craft would it take to kill a battleship... also spacing is a concern to me... how close do the fleets get to each other at the beging? I guess I'll have to wait for the final rules!

[Jaels]

It just occured to me while reading those results: are torpedo attacks executable every round?

Yes, but damage from gunnery attacks are resolved first and could destroy the torpedo-firing ship before it could launch them.

JL

[horacus]

Well, that are interesting things. Very nice.

[Autarch]

Yes, but damage from gunnery attacks are resolved first and could destroy the torpedo-firing ship before it could launch them.

JL

I meant is there a limit on how many times a ship can fire it's torpedo tubes. Japanese DDs had reloads, but I don't think they could be reloadeed in the heat of battle.

[Jaels]

I meant is there a limit on how many times a ship can fire it's torpedo tubes. Japanese DDs had reloads, but I don't think they could be reloadeed in the heat of battle.

No limit in the basic rules that we can see. There might be one in the advanced rules, but that would require the kind of tracking WotC didn't want to introduce in the land game, so my guess would be no limit there either.

JL

[RichardBaker]

No, we decided to let you have your torpedoes evey turn. If you think of a torpedo attack as a "spread" of 3-5 fish, then most torpedo-armed surface ships carried enough launchers to drop multiple spreads. For example, a Kagero-class destroyer normally had two quadruple mounts, while the Tone had four triple mounts. It was typical to empty one mount at a time. Dropping all your torpedoes at once was pretty unusual. So, you could say the Kagero's got 2 torpedo "attacks" under a reasonably historical torpedo doctrine, but the Tone might have as many as 4 weaker ones.

Once you assume that most ships likely have 2 or 3 torpedo "shots" anyway, it's a lot less important to track them. Ships in the game don't often get the opportunity to make more than 2 or 3 torpedo attacks anyway.


No limit in the basic rules that we can see. There might be one in the advanced rules, but that would require the kind of tracking WotC didn't want to introduce in the land game, so my guess would be no limit there either.

JL

[RichardBaker]

Really interesting analysis, by the way. We built tables to figure hit chance vs. armor "x" for number of dice "y" and relied on lots of playtesting, but we didn't do the stat-crunching head to head comparisons you're playing with.

One of the interesting techniques our developers came up with was to create Generic Battleship, Generic Cruiser, Generic Destroyer and compare them against each other extensively. Once you've set the "average" numbers for the Generic Battleship, it's easy to compare the Bismarck and Iowa to those "class averages" and determine how they're better or worse. In any event, we found that generic battleships cleaned up handfuls of generic cruisers, handfuls of generic cruisers cleaned up mobs of generic destroyers, and mobs of destroyers were pretty scary to battleships -- very close to the ideal "rock/paper/scissors" relationship you strive to achieve to see in a game like this.

[Jaels]

Really interesting analysis, by the way. We built tables to figure hit chance vs. armor "x" for number of dice "y" and relied on lots of playtesting, but we didn't do the stat-crunching head to head comparisons you're playing with.

Thanks. The stat-crunching is actually quite easy to do as long as you a little background in programming. My program simply run a battle X amount of time and collect the results for display. A single battle have ships slugging at each other (and recording damage) until one side is wiped out.

Obviously this doesn't take in account all the other elements that would happen in a real game (the major ones being maneuvering, and the influence of other ships and planes, and shot selection depending on special occasions), but it still gives a good account of the basic capabilities of each ship.

One of the interesting techniques our developers came up with was to create Generic Battleship, Generic Cruiser, Generic Destroyer and compare them against each other extensively. Once you've set the "average" numbers for the Generic Battleship, it's easy to compare the Bismarck and Iowa to those "class averages" and determine how they're better or worse. In any event, we found that generic battleships cleaned up handfuls of generic cruisers, handfuls of generic cruisers cleaned up mobs of generic destroyers, and mobs of destroyers were pretty scary to battleships -- very close to the ideal "rock/paper/scissors" relationship you strive to achieve to see in a game like this.

That is indeed the best way to go, and the relationship I would expect to see (in fact, this is why I wasn't hot on running the Iowa/cruisers test at the beginning, as the results seemed a little obvious).

Now I really want to see a basic destroyer... :)

If you ever want some more analysis for your development purposes, just let me know.

JL

[XAos]

I'd guess design & playtesting should start with using a computer to number-crunch the obvious matchups. A computer can do this a few million times, in less time than a playtest team can do it once. Which virtually eliminates luck or personal bias from the playtest results.
You then want to playtest (with several playtesting teams) to check the affect of unusual abilities or unusual tactics. The weakness of software is it only answers the questions you ask it. You need the playtest teams to identify which questions to ask.
So you then go back to the computer to number-cruch the tactics identified by playtesting.

[Photoner Hawkwind]

With "rock, paper, scissors", where do the planes fit in?

[XAos]

One of the interesting techniques our developers came up with was to create Generic Battleship, Generic Cruiser, Generic Destroyer and compare them against each other extensively. Once you've set the "average" numbers for the Generic Battleship, it's easy to compare the Bismarck and Iowa to those "class averages" and determine how they're better or worse. In any event, we found that generic battleships cleaned up handfuls of generic cruisers, handfuls of generic cruisers cleaned up mobs of generic destroyers, and mobs of destroyers were pretty scary to battleships -- very close to the ideal "rock/paper/scissors" relationship you strive to achieve to see in a game like this.
A couple of points there;
1) The mathematical term used to describe the Rock-paper-scissors model of game balence. Is "Dynamic Instability", which means that it's easy to upset the game balence. e.g. If A/H make a misstake on the "rock" unit (and everyone makes some mistakes), the scissors unit becomes immediatly dominant in the metagame. There are more stable game balence models than this one...

2) Deciding as a start point that cruisers will be more cost-effective than destroyers but less cost-effective than battleships. In a rock-paper-scissors cycle. Inevitably results in Cruisers with effective anti-battleship weapons (Torpedo Tubes) being less cost-effective than ones without. i.e. A/H functionally started the design with the axiom that Japanese cruisers (which all carry long lance) would be the least cost-effective & US cruisers (which mostly have no Torpedos) would be the most cost-effective.