
Don Smith
Canada Calgary Alberta

Since no smart people offered to grind some statistics for this game, I have fired up my old Windows Excel 2003 and started to do some numbercrunching.
My goal is to calculate the following:
1. Expected damage per torpedo for each of the following cases: torpedo type, date, range, surface or submerged attack.
2. Expected escort damage inflicted for each of the following cases: date, attack range, torpedo type, day/night, submerged or surface attack.
These two sets of data should assist players in maximizing their UBoat assets in a variety of different circumstances.
I won't attempt to model the millions of variables related to damage or crew status etc... just the "vanilla" undamaged boat numbers.
I will post data which I think is interesting as I grind through the numbers and eventually make a full post with the final numbers and conclusions.
If anyone knows the process for sending an Excel File to the File section here on BGG please feel free to PM me.

Don Smith
Canada Calgary Alberta

Part 1:
Steam Torpedo
Prior to 1941 there is an 80.6% chance that this torpedo will do 1 or less damage per torpedo launched. In 1941 and later this falls to 75.7%. The expected damage per torpedo launched is 0.78 prior to 1941 and 0.97 thereafter.
Numbers based on a submerged attack at medium range.

Lines J. Hutter
Germany Munich

Don Smith wrote: If anyone knows the process for sending an Excel File to the File section here on BGG please feel free to PM me.
I usually make a screenshot, trim it in paint and post it as JPG.

Jim Lederer
United States Farmington Hills Michigan

Just scroll down to the files section on the main page for the game, click the link that says "upload file" (just under the title of the files section), and then on the following screen click "browse" and use the directory box to locate the file on your hard drive which you want to upload...
Jim

Lines J. Hutter
Germany Munich

Ooops, right.
I thought this was about a quick way of adding an Excel into a post. Should have read better. Yes, the file section accepts excel format.

Don Smith
Canada Calgary Alberta

Don Smith wrote: Part 1:
Steam Torpedo
Prior to 1941 there is an 80.6% chance that this torpedo will do 1 or less damage per torpedo launched. In 1941 and later this falls to 75.7%. The expected damage per torpedo launched is 0.78 prior to 1941 and 0.97 thereafter.
Numbers based on a submerged attack at medium range.
Part 1 (continued)
Steam Torpedo
Here is a comparison of expected damage for surface and submerged attacks by range (CloseMediumLong) for steam torpedoes:
1941 and later Submerged: The chances of missing altogether (miss or dud) are: C40%M51%L65% Expected Damage per torpedo launched: C1.20M0.97L0.69
Surface Attack: The chances of missing altogether (miss or dud) are: C31%M40%L51% Expected Damage per torpedo launched: C1.39M1.20L0.97
Prior to 1941 Submerged: The chances of missing altogether (miss or dud) are: C52%M61%L72% Expected Damage per torpedo launched: C0.96M0.78L0.56
Surface Attack: The chances of missing altogether (miss or dud) are: C44%M52%L61% Expected Damage per torpedo launched: C1.11M0.96L0.78
Analysis 1. Close Range attacks appear to make little sense against Escorted Targets. I will crunch the numbers in a later post. Maybe in 1939 when you have the +1 Escort modifier?!
2. Long Range Attacks prior to 1941 will miss so often making the expected damage really pathetic. You will have to fire 4 torpedoes at Long Range to expect to sink a Small Freighter!
3. Surface Attacks increase the expected damage per torpedo by about 25% at Medium Range. Will have to crunch the Escort Detection and Damage numbers to see if this is worth it...



And don't forget that all attacks increase with KCO.

Don Smith
Canada Calgary Alberta

For all you statistics freaks, who don't have any baseball stats to pore over right now, I have posted my Excel spreadsheet in the files section!
http://www.boardgamegeek.com/filepage/98987/damageanddetec...

Dave Young
United States Anacortes Washington

Hey Don,
I'm glad I found your post, because I'm currently working on an Excel spreadsheet that factors in EVERYTHING. I've also calculated the probabilities for encounters (no encounter / benign / hostile) for each of the patrol assignments, which gives you an idea of which to request when you start getting promoted.
Right now, my last hang up is the calculation for probable damage per torpedo, which it sounds like you've cracked the code on. I'll check out your file.
I'll post here when I upload my file.
dave



As a fan of statistics I found a way to continue Don Smith's great analysis.
"Discrete Convolution" allows calculating the distribution of a sum of random variables (identical or different) by combining all ways of reaching a given result.
e.g. P(X+Y=3) = P(X=0)*P(Y=3) + P(X=1)*P(Y=2) + P(X=2)*P(Y=1) + P(X=3)*P(Y=0)
Unescorted or Night Surface, Close Range, 1940 (2/6 Duds) >=2 HP (Small Freighter) 2 Gun 58.85% 2G+1T 79.57% 2G+2T 89.97% 3T 74.76% >=3 HP (Large F <10000t) 2G+1T 50.49% 2G+2T 72.00% 2G+3T 84.63% 4T 73.95% >=4 HP (Large F>=10000t) 2G+2T 52.18% 2G+3T 69.90% 2G+4T 81.84% 4T 60.79% >=5 HP (Capital Ship) 4T 46.07%
and so on...
As strategy, for Unescorted lone ships I used to use the leftcolumn above (2 Gun ammo vs a Small freighter etc.) but found the risk of Additional Rounds significant, so now I recommend the 2nd column (add a torpedo). For Unescorted Two Ships I'd use a nearmaximum salvo on the best target, diverting 2 Guns on the other target to be more likely to damage it and nail it next round.
Did anyone use the aft torpedo/es with escorts around? I think the risk (+1 detection) is not worth the reward, certainly for Type VII's one aft tube (even with KC for no penalty). For Type IX's two tubes maybe?
I still need to make a nicer/more compact way of presenting the results in Excel given the large number of circumstances combined.
Ultimately I want to get to a common measure of risk/reward tradeoffs for each stage of history.



For the 'risk' part of the measure, here is a simplified way to understand the consequences of the [E1] Detection table.
For a modifier 'm', the average number of detections/attacks on [E2] until escaping detection is:
Mod AvgDet(0,+1...) AvgDet=
1 0.2 0.231 0 0.385 0.476 +1 0.714 1 +2 1.4 2.1 +3 2.6 4.333 +4 5 10
AvgDet(0,+1...) is the normal case where the first detection has the base modifier 'm' then the following ones have +1 for Previously Detected. (Either the 1 Exceed Test Depth is never used, or it's used from the start. Obviously that cannot last too many cycles, or the sub will certainly get crushed by the extra 2d6 test)
AvgDet= is the average if the subsequent modifier is the same (e.g. if further rolls use the 1 Exceed Test Depth). OR if the sub was already Previously Detected e.g. air shadowing the sub then calling an Escort.
Both cases do not take into account the increasing chance of detection via specific damages  the Death Spiral.
Practically, risk is close to doubled for each +1 detection DRM. For an undamaged sub it looks quite forgiving for a few attempts at +1, and even fewer at +2 to get important targets. Better never start risking from +3.
For a comprehensive model of all causes of loss, it's a bit harder to compare which comes first: instant crush (13+ on [E2]) vs cumulative Hull vs cumulative Flooding. The Death Spiral has more points of influence directly on [E2] and instant loss than on [E1]. I think an exactsimulation (Monte Carlo on computer) of the game rules being an empiricalsimulation ;) of historical mechanisms is needed to know the whole. Too messy for direct math. statistics.



