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(1) With the exception of some follow up, this officially ends this AAR.
(2) March 11, 2023 - August 12, 2024 (17 months almost to the day) and 161 pages of posts.
(3) Thanks for following, any and all comments regardless are welcomed!
(4) Also, I think it's appropriate that this post is at the start of page 162.
(5) I never know when I start a one of these game whether or not it's going to last a week, month or a year and a half.
(6) Also, for some reason Germany, who no longer exist, still controls one objective city, which is the same number that a crippled but still potent Japan controls.

By the Numbers (Summary).

(1) Why collect and log all this game data if I'm not going to summary and analyze.
(2) I'll make a deal, I'll provide summaries, some initial assessment and you guys provide the critical critique, your own assessment and insights.
(3) I'm starting off with land combat.
(4) The columns by major power (MP), side and total are (a) major power, (b) # of land combats, (c) # won, (d) actual % won, (e) average expected (pre resolution) win or PWIN, (f) difference between actual and expect PWIN, (g) average expect of taking no loss (pre resolution).
(5) The MPs with the lower PWIN & PNL were too more risks and those with the higher values took less risk in their land combats.
(6) One thing that strikes is the actual vs expected PWIN bias in blitz land combat.
(7) The assault (all) looks good -0.08% but the blitz (all) is (-0.96%).
(8) That is my expected calculation is ~1% higher than actual.
(9) I need to go back and look at my blitz calculation, and if that checks, the bias is attributed to entry error (220 blitz entries) or statistics.
(10) The sample standard deviation on the number of expected wins is 3.8 (sqrt(npq)).
(11) That's a one standard deviation of 1.7%, so -1% is (only) a deviation from theoretical mean of -0.6 standard deviations, so maybe it is statistical.
(12) What do you guys think?

Land Combat (All, Assault & Blitz) Summaries.
LC All. LC Assault. LC Blitz. Land Combat (Offensive & Defensive) Support Summary.
(13) 125 instances of offensive and 23 instances of defensive HQ support.
(14) That means HQ support (offensive, defensive or both) was used 21% to 25% of the time (597 total land combats).
(15) When used offensive, the expected (average) PWIN was 84.8% vs 92.9% (all LC expected PWIN).
(16) When used defensive, the expected (average) PWIN was 69% vs 92.9% (all LC expected).

By the Numbers (Summary).

(1) I will (plan to) post these summary tables as I build them.
(2) Next up if air combat, starting with the 4 summaries (strategic bombing, ground strike, ground support, airborne drop) below.
(3) These summaries do NOT include missions that were fully aborted or shot down.
(4) That is, at least one air wing/group of the given type got through to carry out its intended mission.

Strategic Bombing. Ground Strike. Ground Support. Airborne Drop.

By the Numbers (Summary).

Air Combat Mission Count.
(1) Almost 1600 air mission of all sorts played out over the course of the game.
(2) That's a lot of dice rolling!
(3) Or die rolling (depending on the combat; i.e., ground strike (1 die) vs air-to-air (2 dice).

By the Numbers (Summary).

Combat Naval Missions.
(1) Naval Combat Missions were defined as Naval Air, Surface, Submarine (3 top columns on the Naval Combat CRT).
(2) I also included shore bombardment, decided to include those stats separately and not include them as part of the naval combat count.
(3) While a sailor on board during a shore bombardment could claim participation in a given campaign, and awarded a campaign badge for such, their support wouldn't be considered a naval engagement.
(4) My definition for naval combat is participating in a naval engagement against enemy ships, airplanes and/or subs.
(5) Breakdown for each type of naval combat is further broken down by aggressor and defender.
(6) The aggressor is the MP that initiated search.
(7) However; they may not have been the MP that decided combat type.
(8) Perfect example if Germany where subs initiated and committed by failed to find, where the allies did find and elected to fight a naval air battle.
(9) That's why Germany's win % as aggressor for naval air is 0% (because they would looking for a sub or surface but got a naval air).
Mission Counts. Naval Air. Surface.

By the Numbers (Summary).

Combat Naval Missions.
(1) The number of sub combat are overwhelming in favor of the aggressor.
(2) That makes sense as those combat where initiated by an aggressor with subs, that committed their subs, found and elected to fight a sub naval battle.
(3) The defender sub stats are when the non-initiating MP also committed their subs when the initiating MP did too.
(4) The second summary (I think) tells the better story of sub combat, it's derived from the all combats (sub, surface, naval air) originating from an aggressor MP that committed their subs.
Sub. Sub Initiated (Sub, Surface, Naval Air).

By the Numbers (Summary).

Naval Search.
(1) I need to clarify that when multiple MPs, which often happened, were involved in a naval battle, or search, either as the aggressor or the defender, I had to make a call in each case for one "dominant" major power.
(2) Otherwise, these, the previous, and future naval summary charts would get unwieldly very fast.
(3) Also, anything with Vichy (very few samples indeed) I grouped under Germany.
(4) The columns in each of the 3 tables below are total number of searches, number of finds, number of misses, number of combats that resulted and percentages of finds, misses & combats.
(5) A few take aways for me, is that there were a total of 479 naval searches that resulted in naval battle 241 times.
(6) A naval search produce a naval battle half the time (i.e., 50.3%).
(7) Allied searches were successful about one-third of the time (33.2%), while the axis searches were successful a bit over a quarter (27.1%) of the time.
Aggressor. Defender. Overall.

By the Numbers (Summary).

Naval.
Intercept Stats.
(1) The axis attempted over double the naval intercepts than the allies.
(2) The axis were successful 3 out 10 times (29.3%) vs the allies 4 out 10 (40.2%). Shore Bombardment.
(3) The majority of shore bombardment was offensive (95%) vs defensive (5%).
(4) I don't have any stats to prove this, but probably the biggest impact of defensive shore bombardment was to discourage attack against defenders on the coast until the aggressor ran out or possible defensive shore bombardment ships were flipped.
(5) The allies by far used shore bombardment more than the axis.
(6) On average each offensive mission for the allies added 11 GSF (attack factors) and +5.547 to the land combat.
(7) Given that the average land combat odd was +13.6 after shore bombardment, shore bombardment was a significant force multiplier for the allies.

By the Numbers (Summary).

Reorg.
(1) 3 times as many allied units (land, sea & air) were reorg (by HQ, naval & air) as were axis units.
(2) In fact, there were no axis naval reorg mission vs allied 59.
(3) Given that these stats are collected over 37 turns, on average the allies reorg 6 units vs the axis 3 units per turn.

By the Numbers (Summary).

Impulses.
(1) An equal number of impulses (131) for each side over the 37 turns played.
(2) In comparison to the impulse data given in vol 1 of the players manual, this AAR saw greater than "expected" number of impulses in the Jan/Feb, May/June turns.
(3) However; this AAR saw significantly less (by 1 per turn or 6 per game), impulses in in the Jul/Aug turn, which is the best fighting season for the North Temperate and Arctic. Actions. O-chits.
(4) The US produced 44 total O-chits, which cost 660 BPs.
(5) So, 32.5% of US gross war production (2027 BPs) went to O-Chits.
(6) Compare that to 20.9% (240/1149) for the CW, 19.0% (225/1183) for the USSR and 3.6% (45/1240) for Germany.
(7) These percentages do NOT include at-start O-chits (2 for Germany, 1 for Japan, 1 for USSR).
(8) At war (game's) end, the US had 19, CW 7 and USSR 8 in reserve or in production.
(9) Total O-chits played were 5 Germany, 1 Japan, 9 CW, 25 USA, 8 USSR, 48 total.
(10) The vibe I got for all these O-chits was that it was a very good abstraction of how the allied logistics overwhelmed those of the axis.
(11) I believe it was author, Rick Atkinson in one of his books that said the US didn't solve the logistical (and supply) problem in WW2, they overwhelmed it.
(12) That was definitely the vibe I got playing through with the US in regards to O-chits.

By the Numbers (Summary).

Weather.
Counts. Percentage.

Such a great AAR, and really interesting to see overall ending %s, and stats, etc. When I play, ,was always upset that my naval searches didn't turn up much. Well, your overall final numbers also show 25-30%. That is the kind of info that is so useful as it helps me relax, and know that it's normal.

Well,,, as per the norm, my ask and as always, you don't have too, don't feel obliged to, and if you don't want to, no worries. It is proprietary, and you have worked so hard on it, so it's up to you, but if you can, and want, could you once again provide a copy of your amazing spreadsheet. I have an older version from the start of this AAR, and I can't play this game without it. Helps me remember past events, trends, and helps me plan production, etc.

Seen some really nice additions that you have added, so would love to have that.

Well, either way,, thanks Ronnie.

Falken wrote: Sat Aug 17, 2024 1:10 pm Such a great AAR, and really interesting to see overall ending %s, and stats, etc. When I play, ,was always upset that my naval searches didn't turn up much. Well, your overall final numbers also show 25-30%. That is the kind of info that is so useful as it helps me relax, and know that it's normal.

Well,,, as per the norm, my ask and as always, you don't have too, don't feel obliged to, and if you don't want to, no worries. It is proprietary, and you have worked so hard on it, so it's up to you, but if you can, and want, could you once again provide a copy of your amazing spreadsheet. I have an older version from the start of this AAR, and I can't play this game without it. Helps me remember past events, trends, and helps me plan production, etc.

Seen some really nice additions that you have added, so would love to have that.

Well, either way,, thanks Ronnie.

Thanks. Attached below are two copies of my AAR spreadsheet, which I'm calling rev11. The first is a "scrubbed" (i.e., empty) template copy. The second is the populated (final) copy of my completed game.

I'm actually working on a rev 12 which will include refinements from lessons learned from this past iteration.

Also, moving forward I want to resurrect MWIF Magic to start including functionality for speeding up and improving game play. Initially, I'm looking at adding the functionality for speeding up and supporting the the allied player in putting out ASW escorts and patrols. I found this to be a very long and tiresome process the way I did it. What I'm planning on doing is to add tailored reports and tools to help the allied player allocate ships by sea area to either escort or patrol. Then include a form (or module) that allows the player by ship name to divvy up which ships he want to use for escort and patrol by sea area and then have MAGIC make those moves all at once for the player without the player having to click on and move each individual ship.

Next, possibly, I would like to tackle convoy routing, production and (possibly) even trade in MAGIC.

P.S. I think in conjunction with naval assist, I'm going to add Guard Banner Armies (GBA) to MAGIC. That is, basically being able to use MAGIC to play with the GBA optional rules. FYI. The ability is already in MAGIC to implement this part, "Any pocket of non-coastal hexes wholly surrounded by hexes controlled by the other major power becomes controlled by the major power whose hexes surround them.", of the uncoded optional USSR Japan Compulsory Peace [RAW option 50 section 13.7.3].

AAR-Template-rev11-CF-3-Final GW-CF-3-2023MAR07

rkr1958 wrote: Tue Aug 13, 2024 9:14 pm By the Numbers (Summary).

(7) The assault (all) looks good -0.08% but the blitz (all) is (-0.96%).

Land Combat (All, Assault & Blitz) Summaries.
LC All.

LC-All.png (30.24 KiB) Viewed 2398 times

LC Assault.

LC-Assault.png (30.63 KiB) Viewed 2398 times

LC Blitz.

LC-Blitz.png (28.18 KiB) Viewed 2398 times

(1) I was looking at this post and I realized I made an error. Hard to believe, I know (i.e., I made an error).
(2) I wanted to go back and look at the biases in my actual (% Won) vs estimated (PWIN) data.
(3) The difference between % Won & PWIN (i.e., % Won - PWIN) is (as I stated) for assault only -0.08%, which I consider pretty darn good.
(4) To quantify that, assuming that PWIN is correct, the standard deviation for the 378 total samples collected is sqrt(375 x 0.929 x 0.071) = 4.97 ~= 5.
(6) That produces a 1-sigma delta from the mean estimated (i.e., Avg PWIN x Number of Samples = 351.162) of 0.162 or 0.013%.
(7) Given that the total number of actual wins has to be an integer, I call that exact!
(8) Now let's look at the blitz numbers.
(9) The -0.95% difference that I originally looked at was from all (assault + blitz) land combat and not just the blitz.
(10) The blitz actual vs estimated (potential) bias difference is -2.5% NOT -0.96%.
(11) That's a big difference (possibly).
(12) For blitz, the standard deviation for 220 samples, assuming Avg PWIN is correct, is sqrt(220 x 0.929 x 0.071) = 3.8.
(13) The expected number of wins for blitz is then 0.929 x 220 = 204.4
(14) So, the actual difference from expected is 199 - 204.4 = -5.4, or -1.42 standard deviations below expected.
(15) In the world of hypothesis testing, that amount of deviation would be within an 85% confidence interval.
(16) The higher the confidence interval (e.g., 90%, 95%, 99%, 99.9%), the less likely one is to concluded that the actual and estimated came from different distributions.
(17) Or, in other words, that the bias is only a statistical variation and the actual and estimated distributions match (i.e., no error in the estimations).
(18) The reason I phrased (16) in the "negative" is that in the world of hypothesis testing, only rejection of the null hypothesis (i.e., no bias in this case) is a strong conclusion.
(19) Failure to reject (which is what you get with an 85% or higher confidence interval in this case), is the weaker conclusion.
(20) Now to put this in wargaming terms, what we have here is like rolling a 5 on the 1:1 CRT in AH 3rd Reich.
(21) I'm sure that's never happened to anyone here.

Thanks Ronnie for the sheets... Seriously appreciated..

rkr1958 wrote: Sat Aug 17, 2024 4:53 pm Also, moving forward I want to resurrect MWIF Magic to start including functionality for speeding up and improving game play.

That would be greatly appreciated!

rkr1958 wrote: Sat Aug 17, 2024 4:53 pm I think in conjunction with naval assist, I'm going to add Guard Banner Armies (GBA) to MAGIC. That is, basically being able to use MAGIC to play with the GBA optional rules.

An interesting optional, which adds actually fun to play the game and which would have been easy to fully implement into the game a long time ago.

Falken wrote: Sun Aug 18, 2024 5:05 am Thanks Ronnie for the sheets... Seriously appreciated..

Also, I've attached the spreadsheet I used to generate the end of game (EOG) summary tables. I plan to include these table in my next version of my AAR spreadsheet. For now they're separate and I had to copy and paste from the AAR to the EOG spreadsheet to generate the tables.

EOG Spreadsheet.