SBDE equations

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    • SBDE equations

      Hey guys. I figured out the equation for State-based damage efficiency (SBDE) for stacks at max efficiency (lower stack sizes). The SBDE starts at 40 for morale 0 and goes linearly to 100 with slope 0.6. The equation is 40 + 0.6 * morale. Below is a plot showing the equation vs real data. This holds for all the unit types I have looked at. Next I would like to figure out the equation(s) for the higher stacks, which I could do myself but all my troops are spread out too much to get big stacks. I think we could figure this out quickly if people can post some info here. If you could post in this format on one line it would be most useful:

      troop_type troop_count current_hit_points max_hit_points SBDE



      Update: For non-optimal see this: non optimal stack sizes.

      The post was edited 5 times, last by DxC ().

    • troop_type troop_count current_hit_points max_hit_points SBDE
      Battleships, 4, 75HP, 75HP, 90%
      Battleships, 3, 75HP, 75HP, 100%
      Railgun, 4, 20HP, 20HP, 90%
      Railgun, 3, 75HP, 75HP, 100%
      Destroyer, 8, 30HP, 30HP, 91%
      Destroyer, 7, 30HP, 30HP, 100%

      Just what I had on hand.
      Small units like destroyers follow the same/similar pattern I think.
      Kalantigos
      Master Chief Petty Officer.
      Game Moderator
      EN Community Support
      Bytro Labs | Call of War
    • Thank you Kalantigos. This gives one data point, that at 100 percent morale the SBDE is 90. Charles Mallahan Jr gave me one other data point for morale 98.4375%. From these 2 points I can estimate that the intercept is around 25 and the slope around 0.65. If I could get a few more data points for large stacks and lower morale, we could unambiguously figure out equation.
    • So it looks like the SBDE does drop cumulatively with increasing troops after you reach the threshold. I did some tests with infantry and from 1-8 units it is 100% efficient. After that it drops approximately 3.8% per unit added. In the plot below the x-axis is the (troop count) - (highest optimal troop count), so for infantry with 10 troops the x value would be 10-8=2. The y-axis is the percentage relative to optimal stack size, so at x=0, y=100 and it drops from there. It's a bit confusing but these are not absolute SBDE values on the y-axis but SBDE relative to optimal. Anyway, the take home is that after the optimal threshold there is a steep drop as you add more troops. According to this the SBDE will drop to near zero after about 25 infantry. We need to test this with higher stack sizes to confirm. We also need to test this on different unit types and at different levels of morale to see if it holds.

      click for plot
    • Tactical bombers. all full health. 25health each.
      5 TB 100%
      6 TB 93%
      7 TB 89%
      8 TB 81%
      9 TB 73%
      10 TB 67%
      11 TB 61%
      12 TB 7%
      13 TB 53%
      14 TB 49%


      Medium tanks, full health.
      5 MT 100%
      6 MT 93%
      7 MT 89%
      8 MT 81%
      9 MT 76%
      10 MT 69%
      11 MT 64%
      12 MT 59%
      13 MT 55%
      14 MT 51%
      15 MT 48%


      Heavy tanks, full health. Same results as for the medium tanks.
      5 HT 100%
      6 HT 93%
      7 HT 89%
      8 HT 81%
      9 HT 76%
      10 HT 69%


      Mechanised infantery full health
      6 MI 100% (don't have more at 1 place), but noteworthy IMHO since 6 have 100%.


      Submarines, full health.
      8 S 100%
      9 S 92%
      10 S 84%
      11 S 77%
      12 S 71%
    • I plotted the SBDE vs units from AzKazan's and my data here. A few observations are that it seems like infantry lose SBDE a bit more slowly than tanks/TAC and subs lose it a bit more quickly. Also, if you look at the curves where the troop counts go above about 12 they seem to not drop as fast (seems like it might be happening for subs/inf also also). This suggests that the SBDE may flatten out to some minimum value (40 ?) as troop count goes up.
    • I've been developing a spreadsheet over the last few weeks to go over exactly this data, so I'll submit what I have so far. All units involved were full health.

      Unit 1, unit 1 level,/unit 2, unit 2 level/etc

      Infantry, 5/Commandos, 1

      1-8 - 100%
      9 - 96%
      10 - 92%
      11 - 89%
      12 - 84%
      13 - 80%
      14 - 86%
      15 - 72%
      16 - 68%
      17 - 65%
      18 - 61%
      19 - 58%
      20 - 56%
      21 - 53%
      22 - 51%
      23 - 49%
      24 - 47%
      25 - 46%

      Medium Tanks, 3 (picking up at 16 since my data is the same as Azkazan's)
      16 - 45%
      17 - 43%
      18 - 41%
      19 - 39%
      20 - 37%
      21 - 36%
      22 - 34%
      23 - 33%
      24 - 32%
      25 - 31%

      SP Artillery, 3
      1-6 - 100%
      7 - 94%
      8 - 90%
      9 - 83%
      10 - 78%
      11 - 72%

      Battleship, 6
      1-3 - 100%
      4 - 90%
      5 - 78%
      6 - 67%
      7 - 58%
      8 - 51%
      9 - 46%
      10 - 42%
      11 - 39%
      12 - 36%
      13 - 33%
      14 - 31%
      15 - 30%
      16 - 28%
      17 - 27%
      18 - 26%
      19 - 24%
      20 - 23%

      I'll try to add more as I get different stacks of units built up. I find it interesting that in some very rare cases (Infantry stack from 20 to 21 for example) that adding a unit actually DECREASES the total damage output of the stack after accounting for SBDE.
    • Javman wrote:

      I find it interesting that in some very rare cases (Infantry stack from 20 to 21 for example) that adding a unit actually DECREASES the total damage output of the stack after accounting for SBDE.
      That does seem true in that case, but I'd imagine if the decimals were included it might not, but it's possible. I'll check these out more later, thanks! Today, I noticed that 37 LT lvl.3 at 95% morale gave SBDE:23. Before I thought there might be a lower limit but maybe not. BTW, anyone wanting to do their own tabulations, you don't have to march your troops to the same place. You can just ctrl-click them into a group and look at the stats for the group.
    • Here is an updated SBDE as a function of troop count plot with Javman's data included. As suspected, the curves do flatten out as the counts get large. Javman, I excluded your infantry 14 point because it seemed like it might have been a typo. Maybe 76 instead of 86? Also, note that the data for light tanks and interceptors are not at 100% morale. I suspect that if they were checked with 100% morale, the light tanks would superimpose with SP artillery and the interceptors would superimpose with TAC, medium tank and heavy tank. The consistent "wiggle" along counts 5-8 for INT, TAC, M & H tanks is probably because of rounding the SBDE to the nearest integer. The same wiggle can be seen for the other units, except for subs and battleships.

      The post was edited 1 time, last by DxC ().

    • First let me commend you all for sharing this information. Some would keep it to themselves to garner an advantage over others.
      You show a real appreciation for the 'art' of war gaming and the community involved here.

      Now I am no math genius, but I occasionally have a 'good' idea.

      What I propose is a 'TEST' game.. where each nation concentrates on a few units, sets a common rally point for various battles and shares all info with other board members.

      Obviously UK does fleets best, and perhaps air?

      mainland can opt for various units and free discussion about who/what/where/when is encouraged...rather like appointmetns for battles so that there is no surprises.

      Is this a good idea? New to the game, liking it very much so far and pleased with the community in general, (although there seems to be a few folks with multiple accounts..win at any cost much?) i would like to know if it is possible to set up the tech levels to any degree when starting a game? this may help as far as having an early, mid and late game testing boards.
      let me know what you all think, and once again many thanks for all of your hard work and dedication.

      regards.
    • Strategos420 wrote:



      What I propose is a 'TEST' game.. where each nation concentrates on a few units, sets a common rally point for various battles and shares all info with other board members.

      Obviously UK does fleets best, and perhaps air?

      mainland can opt for various units and free discussion about who/what/where/when is encouraged...rather like appointments for battles so that there is no surprises.

      Is this a good idea? New to the game, liking it very much so far and pleased with the community in general, (although there seems to be a few folks with multiple accounts..win at any cost much?) i would like to know if it is possible to set up the tech levels to any degree when starting a game? this may help as far as having an early, mid and late game testing boards.
      let me know what you all think, and once again many thanks for all of your hard work and dedication.
      I think that would be the best way to get the data for all units over the shortest period of time, yes. I would also gladly join such a "game." Currently I have to run all of my opponents out of town as quickly as possible to secure my current "test" environments.

      I'd be particularly interested in the fixed battle implementation, as I have been trying to gather data on the battle mechanics but the scales of each battle have been relatively minor (and lopsided) so far.

      As far as setting up tech levels, gold and time are the only ways I know of doing this (if I am mistaken please correct me), and as a non-gold purchaser I would be unable to assist for end game units if that was the plan.
    • my apologies if it seems like am hijacking the thread. maybe we should start one for the "TEST BOARD"?
      I am not sure what protocols/conventions are followed here yet and I did not mean to cause any offense.
      I just thought of the idea and posted since it seemed to tie into the data collection. Some guidance from some of you "old timers" on these forums would also be appreciated. I am not sure if there is a casual approach to subjects or if the 'rules lawyer' comes out when a thread tends to stray off topic.

      please advise.
      regards.