So I did a bit of maths involving the costs to upgrade for every troop type for every tribe
to find that 1 balancing point
I also know that u will either upgrade offense or defense and the values I will now throw forward are based on total army sizes
so there are some things they do not take into consideration
these include
The fact that if u break the army up as what usually happens in raids the bonus added here is taken with them
The fact that the costs here are either for 1 upgrade in the armory (defense) upgrade or blacksmith(offense) upgrade [the costs of both of these are identical to each other], not both so u are not improving ur army by 1.5 % across the board just selecting one.
It gets really complicated if u mix these 2 factors(more combinations) e.g. level 20 defense and lvl 1 off or lvl 2 off....etc
ok firstly I want to say how I did this:
basically I took the total cost to upgrade divided this by the cost of a single troop and u get a certain value that represents how many troops u need to reach 1.5% of ur army force
for example:
the clubswinger costs 250 and its first upgrade costs in total is 2310
so if u go 2310/250 = 9.24 troops will equal 1.5 % of the army when it becomes equal value to upgrade or buy more troops as the costs are balanced at that point
now u take the 9.24 and u multiply it by the numbers u would need to work out 100% of the army in and thats the number of troops that make up 1.5% (9.24) multiplied by 100/1.5.
that means a clubswinger results are as follows for level 1:
9.24*100/1.5 = 616 clubswingers before its worthwhile to upgrade from level 0 to level 1
I used the estimated formula rather than the exponential one simply because I only wanted a good estimate(explains the 1.5 %)
Teutons:
(Clubswinger)
Level number of troops(before upgrade considered)
0 616
1 1072
2 1482.666667
3 1868
4 2232
5 2584
6 2921.333333
7 3252
8 3572
9 3886.666667
10 4194.666667
11 4497.333333
12 4794.666667
13 5088
14 5376
15 5661.333333
16 5942.666667
17 6220
18 6494.666667
19 6768
20 7037.333333
(Spearman)
Level number of troops(before upgrade considered)
0 576.4705882
1 1002.941176
2 1388.235294
3 1748.039216
4 2089.215686
5 2417.647059
6 2734.313725
7 3042.156863
8 3342.156863
9 3637.254902
10 3926.470588
11 4207.843137
12 4487.254902
13 4761.764706
14 5031.372549
15 5297.058824
16 5560.784314
17 5822.54902
18 6077.45098
19 6333.333333
20 6584.313725
(Axeman)
Level number of troops(before upgrade considered)
0 542.8571429
1 944.8979592
2 1306.802721
3 1645.578231
4 1966.666667
5 2276.190476
6 2575.510204
7 2864.62585
8 3148.29932
9 3425.170068
10 3696.598639
11 3963.265306
12 4225.170068
13 4483.673469
14 4738.095238
15 4989.115646
16 5236.734694
17 5481.632653
18 5723.809524
19 5963.265306
20 6201.360544
(Scout)
Level number of troops(before upgrade considered)
0 570.3703704
1 994.4444444
2 1374.074074
3 1728.703704
4 2067.592593
5 2391.666667
6 2705.555556
7 3010.185185
8 3308.333333
9 3600
10 3885.185185
11 4163.888889
12 4438.888889
13 4709.259259
14 4976.851852
15 5240.740741
16 5501.851852
17 5760.185185
18 6013.888889
19 6265.740741
20 6515.740741
(Paladin)
Level number of troops(before upgrade considered)
0 252.0729685
1 438.1426202
2 606.6334992
3 763.5157546
4 912.7694859
5 1056.053068
6 1195.024876
7 1329.684909
8 1460.696517
9 1589.386401
10 1715.422886
11 1839.137645
12 1960.862355
13 2080.597015
14 2198.6733
15 2314.759536
16 2430.182421
17 2543.615257
18 2655.721393
19 2767.495854
20 2877.280265
(Teutonic Knight)
Level number of troops(before upgrade considered)
0 163.715847
1 285.0273224
2 394.5355191
3 496.3934426
4 593.2240437
5 686.3387978
6 776.8306011
7 864.2622951
8 949.2896175
9 1032.786885
10 1114.754098
11 1195.191257
12 1274.098361
13 1351.912568
14 1428.852459
15 1504.480874
16 1579.234973
17 1653.114754
18 1726.120219
19 1798.251366
20 1869.945355
(Ram)
Level number of troops(before upgrade considered)
0 162.7906977
1 283.3333333
2 391.8604651
3 493.6046512
4 589.9224806
5 682.751938
6 772.2868217
7 859.1085271
8 944.1860465
9 1027.131783
10 1108.527132
11 1188.565891
12 1267.054264
13 1344.379845
14 1420.736434
15 1495.930233
16 1570.348837
17 1643.992248
18 1716.472868
19 1788.372093
20 1859.496124
(Catapult)
Level number of troops(before upgrade considered)
0 79.95169082
1 139.2512077
2 192.7536232
3 242.7536232
4 290.0966184
5 335.5072464
6 379.7101449
7 422.3429952
8 464.1304348
9 504.9516908
10 545.0483092
11 584.178744
12 622.826087
13 660.9903382
14 698.5507246
15 735.5072464
16 771.9806763
17 808.0917874
18 843.7198068
19 879.2270531
20 914.1304348
Romans:
(Legionnaire)
Level troops needed (before upgrade is considered)
0 551.5151515
1 959.8484848
2 1328.030303
3 1671.969697
4 1998.484848
5 2312.121212
6 2615.909091
7 2909.848485
8 3197.727273
9 3479.545455
10 3755.30303
11 4025.757576
12 4292.424242
13 4554.545455
14 4812.878788
15 5068.181818
16 5319.69697
17 5568.939394
18 5815.151515
19 6059.090909
20 6300
(Praetorian)
Level troops needed (before upgrade is considered)
0 547.826087
1 954.3478261
2 1318.84058
3 1660.144928
4 1985.507246
5 2297.101449
6 2598.550725
7 2890.57971
8 3177.536232
9 3457.246377
10 3731.15942
11 3999.275362
12 4263.768116
13 4523.913043
14 4781.15942
15 5034.057971
16 5284.782609
17 5532.608696
18 5776.811594
19 6018.115942
20 6257.971014
(Imperian)
Level troops needed (before upgrade is considered)
0 528.8888889
1 921.1111111
2 1273.888889
3 1603.333333
4 1916.111111
5 2217.222222
6 2508.333333
7 2791.666667
8 3067.222222
9 3337.222222
10 3601.666667
11 3860.555556
12 4116.666667
13 4367.222222
14 4615.555556
15 4860
16 5102.222222
17 5340.555556
18 5576.666667
19 5810
20 6041.111111
(Equites Legati)
Level troops needed (before upgrade is considered)
0 285.1851852
1 496.2962963
2 687.037037
3 863.8888889
4 1032.407407
5 1196.296296
6 1352.777778
7 1504.62963
8 1653.703704
9 1800
10 1942.592593
11 2081.481481
12 2220.37037
13 2355.555556
14 2489.814815
15 2619.444444
16 2750.925926
17 2879.62963
18 3006.481481
19 3132.407407
20 3258.333333
(Equites Imperatoris)
Level troops needed (before upgrade is considered)
0 164.3026005
1 286.0520095
2 395.9810875
3 498.3451537
4 595.5082742
5 689.1252955
6 779.9054374
7 867.8486998
8 953.427896
9 1037.352246
10 1119.385343
11 1200.236407
12 1279.432624
13 1357.446809
14 1434.515366
15 1510.638298
16 1585.579196
17 1660.047281
18 1733.333333
19 1805.910165
20 1877.777778
(Equites Caesaris)
Level troops needed (before upgrade is considered)
0 121.0445469
1 210.7526882
2 291.2442396
3 366.6666667
4 438.4024578
5 507.2196621
6 573.8863287
7 638.5560676
8 701.5360983
9 763.2872504
10 823.655914
11 883.1029186
12 941.4746544
13 998.9247312
14 1055.913978
15 1111.520737
16 1166.820276
17 1221.351767
18 1275.576037
19 1329.032258
20 1381.87404
(Battering Ram)
Level troops needed (before upgrade is considered)
0 162.4772313
1 282.5136612
2 391.0746812
3 491.9854281
4 588.3424408
5 680.6921676
6 770.1275046
7 857.0127505
8 941.5300546
9 1024.225865
10 1105.464481
11 1185.245902
12 1263.570128
13 1340.801457
14 1416.939891
15 1491.985428
16 1566.120219
17 1639.526412
18 1712.021858
19 1783.606557
20 1854.644809
(Fire Catapult)
Level troops needed (before upgrade is considered)
0 79.82162765
1 139.0189521
2 192.3076923
3 242.1404682
4 289.4091416
5 334.7826087
6 378.8182832
7 421.516165
8 463.2107023
9 503.9018952
10 543.812709
11 583.0546265
12 621.6276477
13 659.4202899
14 696.9899666
15 733.8907469
16 770.3455964
17 806.3545151
18 841.9175028
19 877.2575251
20 912.1516165
Gauls:
(Phalanx)
Level number of troops(before upgrade considered)
0 585.1851852
1 1020.10582
2 1408.465608
3 1773.544974
4 2120.634921
5 2453.968254
6 2775.661376
7 3088.888889
8 3394.708995
9 3693.121693
10 3986.243386
11 4271.957672
12 4554.497354
13 4831.746032
14 5106.878307
15 5376.719577
16 5645.502646
17 5908.994709
18 6170.37037
19 6428.571429
20 6683.597884
(Swordsman)
Level number of troops(before upgrade considered)
0 536.4485981
1 933.9563863
2 1291.588785
3 1626.168224
4 1943.925234
5 2249.221184
6 2544.548287
7 2831.152648
8 3111.52648
9 3385.046729
10 3652.959502
11 3916.510903
12 4175.077882
13 4429.906542
14 4680.996885
15 4930.218069
16 5175.077882
17 5416.199377
18 5656.074766
19 5893.457944
20 6127.102804
(Pathfinder)
Level number of troops(before upgrade considered)
0 282.4561404
1 492.1052632
2 680.7017544
3 856.1403509
4 1022.807018
5 1184.210526
6 1339.473684
7 1490.350877
8 1637.719298
9 1783.333333
10 1923.684211
11 2062.280702
12 2198.245614
13 2332.45614
14 2465.789474
15 2594.736842
16 2723.684211
17 2851.754386
18 2978.070175
19 3102.631579
20 3227.192982
(Theutates Thunder)
Level number of troops(before upgrade considered)
0 250.4587156
1 436.0856269
2 603.3639144
3 759.3272171
4 907.6452599
5 1050.152905
6 1188.379205
7 1321.712538
8 1452.599388
9 1580.428135
10 1705.504587
11 1828.440367
12 1949.541284
13 2068.501529
14 2185.626911
15 2301.529052
16 2415.902141
17 2529.357798
18 2640.978593
19 2751.070336
20 2861.16208
(Druidrider)
Level number of troops(before upgrade considered)
0 250.4587156
1 436.0856269
2 603.058104
3 759.3272171
4 907.3394495
5 1050.458716
6 1188.073394
7 1322.018349
8 1452.599388
9 1580.428135
10 1705.504587
11 1828.440367
12 1949.235474
13 2068.501529
14 2185.932722
15 2301.834862
16 2416.207951
17 2529.357798
18 2640.672783
19 2751.681957
20 2860.856269
(Haeduan)
Level number of troops(before upgrade considered)
0 161.8320611
1 281.9338422
2 389.9915182
3 490.754877
4 586.7684478
5 678.7107718
6 767.769296
7 854.4529262
8 938.9312977
9 1021.543681
10 1102.459712
11 1181.849025
12 1259.881255
13 1337.06531
14 1412.722646
15 1487.701442
16 1561.492791
17 1634.605598
18 1707.039864
19 1778.625954
20 1849.194232
(Ram)
Level number of troops(before upgrade considered)
0 162.1291449
1 282.1989529
2 390.4013962
3 491.0994764
4 587.2600349
5 679.5811518
6 768.7609075
7 855.3228621
8 939.965096
9 1022.513089
10 1103.490401
11 1183.071553
12 1261.256545
13 1338.394415
14 1414.485166
15 1489.354276
16 1563.525305
17 1636.649215
18 1708.900524
19 1780.628272
20 1851.308901
(Trebuchet)
Level number of troops(before upgrade considered)
0 79.7657082
1 138.9776358
2 192.0127796
3 241.8530351
4 289.0308839
5 334.3982961
6 378.3812567
7 420.9797657
8 462.6198083
9 503.3013845
10 543.1309904
11 582.3216187
12 620.7667732
13 658.6794462
14 696.1661342
15 733.0138445
16 769.4355698
17 805.5378062
18 841.1075612
19 876.1448349
20 911.1821086
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