Efficiency Calculation and Further Analysis

By Aaron Janusz

**WARNING** A lot of math is about to be discussed.

 

**CAUTION** The information and calculations below contain estimates and assumptions based on experiences with hundreds of Persian Positions. They will provide a very good estimate, but are just that, estimates.

All of the information above will give you a general idea of how to scout and attack or defend the Persian Positions and minimize troop loss. With some additional information and some more detailed calculations you can fine tune your analysis and come up with a very good estimate of exactly how many of a specific troop type is required to defeat a Position. There are tables and spreadsheets available that can be used to assist with this effort, but we will now discuss the principles behind the calculations.

The table below has been compiled from the results of numerous battles with the Persians. It is valid for both Defensive and Offensive Positions and is the total offensive strength of the Persians for Defensive Positions and the average defensive strength of the Persians for Offensive Positions. This is not the strength required to defeat a Position.

As discussed above, the strength required to defeat the Position will depend on the mix of Persian units and what units you send. Note that these are average values and the actual Persian strength may vary up or down a couple of percentage points.

Average Persian Strength by Level

Position Level

Avg Strength

Position Level

Avg Strength

Position Level

Avg Strength

Position Level

Avg Strength

Position Level

Avg Strength

1

80

26

20,000

51

170,700

76

612,400

101

1,496,000

2

100

27

22,600

52

178,400

77

636,600

102

1,551,000

3

150

28

25,000

53

188,000

78

656,000

103

1,594,000

4

180

29

28,100

54

203,000

79

685,600

104

1,672,000

5

220

30

30,900

55

216,000

80

717,600

105

1,689,000

6

300

31

34,000

56

228,000

81

749,100

106

1,780,000

7

500

32

38,000

57

243,000

82

773,500

107

1,816,000

8

700

33

42,800

58

553,900

83

801,600

108

1,878,000

9

1,000

34

46,300

59

270,800

84

825,000

109

1,948,000

10

1,200

35

52,000

60

284,400

85

877,800

110

2,006,000

11

1,400

36

56,500

61

297,900

86

897,200

111

2,042,000

12

2,000

37

61,000

62

313,600

87

927,700

112

2,109,000

13

2,400

38

66,000

63

331,600

88

976,300

113

2,164,000

14

3,000

39

72,000

64

347,200

89

1,007,000

114

2,216,000

15

3,600

40

78,000

65

369,200

90

1,036,000

115

2,323,000

16

4,200

41

84,800

66

392,000

91

1,067,000

116

2,380,000

17

4,800

42

89,800

67

411,100

92

1,101,000

117

2,404,000

18

6,000

43

100,000

68

423,900

93

1,154,000

118

2,491,000

19

7,500

44

105,000

69

445,400

94

1,217,000

119

2,564,000

20

8,700

45

114,200

70

462,300

95

1,257,000

120

2,604,000

21

10,100

46

122,300

71

497,500

96

1,280,000

121

2,684,000

22

11,600

47

130,500

72

508,700

97

1,336,000

122

2,754,000

23

13,600

48

139,600

73

537,000

98

1,358,000

123

2,851,000

24

15,600

49

151,300

74

551,600

99

1,380,000

124

2,929,000

25

17,500

50

159,100

75

579,800

100

1,472,000

125

3,007,000

Offensive Positions

While a scouting report from an Offensive Position will provide a very good idea of the relative strength of the Persians additional information is required for more specific calculations. Using the average strength of the Persians in the Position, we will be able to calculate an estimate remaining Persian strength by class.

Using the scouting report above from the level 57 Offensive Position and the information in the Average Persian Strength by Level table the calculations look like this. Here is what we know:

Average Persian strength of a level 57 Position equals 243,000.

Average Persian strength killed in the scouting mission equals 840.

The ratio of these two numbers is also the ratio of the number of Persian units killed to the total number of Persian units per class. So we can now calculate the estimated number of original Persian units at the Position, an estimated number of Persian units remaining, and an estimated remaining strength per unit class.

Calculations

840 (scouting mission strength) / 243,000 (estimated total strength) = 0.00346 (ratio of units killed per class to the total present)

Using this ratio and the numbers from the scouting report we can calculate the estimated number of total Persians and the estimated number of Persians remaining.

Cavalry – (2 killed in scouting mission / 0.00346) = 578 (total present) – 2 (cavalry killed) = 576 estimated remaining cavalry

Light Infantry – (3 killed / 0.00346) = 867 – 3 = 864 estimated remaining light infantry

Heavy Infantry – (1 killed / 0.00346) = 289 – 1 = 288 estimated remaining heavy infantry

Phalanx – (5 killed / 0.00346) = 1,445 – 5 = 1,440 estimated remaining phalanx

We can now calculate an estimated remaining Persian strength

 

Persian Defensive Strength

Unit

Units

L Inf

H Inf

Phalanx

Cavalry

Avg Defense

Asvaran (Cavalry)

576

46080

46080

46080

138240

69120

Dailamite (Light Infantry)

864

51840

17280

17280

17280

25920

Archer (Heavy Infantry)

288

11520

34560

11520

11520

17280

Immortal (Phalanx)

1440

86400

86400

259200

86400

129600

 

Total

195840

184320

334080

253440

241920

The estimated remaining Persian defensive strength per unit class is now summed at the bottom of the table. If we only send heavy infantry at this Position it will take approximately 184,000 in offensive strength. If we only send phalanx at this Position it will take approximately 334,000 in offensive strength. Remember these are just estimates. We used an average Persian strength and only a small sample size from our scouting report.

If you want better information you could send a second, larger scouting force of heavy infantry; add those numbers killed to the numbers from the first scouting mission; and recalculate a new estimated remaining strength.

It is not efficient to manually calculate these numbers every time. There are spreadsheets that have been developed that easily perform the calculations or you can develop your own spreadsheet using the above methodology. If you don’t want to calculate anything at all, you can just use the average strength spreadsheet and know that if you attack their strength you will need to send more than the average and if you attack their weakness you will need to send less than the average.

Defensive Positions

As mentioned previously, the efficiencies that can be gained from Defensive Positions are not as drastic as from Offensive Positions, but unit loss can be minimized with some additional calculations. Through trial and error the following formula has been developed as a method for estimating the actual average defensive strength of a defensive unit when facing a known Persian force. This calculation will need to be performed for each of your individual units since each unit has a different defensive strength against each unit class.

The first step is to calculate the ratio of the Persian attacking strength for each unit class to the total Persian attacking strength. For the example scouting report above this calculation looks like this.

Persian Offense

Units

Offense

Percentage 

Asvaran (Cavalry)

1316

105280

31.4%

Dailamite (Light Infantry)

5276

105520

31.4%

Archer (Heavy Infantry)

1419

56760

16.9%

Immortal (Phalanx)

1134

68040

20.3%

Total

9145

335600

100.0%

The percentage for each class is then multiplied by the defensive strength for each unit class for each individual troop type. Using the base stats for M Peltast, the calculation would look like this.

 

 

Mounted Peltast

Persian Offense

Persian Percentage

Base Stats

Adjusted

Stats

Asvaran (Cavalry)

31.4%

725

227.4

Dailamite (Light Infantry)

31.4%

400

125.8

Archer (Heavy Infantry)

16.9%

500

84.6

Immortal (Phalanx)

20.3%

725

147.0

Total

100.0%

587.5 (Avg)

584.8

Based on this calculation, the M Peltast is slightly less efficient in the Position – would defend with a strength of 584.8 versus the base average of 587.5. With a Persian offensive strength of 335,600, it should take approximately (335,600 / 584.5) = 575 M Peltast to defeat this Position.

You can complete the same calculation for each of your defensive units to calculate an estimate of how many of each unit it will take to defeat the Position. This is a lot of calculating. Again, you can create your own spreadsheet to perform the calculations or there are spreadsheets available for use.

 

 

This article was written by Aaron Janusz, who granted permission for it to be posted on Plarium.com. Any thoughts or views expressed herein are the player's own, and do not necessarily reflect the views of Plarium Global.

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