Sagacious' Unit Ranking System

		hb (100% + m)
h	=
		100%

Where:

h	=	The total number of hit points that a given unit possesses after modifiers are taken into account
hb	=	The base number of hit points that a given unit possesses
m	=	The percentage by which the sum of all modifiers to a unit increases its hit points

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate the rate at which a given unit is damaged by an unspecified source.

Consider the graph given below.


In the graph above, we observe that, at t = 0 seconds, an unspecified unit is said to have 100 hit points. We then observe that, at t = 10 seconds, the unit is said to have 0 hit points. By calculating the quotient of these differences in time and damage, we can determine the rate at which this unit was damaged over time, as demonstrated below.


In this case, the unit sustained 10 damage every second for a period of 10 seconds, resulting in a total of 100 damage.

You'll be pleased to know that such computations are not entirely necessary, as the amount of damage dealt by a given unit per second is conveniently listed on the corresponding unit table for that unit.

Modifiers to Damage

Like many properties, the amount of damage that a given unit inflicts can be modified in a variety of different ways. The equation used to determine the amount of damage that a given unit will inflict after modifiers are taken into account is given below.


I will demonstrate the proper use of this equation in the following example, where a unit that inflicts 10 damage/second receives a 20% bonus from one research upgrade and a 5% bonus from another.

Because m is defined as the percentage by which the sum of all modifiers to a unit increases its output of damage over time, we will have to solve for the value of m by calculating the sum of each bonus that the unit in question receives before we can solve for d. The unit is said to receive a bonus of 20% and 5%, so the sum of these modifiers will be equal to m, as demonstrated below.


Once the value of m has been found, it can be substituted directly into the equation used to determine the total output of damage that a given unit inflicts over time after modifiers are taken into account, as demonstrated below.


In this case, the unit in question received a total bonus of 25%, which resulted in a final output of 12.5 damage/second.

While all modifiers to damage can be accounted for in this manner, you'll be pleased to know that such computations are not entirely necessary, as the total output of damage that a given unit inflicts over time after modifiers are taken into account is conveniently listed on the corresponding unit table for that unit. As an added bonus, each contributing modifier is listed on the unit table as well.

While the amount of damage that a given unit inflicts is of great importance, another important variable to consider is the type of damage inflicted as well, as certain types of damage are less effective against certain targets and more effective against others. In Age of Mythology, there are essentially three types of damage. They include: crush damage, pierce damage, and hack damage. For each of these types of damage, the amount inflicted is dependent upon the properties of the target to which the type of damage is applied, as certain targets are more resistant to one type of damage than they are to another. This leads us to the next important topic in this section: armor.

Armor

Armor is a measure of how resistant a given target is to a given type of damage, so it can be thought of as a modifier to the damage that it sustains, and thus, an external modifier to the damage that the opposing source inflicts. Units have an armor rating for each of the three types of damage previously discussed, which are usually represented as a percentage on the unit table. The equation given below can be used to calculate the modifier to an opposing source of damage that results from a given units armor rating against a particular type of damage.


Note that it is essential that the unit’s armor correspond to the type of damage inflicted, otherwise, your calculations will be incorrect.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate the modifier resulting from a unit that is 35% resistant to hack damage.

Because a_b is defined as the base percentage by which the designated type of damage is reduced, it can be substituted directly into the equation used to determine the resulting modifier for the source of incoming damage, as demonstrated below.


In this case, the unit in question was 35% resistant to hack damage, which means that the resulting modifier to all external sources of this type of damage will be equal to 0.35 when applied to this unit. Note that this does not mean that the incoming damage will be multiplied by this amount, rather, this amount will be subtracted from one, and the resulting difference will then be multiplied by the source of incoming damage in order to determine the amount of damage sustained.

Modifiers to Armor

Like many properties, the percentage of armor, and, consequently, its resulting modifier to damage, can be altered in a variety of different ways. The equation used to determine the final value of the modifier to the damage that a given unit sustains, after all modifiers to its armor are taken into account, is given below.


I will demonstrate the proper use of this equation in the following example, where I will use it to calculate the final value of the modifier resulting from a unit that is 35% resistant to hack damage that receives a 5% bonus from one research upgrade and a 5% bonus from another.

Because m is defined as the percentage by which the sum of all modifiers to a unit increases its armor to a particular type of damage, we will have to solve for the value of m by calculating the sum of each bonus that the unit in question receives before we can solve for a. The unit is said to receive a bonus of 5% and 5%, so the sum of these modifiers will be equal to m, as demonstrated below.


Once the value of m has been found, it can be substituted directly into the equation used to determine the value of the final modifier to the damage that a given unit will sustain after all modifiers to a unit’s armor are taken into account, as demonstrated below.


In this case, the unit in question received a total bonus of 10% to its armor, which resulted in a final modifier of 0.385.

While all modifiers to a units armor can be accounted for in this manner, you'll be pleased to know that such computations are not entirely necessary, as the total percentage by which a given type of damage is reduced after modifiers are taken into account is conveniently listed on the corresponding unit table for that unit. As an added bonus, each contributing modifier is listed on the unit table as well.

Speed

Speed is the absolute value of any change in the position of an object over any change in time, as illustrated in the figure given below.


I will demonstrate the proper use of this equation in the following example, where I will use it to calculate the rate at which a given unit moved from one position to another over a given period of time.

Consider the graph given below.


In the graph above, we observe that, at t = 0 seconds, an unspecified unit is said to have a position that lies 30 meters away from a designated origin in space. We then observe that, at t = 10 seconds, the unit is said to have a position that lies o meters away from a designated origin in space. By calculating the quotient of these differences in time and position, we can determine the rate at which this unit traveled through space, as demonstrated below.


In this case, the unit traveled at a rate of 3 meters per second for a period of 10 seconds, resulting in a total distance of 30 meters.

You'll be pleased to know that such computations are not entirely necessary, as the speed of a given unit is conveniently listed on the corresponding unit table for that unit.

Modifiers to Speed

Like many properties, the speed of a given unit can be modified in a variety of different ways. The equation used to determine the final speed of a unit after modifiers are taken into account is given below.


I will demonstrate the proper use of this equation in the following example, where a unit that travels at a default speed of 5 meters/second receives a 10% bonus from one research upgrade and a 10% bonus from another.

Because m is defined as the percentage by which the sum of all modifiers to a unit increases its speed, we will have to solve for the value of m by calculating the sum of each bonus that the unit in question receives before we can solve for s. The unit is said to receive a bonus of 10% and 10%, so the sum of these modifiers will be equal to m, as demonstrated below.


Once the value of m has been found, it can be substituted directly into the equation used to determine the final speed of a unit after all modifiers have been taken into account, as demonstrated below.


In this case, the unit in question received a total bonus of 20%, which resulted in a final speed of 6 meters/second.

While all modifiers to speed can be accounted for in this manner, you'll be pleased to know that such computations are not entirely necessary, as the final speed of a unit all after modifiers have been taken into account is conveniently listed on the corresponding unit table for that unit. As an added bonus, each contributing modifier is listed on the unit table as well.

Range

Range is a measure of the maximum distance at which a unit can attack others, and is represented by the variable r. The maximum range that a unit possesses is listed on the corresponding unit table for that unit.

Modifiers to Range

Like many properties, the range that a given unit possesses can be modified in a variety of different ways. The equation used to determine the final value of the range of a given unit after the application of modifiers is given below.


I will demonstrate the proper use of this equation in the following example, where a unit with a range of 10 meters receives a 10% bonus from one research upgrade and a 5% bonus from another.

Because m is defined as the percentage by which the sum of all modifiers to a unit increases its range, we will have to solve for the value of m by calculating the sum of each bonus that the unit in question receives before we can solve for r. The unit is said to receive a bonus of 10% and 5%, so the sum of these modifiers will be equal to m, as demonstrated below.


Once the value of m has been found, it can be substituted directly into the equation used to determine the final value of the range that a given unit possesses after the application of modifiers, as demonstrated below.


In this case, the unit in question received a total bonus of 15%, which resulted in a final range of 11.5 meters.

While all modifiers to range can be accounted for in this manner, you'll be pleased to know that such computations are not entirely necessary, as the final range of a unit after the application of modifiers is taken into account is conveniently listed on the corresponding unit table for that unit. As an added bonus, each contributing modifier is listed on the unit table as well.

The Period of One Killing Cycle

Now that we have discussed the various properties of units that will be used in this system of ranking, we are ready to explore how these properties relate to one another. Although the properties of each unit can vary widely from one another, you will find that the ultimate measure of a military unit's value is its performance in combat – its killing speed. As you will soon see, a unit's killing speed is a reflection of almost every attribute it possesses.

How long would it take for unit A to kill unit B?

The equation below can be used to calculate the time taken for unit A to kill unit B.

It should be noted that this equation does not account for shortcomings in range, nor does it account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A's range is greater than or equal to that of unit B and unit A has an accuracy of 100%. Also, it is essential that unit B's armor correspond to the type of damage inflicted by unit A. Lastly, this equation always assumes that unit A initiates the first attack in the sequence of attacks exchanged between the two units.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how long it would take for one Hoplite (unit A) to kill another Hoplite (unit B). This scenario is illustrated in the image below.


Hoplites possess 115 HP, which means that they can sustain 115 damage before dying. In order to discern how long it would take for one Hoplite (Hoplite A) to kill another Hoplite (Hoplite B), you need to divide the amount of damage that Hoplite B can sustain (115 damage) by the amount that Hoplite A inflicts every second (8 damage/second), as demonstrated below.

However, before dividing, you must account for any modifiers to the damage that Hoplite A inflicts.

Ask yourself the following questions:

• Do Hoplites receive a bonus to the damage they inflict when battling other Hoplites?
• How resistant are Hoplites to the type of damage that other Hoplites inflict?

Hoplites receive no bonus to the damage they inflict when battling other Hoplites. As a result, the modifier to Hoplite A's damage per second will be equal to 1 (the default value of m), as demonstrated below.

Hoplites are 35% resistant to hack attacks, which means, according to the definition of armor previously established, that the modifier by which Hoplite A's damage is reduced will be equal to 0.35, as demonstrated below.

Once you have accounted for any modifiers to the damage that Hoplite A inflicts, you can proceed with the arithmetic.


Note that these are the base statistics for each unit without the inclusion of any upgrades.

One might speculate that a unit A's resilience in combat, that is, its ability to sustain damage, rather than deal it, is also of vital importance. However, doing so would overlook the fact that unit A's survival is actually dependent upon the killing speed of the unit it faces (unit B), and thus, equal to the killing speed of the unit it faces (unit B). As a result, it is by calculating the period of one killing cycle for unit B that we discern the resilience of unit A, which leads us to the next equation used in this system of ranking: the equation for the period of one killing cycle for unit B.

How long would it take for unit B to kill unit A?

The equation below can be used to calculate the time taken for unit B to kill unit A.

It should be noted that this equation does not account for shortcomings in range, nor does it account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit B's range is greater than or equal to that of unit A and unit B has an accuracy of 100%. Also, it is essential that unit A's armor correspond to the type of damage inflicted by unit B. Lastly, this equation always assumes that unit B initiates the first attack in the sequence of attacks exchanged between the two units.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how long it would take for one Hoplite (Hoplite B) to kill another Hoplite (Hoplite A). This scenario is illustrated in the image below.


Hoplites possess 115 HP, which means that they can sustain 115 damage before dying. In order to discern how long it would take for one Hoplite (Hoplite B) to kill another Hoplite (Hoplite A), you need to divide the amount of damage that Hoplite A can sustain (115 damage) by the amount that Hoplite B inflicts every second (8 damage/second), as demonstrated below.

However, before dividing, you must account for any modifiers to the damage that Hoplite B inflicts.

Ask yourself the following questions:

• Do Hoplites receive a bonus to the damage they inflict when battling other Hoplites?
• How resistant are Hoplites to the type of damage that other Hoplites inflict?

Hoplites receive no bonus to the damage they inflict when battling other Hoplites. As a result, the modifier to Hoplite B's damage per second will be equal to 1 (the default value of m), as demonstrated below.

Hoplites are 35% resistant to hack attacks, which means, according to the definition of armor previously established, that the modifier by which Hoplite B's damage is reduced will be equal to 0.35, as demonstrated below.

Once you have accounted for any modifiers to the damage that Hoplite B inflicts, you can proceed with the arithmetic.


Note that these are the base statistics for each unit without the inclusion of any upgrades.

In this case, because unit A and B are both Hoplites, the period of one killing cycle for unit A is equal to that of unit B. Thus, in the event that either of the two Hoplites initiates the first attack, the time taken for Hoplite A to kill Hoplite B will be identical to the time taken for Hoplite B to kill Hoplite A.

As previously stated, these equations do not account for shortcomings in range. Because this system of ranking evaluates units based upon their comparative performance in combat, the advantage of additional range should be taken into account, otherwise, units with ranged attacks will appear less valuable than they actually are. Why? Because, units with superior range can attack units of inferring range while they close ground, which gives them a couple of free shots. This leads us to the next equation used in this system of ranking: the equation for the period of one killing cycle for unit A in the event that its range is less than that of unit B.

How long would it take for unit A to kill unit B if unit B outranges unit A?

The equation below can be used to calculate the time taken for unit A to kill unit B if the range of unit B exceeds that of unit A and unit A be must cover ground before engaging unit B directly in combat.


It should be noted that this equation does not account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A has an accuracy of 100%. Also, it is essential that unit B's armor correspond to the type of damage inflicted by unit A. Lastly, this equation always assumes that unit A initiates the first attack in the sequence of attacks exchanged between the two units.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how long it would take for one Hoplite (unit A) to kill one Toxotes (unit B). This scenario is illustrated in the image given below.

In this example, the Hoplite (unit A) is out-ranged, and consequently, must first cover a certain amount of ground before it can engage the Toxotes (unit B) in direct combat. The question is: How much ground does the Hoplite have to cover?

In order to discern the distance that the Hoplite (unit A) must travel before it can engage in direct combat with the Toxotes (unit B), you must discern both the range of the Hoplite (unit A) and the Toxotes (unit B), and then find the difference between these two values. Toxotai have a range of 15 meters, while Hoplites possess a range of 0.3 meters. This means that the Hoplite must travel a minimum of 14.7 meters before it is within range of attack, as demonstrated in the equation given below.

Once you have discerned the distance that the Hoplite (unit A) must travel before it is within range of attack (14.7 meters), you must determine how long it will take the Hoplite to travel this distance by dividing it by the speed at which Hoplites travel (4.2 meters/second), as demonstrated below.

Toxotai possess 60 HP, which means that they can sustain 60 damage before dying. In order to discern how long it would take for the Hoplite (Unit A) to kill the Toxotes (Unit B) once it was within range of attack, you need to divide the amount of damage that Toxotai can sustain (60 damage) by the amount that the Hoplite inflicts every second (8 damage/second), as demonstrated below.
However, before dividing, you must account for any modifiers to the damage that the Hoplite (unit A) inflicts.

Ask yourself the following questions:

• Do Hoplites receive a bonus to the damage they inflict when battling Toxotai?
• How resistant are Toxotai to the type of damage that Hoplites inflict?

Hoplites receive no bonus to the damage they inflict when battling Toxotai. As a result, the modifier to the Hoplite's damage per second will be equal to 1 (the default value of m), as demonstrated below.

Toxotai are 15% resistant to hack attacks, which means, according to the definition of armor previously established, that the modifier by which the Hoplite's damage is reduced will be equal to 0.15, as demonstrated below.

Once you have accounted for any modifiers to the damage that the Hoplite inflicts, you can proceed with the arithmetic.


Note that these are the base statistics for each unit without the inclusion of any upgrades.

As previously stated, unit A's survival is dependent upon the killing speed of the unit it faces (unit B), and thus, equal to the killing speed of the unit it faces (unit B). As a result, it is by calculating the period of one killing cycle for unit B that we discern the resilience of unit A. Thus, if unit B is out-ranged by unit A, such an advantage must be taken into account because it will extend the period of unit B's killing cycle, rendering unit A more resilient. This leads us to the next equation used in this system of ranking: the equation for the period of one killing cycle for unit B in the event that its range is less than that of unit A.

How long would it take for unit B to kill unit A if unit A outranges unit B?

The equation below can be used to calculate the time taken for unit B to kill unit A if the range of unit A exceeds that of unit B and unit B be must cover ground before engaging unit A directly in combat.


It should be noted that this equation does not account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A has an accuracy of 100%. Also, it is essential that unit B's armor correspond to the type of damage inflicted by unit A. Lastly, this equation always assumes that unit A initiates the first attack in the sequence of attacks exchanged between the two units.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how long it would take for one Hoplite (unit B) to kill one Toxotes (unit A). This scenario is illustrated in the image given below.

In this example, the Hoplite (unit B) is out-ranged, and consequently, must first cover a certain amount of ground before it can engage the Toxotes (unit A) in direct combat. The question is: How much ground does the Hoplite have to cover?

In order to discern the distance that the Hoplite (unit B) must travel before it can engage in direct combat with the Toxotes (unit A), you must discern both the range of the Hoplite (unit B) and the Toxotes (unit A), and then find the difference between these two values. Toxotai have a range of 15 meters, while Hoplites possess a range of 0.3 meters. This means that the Hoplite must travel a minimum of 14.7 meters before it is within range of attack, as demonstrated in the equation given below.

Once you have discerned the distance that the Hoplite (unit B) must travel before it is within range of attack (14.7 meters), you must determine how long it will take the Hoplite to travel this distance by dividing it by the speed at which Hoplites travel (4.2 meters/second), as demonstrated below.

Toxotai possess 60 HP, which means that they can sustain 60 damage before dying. In order to discern how long it would take for the Hoplite (Unit B) to kill the Toxotes (Unit A) once it was within range of attack, you need to divide the amount of damage that Toxotai can sustain (60 damage) by the amount that the Hoplite inflicts every second (8 damage/second), as demonstrated below.
However, before dividing, you must account for any modifiers to the damage that the Hoplite (unit B) inflicts.

Ask yourself the following questions:

• Do Hoplites receive a bonus to the damage they inflict when battling Toxotai?
• How resistant are Toxotai to the type of damage that Hoplites inflict?

Hoplites receive no bonus to the damage they inflict when battling Toxotai. As a result, the modifier to the Hoplite's damage per second will be equal to 1 (the default value of m), as demonstrated below.

Toxotai are 15% resistant to hack attacks, which means, according to the definition of armor previously established, that the modifier by which the Hoplite's damage is reduced is equal to 0.15, as demonstrated below.

Once you have accounted for any modifiers to the damage that the Hoplite inflicts, you can proceed with the arithmetic.


Note that these are the base statistics for each unit without the inclusion of any upgrades.

The Unit Ratio

If we assume that each unit’s output of damage over time is relatively constant, then we can also surmise that each unit will continue to damage the other at a constant rate until one unit kills the other. Following this logic, we can use the period of one killing cycle for unit B to determine not only how long unit A will survive, but also, how much unit A will damage unit B, vice versa. Thus, by calculating the period of one killing cycle for both unit A and B, we can compare the killing speed of each unit and calculate how many of one unit is required in order to kill one of the other.

How many of unit B is required to kill one of unit A?

The equation below can be used to calculate the unit ratio for unit A.


It should be noted that this equation does not account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A and B have an accuracy of 100%. Also, it is essential that each unit’s armor correspond to the type of damage inflicted by the one in opposition. Lastly, this equation always assumes that both units initiate the first attack in the sequence of attacks exchanged between them.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how many Hoplites (unit B) it would take in order to kill one Hoplite (unit A). This scenario is illustrated in the image below.


Recall that, in the previous examples, we determined that the period of one killing cycle for Hoplite A was identical to that of Hoplite B (both were equal to 22.1153846154 seconds). If we calculate the quotient of these two values by substituting them directly into the equation given above, we can calculate the unit ratio for unit A, as demonstrated below.


In this case, since both units are identical, the unit ratio for unit A is equal to 1, indicating that it will kill one of unit B.

In order to calculate the unit ratio for unit B, you need only observe that the value of that ratio will always be inversely proportional to the value of the unit ratio for unit A, and vice versa.

How many of unit A is required to kill one of unit B?

The equations below can be used to calculate the unit ratio for unit B.


It should be noted that this equation does not account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A and B have an accuracy of 100%. Also, it is essential that each unit’s armor correspond to the type of damage inflicted by the one in opposition. Lastly, this equation always assumes that both units initiate the first attack in the sequence of attacks exchanged between them.

I will demonstrate the proper use of each of these equations in the following example, where I will use them to calculate how many Hoplites (unit A) it would take in order to kill one Hoplite (unit B). This scenario is illustrated in the image below.


Recall that, in the previous examples, we determined that the period of one killing cycle for Hoplite B was identical to that of Hoplite A (both were equal to 22.1153846154 seconds). If we calculate the quotient of these two values by substituting them directly into the equation given above, we can calculate the unit ratio for unit B, as demonstrated below.


In this case, since both units are identical, the unit ratio for unit B is equal to that of unit A, even though, by definition, it is inversely proportional to that of unit A, as demonstrated below.


Because both units are identical, it makes sense that the resulting unit ratios for each unit are equal.

As we have observed, the unit ratio is a powerful tool with which we can measure minute discrepancies in the performance of units in melee combat, at least in situations involving the interaction of only two units at any one time (one of unit A and one of unit B). But are such comparisons really meaningful if the frequency of such encounters is scarce? After all, more often than not, several units are interacting at any one time, if not because they were deployed in such a manner, then because they are literally of limited production due to their population cost (a topic we will explore later). It is therefore necessary to include an equation by which we can assess a unit’s performance in combat, even in situations involving the interaction of multiple opposing units.

If we consider that fact that most normal units are only capable of attacking a single target at any one time, and we observe that such units are typically produced in mass quantities, we can recognize that most situations involving the interaction of multiple units only require us the calculate how many units (how many of unit B) are in opposition to the unit that we care to evaluate (unit A). This brings us to the next equation used in this system of ranking: the equation used to calculate the unit ratio for unit A against a variable number of unit B.

How many of unit A is required to kill n number of unit B?

The equation below can be used to calculate the unit ratio for unit A against a variable number of unit B.


It should be noted that this equation does not account for units whose accuracy in combat is less than 100%. As a result, this equation should only be used if unit A and units B have an accuracy of 100%. Also, it is essential that each unit’s armor correspond to the type of damage inflicted by the one in opposition. Lastly, this equation always assumes that all units initiate the first attack in the sequence of attacks exchanged between any number of units.

I will demonstrate the proper use of this equation in the following example, where I will use it to calculate how many Hoplites (units B) that a single Hoplite (unit A) could kill when faced with two in opposition.


In this case, the Hoplite (unit A) is half as effective against two opposing Hoplites (units B) as it was against one, as suggested by the unit ratio of 0.5. This means that, at best, this Hoplite will kill only one half of an opposing Hoplite (units B). This is because the Hoplite (unit A) will live half as long, as two opposing Hoplites (units B) equals two times the output of damage over time, which means that the total damage that it (unit A) will inflict will be equal to half its original amount.

If we were to continue to calculate the unit ratio of a Hoplite (unit A) against increasing numbers of opposing Hoplites (units B), we would observe the trend illustrated in the graph given below.



In the graph above, we observe that, when the number of opposing Hoplites (units B) faced at one time increases, the efficiency of the unit itself (unit A) decreases proportionally to the number of units in opposition (units B). In fact, this trend is also present in other unit ratios as well, not simply those shared between Hoplites. The figure below shows a trend of Hoplites to Hoplites (black) and Hoplites to Spearmen (blue).



SPOILER ALERT!

Whether you can or cannot see how the equation previously discussed could be integrated into another in order to predict the outcome of battles in progress, stay tuned, as I plan on releasing this equation to the general public within the near future.

Ideas to expand upon...

The concepts below are to be reformatted, updated, and expanded upon within the near future.

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Averaging Unit Ratios

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If you calculate a particular unit's unit ratio for every other type of unit, you can assess its average efficiency in combat and compare it to that of other units. For example, let's say I calculated a Hoplite's unit ratio for each of the basic human units accessible to civilizations during the classical age:

Note that these are base statistics for each unit without the inclusion of any upgrades.

Notice how the table above lists the units in order of increasing unit ratio. This allows you to see exactly how much more or less effective Hoplites are against each type of unit in a way that was not possible before. For example, we can observe that Hoplites are least effective against Axemen and most effective against Turma. If you divide these two ratios, you can actually see how much more or less efficient (Hoplites are 81% less effective against Axeman than they are against Turma). You can also use the unit ratio to determine the number of Hoplites you would require in order to be successful, were you to deploy them against a certain unit type.

Another interesting thing you can do is average these ratios to see which civilization Hoplites excel at fighting against.


Note that these are base statistics for each unit without the inclusion of any upgrades.

We can see from these averages that Hoplites are the most effective against Atlanteans and least effective against Greeks.

You can also calculate a units average unit ratio by averaging its unit ratio for all other types of units. For example, the average of all the above statistics would be 1.594542227. This overall average would obviously include many more units, but it could then be compared to other units (which would all have an average unit ratio as well) in a distribution.

The table below displays the unit ratio for each of the basic human units accessible to civilizations during the classical age. Note that each unit's corresponding unit ratios are listed vertically beneath its corresponding picture.

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Unit Ratio Percentiles

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After compiling the various average unit ratios to be found in the game, you could plot them all on a distribution and then assign each unit a percentile, telling you even more about how it compares to all other units in the game.

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Unit Costs

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You can also evaluate units based upon their cost and whether or not they pay for themselves (more information on this is pending). The equations previously discussed regarding your acquisition of resources over time will also be incorporated once all of this is sorted out. You can find the original post pertaining to calculations of your acquisition of resources over time here.

Additional notes...

All of the equations are finished, but some are still in the process of being simplified.

On a side note, all numbers used are rough approximations. Depending on your computer, or your own personal estimations, you will have different variations in answers. For example, your computer may be running slow, and this may cause the unit speeds to decrease. It is also noted that the hills in a game of AoM can cause your units to go faster or slower, depending on the height of the incline.

If this explanation seems incomplete, that's because it is. I have a lot of things to contribute, but I am very limited on time.

Some of the things that are pending include:

- Equations accounting for unit accuracy in combat
- Equations accounting for unit special abilities/attacks
- Revision of the above subject matter and an update of the statistics
- Examples for each equation
- Database of all of the said statistics for each unit