An Explanation for Uncle Wang's Damage Formula
Sept 10, 2019 10:43:47 GMT
andrei, Nobunaga Oda, and 4 more like this
Post by kanue on Sept 10, 2019 10:43:47 GMT
I create this thread to share the findings from my little experiment. The objective is to comprehensively look into factors that impact the panel attack (the attack that appears on the unit info interface) and how. The formula has already been given in this thread european-war-4.boards.net/thread/11325/ and can be summarized as follow,
Panel Attack = Basic Attack * Formation Coefficient * Morale Bonus * Buff Effect III + Weapon Props + Generals Individual Arms Ability Bonus + Individual Rank Plus + Elementary School Bonus
In this thread, I try to provide the explanations for the formula above.
I remove all of the infantry upgrade from the Training in Senate Mode so that it will no interfere with the calculation. The test unit is Auxiliary Infantry, starred by three of my infantry generals...
General: Vercingetorix
Nick Name: Verc
Rank: General (30%,40%,50%,58%,65%)
Inf Ability Level: 9 (+40)
General: Pompey
Nick Name: Pomp
Rank: General (30%,40%,50%,58%,65%)
Inf Ability Level: 8 (+34)
General: Commander
Nick Name: Comm
Rank: Legatus (25%,35%,45%,53%,-)
Inf Ability Level: 9 (+40)
What I did were to make several combinations of things (e.g. general, formation, morale, aura, %HP, etc...) and record the stat of the unit (Auxiliary Infantry) unit each combination of factors. The results are shown below,
So, here are the keys take away and explanations
1) Damage formula
This shows that the panel attack can be explained by the formula given earlier. However, there are many things that do not work as I thought it would. I will explain each of the factor.
1.1 Formation Coefficient: Let's look at unit without general first (Row 1-3). The Avg Atk (average of max and min) are 34.0, 37.5, and 41.0 for 1, 2, and 3 stacks of formation respectively. That gives the approximate values for formation coefficients as 1.0, 1.1, and 1.2. (without general)
1.2 Bonus from general ability: Since when assign a general to a unit, its attack is affected by both ability and rank, I will compare Verc and Pomp who are at the same rank. This will cancel out the effect from Rank and the difference will be the result of Ability Bonus. Compare Avg Atk of Verc (Row 15-19) to those of Pomp (Row 20-24) and the differences are always 6. This is the same as the difference from bonus from Verc (40) and Pomp (34). So the impact from General Ability Bonus is a flat damage.
1.3 Bonus from general rank: This is what appears when you try to promote the Rank (e.g. General, Marshal, Consul) of your general. Unlike what we originally believe that it would be some extra damage added on top of the normal damage of a unit without general, instead, these numbers will replace the normal formation coefficients. For example, formation coefficients of a unit without general are 1.0, 1.1, and 1.2 (for 1 to 3 stacks), but when I assign a general with a rank of General to that unit, the formation coefficients will change to 1.30, 1.40, 1.50, 1.58, and 1.65 (for 1 to 5 stacks).
So based on what we know from 1.1 to 1.3, the Avg Atk of my Verc on a 3 stacks of Auxiliary Infantry will be...
Base Attack x Formation Coefficient + Ability Bonus
= 34.0 x 1.50 + 40 = 91.0 ;This is consistent with the observation on Row 17
Another example, Pomp on a 5 stacks of Auxiliary Infantry
34.0 x 1.65 + 34 = 90.1 ;This is consistent with the observation on Row 24
1.4 Aura: Aura is a 15% bonus multiplied to base attack so it is not that big deal as we wish. So now, let's add the aura effect to the equation and look at my commander on a double stacks of Auxiliary Infantry (of course, he has infantry aura).
Base Attack x Formation Coefficient x Aura Buff + Ability Bonus
= 34.0 x 1.35 x 1.15 + 40 = 92.7 ;This is consistent with the observation on Row 16
1.5 Morale: Compare units with normal morale (Row 1 - 3) to those with high morale (Row 6 - 8). It can be easily seen that the bonus from high morale is 25% (e.g. 34 x 1.25 = 42.5). Now, add the morale effect of morale to the equation and see Verc on a double stacks of Auxiliary Infantry with high morale but no aura buff.
Base Attack x Formation Coefficient x Morale x Aura Buff + Ability Bonus
= 34.0 x 1.40 x 1.25 x 1.00 + 40 = 99.5 ;This is consistent with the observation on Row 30
1.6 Conclusion: I do not include the effect of items, unit rank, and upgrade because these effects should be straight forward and it will be too much of work. This experiment basically confirms the formula given by uncle wangchengxy . But with a better understanding and explanation, I hope we now have a clearer perception on the benefit of each factor. Still keep in mind that this is only panel attack, not the net output. One major factor that greatly impacts the output is critical mechanism (crit rate and bonus) which I hope we will have more info soon.
2) Unit HP
2.1 Max HP: This is straight forward. The unit max HP is just a multiplication of HP at one stack and number of stack.
2.2 Effect of HP on damage: I had my units take some damage and record the panel attack of those units (Row 10 - 14). The second column from the right is the percentage of HP from max HP and the rightmost column shows the percentage of HP left on the last HP globe (the right most bubble that appears under the unit). What I find is that if the HP of the last globe is more than 50%, the unit still has the same panel attack as full HP (Row 10 and 13). But if the HP of the last globe is less than 50% then the unit panel attack is reduced to the previous formation coefficient (Row 11, 12, and 14). For example, a unit with 2.7 globes (70% on the last globe) has formation coefficient of 1.2 (3 stacks) while another unit with 2.4 globes (40% on the last globe) has formation coefficient of 1.1 (2 stacks) even though it still is in a 3 stacks formation.
3) Implications
3.1: The marginal effect of formation coefficient for higher stack is not that big. For it might be a good idea not to waste time to get your general up to 4 or 5 stacks, as long as you are confident that the general HP is not too low and at risk of being killed.
3.2: Damage bonus from Rank is very small compared to Ability Bonus. This is why cheap generals with max ability perform pretty well.
3.3 Since the effect of formation coefficient (and damage reduction from injury) is not that big, the same goes for Verc's Fearless talent. But his bad *Auto corrected* look can compensate for his not so bad *Auto corrected* talent.
Panel Attack = Basic Attack * Formation Coefficient * Morale Bonus * Buff Effect III + Weapon Props + Generals Individual Arms Ability Bonus + Individual Rank Plus + Elementary School Bonus
In this thread, I try to provide the explanations for the formula above.
I remove all of the infantry upgrade from the Training in Senate Mode so that it will no interfere with the calculation. The test unit is Auxiliary Infantry, starred by three of my infantry generals...
General: Vercingetorix
Nick Name: Verc
Rank: General (30%,40%,50%,58%,65%)
Inf Ability Level: 9 (+40)
General: Pompey
Nick Name: Pomp
Rank: General (30%,40%,50%,58%,65%)
Inf Ability Level: 8 (+34)
General: Commander
Nick Name: Comm
Rank: Legatus (25%,35%,45%,53%,-)
Inf Ability Level: 9 (+40)
What I did were to make several combinations of things (e.g. general, formation, morale, aura, %HP, etc...) and record the stat of the unit (Auxiliary Infantry) unit each combination of factors. The results are shown below,
So, here are the keys take away and explanations
1) Damage formula
This shows that the panel attack can be explained by the formula given earlier. However, there are many things that do not work as I thought it would. I will explain each of the factor.
1.1 Formation Coefficient: Let's look at unit without general first (Row 1-3). The Avg Atk (average of max and min) are 34.0, 37.5, and 41.0 for 1, 2, and 3 stacks of formation respectively. That gives the approximate values for formation coefficients as 1.0, 1.1, and 1.2. (without general)
1.2 Bonus from general ability: Since when assign a general to a unit, its attack is affected by both ability and rank, I will compare Verc and Pomp who are at the same rank. This will cancel out the effect from Rank and the difference will be the result of Ability Bonus. Compare Avg Atk of Verc (Row 15-19) to those of Pomp (Row 20-24) and the differences are always 6. This is the same as the difference from bonus from Verc (40) and Pomp (34). So the impact from General Ability Bonus is a flat damage.
1.3 Bonus from general rank: This is what appears when you try to promote the Rank (e.g. General, Marshal, Consul) of your general. Unlike what we originally believe that it would be some extra damage added on top of the normal damage of a unit without general, instead, these numbers will replace the normal formation coefficients. For example, formation coefficients of a unit without general are 1.0, 1.1, and 1.2 (for 1 to 3 stacks), but when I assign a general with a rank of General to that unit, the formation coefficients will change to 1.30, 1.40, 1.50, 1.58, and 1.65 (for 1 to 5 stacks).
So based on what we know from 1.1 to 1.3, the Avg Atk of my Verc on a 3 stacks of Auxiliary Infantry will be...
Base Attack x Formation Coefficient + Ability Bonus
= 34.0 x 1.50 + 40 = 91.0 ;This is consistent with the observation on Row 17
Another example, Pomp on a 5 stacks of Auxiliary Infantry
34.0 x 1.65 + 34 = 90.1 ;This is consistent with the observation on Row 24
1.4 Aura: Aura is a 15% bonus multiplied to base attack so it is not that big deal as we wish. So now, let's add the aura effect to the equation and look at my commander on a double stacks of Auxiliary Infantry (of course, he has infantry aura).
Base Attack x Formation Coefficient x Aura Buff + Ability Bonus
= 34.0 x 1.35 x 1.15 + 40 = 92.7 ;This is consistent with the observation on Row 16
1.5 Morale: Compare units with normal morale (Row 1 - 3) to those with high morale (Row 6 - 8). It can be easily seen that the bonus from high morale is 25% (e.g. 34 x 1.25 = 42.5). Now, add the morale effect of morale to the equation and see Verc on a double stacks of Auxiliary Infantry with high morale but no aura buff.
Base Attack x Formation Coefficient x Morale x Aura Buff + Ability Bonus
= 34.0 x 1.40 x 1.25 x 1.00 + 40 = 99.5 ;This is consistent with the observation on Row 30
1.6 Conclusion: I do not include the effect of items, unit rank, and upgrade because these effects should be straight forward and it will be too much of work. This experiment basically confirms the formula given by uncle wangchengxy . But with a better understanding and explanation, I hope we now have a clearer perception on the benefit of each factor. Still keep in mind that this is only panel attack, not the net output. One major factor that greatly impacts the output is critical mechanism (crit rate and bonus) which I hope we will have more info soon.
2) Unit HP
2.1 Max HP: This is straight forward. The unit max HP is just a multiplication of HP at one stack and number of stack.
2.2 Effect of HP on damage: I had my units take some damage and record the panel attack of those units (Row 10 - 14). The second column from the right is the percentage of HP from max HP and the rightmost column shows the percentage of HP left on the last HP globe (the right most bubble that appears under the unit). What I find is that if the HP of the last globe is more than 50%, the unit still has the same panel attack as full HP (Row 10 and 13). But if the HP of the last globe is less than 50% then the unit panel attack is reduced to the previous formation coefficient (Row 11, 12, and 14). For example, a unit with 2.7 globes (70% on the last globe) has formation coefficient of 1.2 (3 stacks) while another unit with 2.4 globes (40% on the last globe) has formation coefficient of 1.1 (2 stacks) even though it still is in a 3 stacks formation.
3) Implications
3.1: The marginal effect of formation coefficient for higher stack is not that big. For it might be a good idea not to waste time to get your general up to 4 or 5 stacks, as long as you are confident that the general HP is not too low and at risk of being killed.
3.2: Damage bonus from Rank is very small compared to Ability Bonus. This is why cheap generals with max ability perform pretty well.
3.3 Since the effect of formation coefficient (and damage reduction from injury) is not that big, the same goes for Verc's Fearless talent. But his bad *Auto corrected* look can compensate for his not so bad *Auto corrected* talent.
