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Character "Overall Power" Calculation Factors.


Alondite
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I posted this in General FE, but I thought it would be useful here too, so I'm posting it here.

Ok, so I was trying to make a balanced edit of Blazing Sword and I ran into a roadblock when I came to the conclusion that all stats are not equal. Luck is not as important as Strength, there's just no way. So when trying to decide how to balance character stats/growths I decided to do this:

Find out exactly how much each stat effects the amount of damage done or reduced (or in the case of luck and speed, both) in a round of battle. HP calculation was a little bit different (and it took me even longer to get it where it seemed right), and Resistance was based on the percentage of magic users compared to non-magic users.

This is what I came up with:

*note* I'm not claiming this to be perfect. Most of the calculations I did were fairly simple, and I'm decent with math, but certainly no math whiz. This is only my first set of calculations that I'm using for the first build of my game.

*note* The actual numbers don't matter. What matters is how they are proportionally to the other stats.

*note* HP is an average. It effects the percentage of total health taken as damage more at lower levels, and less at higher.

*note* Calculating the Magic is dependent on the stats of the characters/enemies in the game, so for the purpose of this post I just left it equal to Strength. Resistance is less important because there are far fewer magic users.

*note* Just because some stats are more important than others doesn't mean that a theoretical character with nothing but Strength and Defense is going to be better. All values are above zero, so all stats are important.

HP Str/Mag Skill Speed Luck Defense Resistance

10.94% 52.50% 21.50% 23.90% 7.09% 52.50% 10.50%

To calculate character overall power, just multiply their stats by the corresponding values, and add them together. Again, I'm sure it's not perfect, but it should be close. This could also be useful in tier debates.

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I posted this in General FE, but I thought it would be useful here too, so I'm posting it here.

Ok, so I was trying to make a balanced edit of Blazing Sword and I ran into a roadblock when I came to the conclusion that all stats are not equal. Luck is not as important as Strength, there's just no way. So when trying to decide how to balance character stats/growths I decided to do this:

Find out exactly how much each stat effects the amount of damage done or reduced (or in the case of luck and speed, both) in a round of battle. HP calculation was a little bit different (and it took me even longer to get it where it seemed right), and Resistance was based on the percentage of magic users compared to non-magic users.

This is what I came up with:

*note* I'm not claiming this to be perfect. Most of the calculations I did were fairly simple, and I'm decent with math, but certainly no math whiz. This is only my first set of calculations that I'm using for the first build of my game.

*note* The actual numbers don't matter. What matters is how they are proportionally to the other stats.

*note* HP is an average. It effects the percentage of total health taken as damage more at lower levels, and less at higher.

*note* Calculating the Magic is dependent on the stats of the characters/enemies in the game, so for the purpose of this post I just left it equal to Strength. Resistance is less important because there are far fewer magic users.

*note* Just because some stats are more important than others doesn't mean that a theoretical character with nothing but Strength and Defense is going to be better. All values are above zero, so all stats are important.

HP Str/Mag Skill Speed Luck Defense Resistance

10.94% 52.50% 21.50% 23.90% 7.09% 52.50% 10.50%

To calculate character overall power, just multiply their stats by the corresponding values, and add them together. Again, I'm sure it's not perfect, but it should be close. This could also be useful in tier debates.

I have a bit of trouble understanding your calculations. How did you get these numbers?

A quick one by me gives this:

(note that this was done very quickly. I may have missed a lot of stuff, or done some miscalculations, so I added all the stuff I thought here)

Strength: Adds 1 damage. Well, potentially a bit more than that in Path of Radiance and Radiant Dawn, as higher Strength means you can use heavier weapons without a speed slowdown. Still, let's put it at a simple 1.00 damage added. Now, we have to consider how powerful the unit already is. A unit who, on average, normally deals 10 damage gets a 10% bonus. One who deals more gets less of a bonus.

Essentially, it has a 5%-15% damage bonus the majority of the time.

Magic: Ends up for the same as Strength

Skill:

-Adds a 2% displayed hit chance. This will generally mean a bit more than 2% truehit, so I'd guesstimate a 2-3% added damage from this for FE6 and out, and a 2% addition for the ones prior to FE6.

-Adds a 0.5% crit chance. A crit adds 2x the regular damage (totalling up to 3x), so a 1% addition.

- In Path of Radiance and Radiant Dawn (and FE4? I don't quite remember), it increases the chance of a skill occuring. It's generally a 0.5% to 1% addition, and the skills usually tie or outdo a crit. I'd say it gives a 2-3% addition.

So for FE1-FE5 (possibly save FE4), it gives a mere 3% bonus, in FE6-FE8 and FE11, it gives a 4-5% bonus, and in FE9 and FE10 it gives a 6-8% bonus.

Speed:

This is a tricky one.

- Can make your unit double. If so, it's a 100% damage dealt increase to certain units.

- Can make your unit avoid being doubled, if so, it's a 50% damage taken decrease.

- Gives you +2% evasion.

For a unit that already doubles everything, speed is a mere 2% addition evasion addition, and nothing else. For a unit that neither doubles nor gets doubled, it can be incredibly valuable. As in, a 30% damage increase and a 10% damage decrease.

It goes from a 2% evasion to 12% evasion, and 0% damage increase to 30% damage increase in most scenarios. It's ludicrously hard to place this stat somewhere, as it's the stat whose importance differs most from unit to unit.

For a relatively slow unit, one point could make you double 10-20% of the enemies, thus giving you a damage increase in that area.

For a very fast unit, it might merely make you double very fast opponents, giving you a 3-5% bonus, or something, as few units are that quick.

Luck:

- Adds 1% hit rate. Generally means 1% damage dealt addition.

- Adds 1% evasion. Generally means 1% damage taken reduction.

- Adds 1% dodge. Generally means 2% damage taken reduction, but a bit less in cases where the opposing unit already has 0% crit, so say 1.5%.

Total: Roughly 2.5% damage taken reduction and 1% damage dealt addition.

Defence:

- Reduces physical damage taken by 1. Generally, you take less damage than you deal. Most opponents deal damage within the 3-7 range, or something like that. This effectively means that a point of defence gives you a 20% damage taken reduction. This stat actually increases in usefullness the more you get of it, unlike any of the above.

I'd give it around 20% worthiness of damage reduction from physical units. Of course, it has no use on the ~ 1/4th of all units that are magical, so say 15% damage reduction.

Resistance:

- Reduces magical damage taken by 1. Generally, mages deal more damage to you than physical units do. Thus, the decrease in damage from 1 resistance is lower, ala 10-15%. It also works solely on 1/4th of enemy units, so it's in the 3-4% damage reduction area. It's worth a bit more for mages, and it is more valuable the more you get of it.

This gives us the following

Damage done additions:

Speed (slow unit): 10-20%

Strength: 5-15%

Skill: (Tellius): ~ 7%

Skill: (Handhelds): 4-5%

Speed (fast unit): 3-5%

Skill (FE1-FE5): 3%

Luck: 1%

Defence: 0%

Resistance: 0%

Damage taken reductions:

Defence: 15%

Speed: (slow unit): ~ 10%

Resistance: 3-5%

Luck: 2.5%

Speed: (fast unit): 2%

Skill: 0%

Strength: 0%

Magic: 0%

So if I were to put them out of a total of 179 (which you did, not sure about why you picked that number), I'd get

(I'm making averages for the speeds and skills. That's quite silly, so don't trust anything from here on out too much)

For offence:

Strength: 40-100% (70%)

Speed: 20-70% (45%)

Skill: 35%

Luck: 10%

For defence:

Defence: 97%

Speed: 32%

Resistance: 32%

Luck: 15%

If we now chose to put defence and offence as equally important (this too is quite silly), we'd get this:

Silly overall estimation:

Defence: 50%

Speed: 25-50% (38%)

Strength: 20-50% (35%)

Skill: 18%

Resistance: 16%

Luck: 13%

(This totals to 170, and I figured that the last 10% or so would go to hp, as I don't really know how to calculate that. Actually, 10% seems way too much for hp.)

My final numbers became incredibly estimate-y here. They actually do make a fair bit of sense in my head, though, so I'd really love to see your calculations for why Strength more than doubles speed in importance.

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I have a bit of trouble understanding your calculations. How did you get these numbers?

A quick one by me gives this:

(note that this was done very quickly. I may have missed a lot of stuff, or done some miscalculations, so I added all the stuff I thought here)

Strength: Adds 1 damage. Well, potentially a bit more than that in Path of Radiance and Radiant Dawn, as higher Strength means you can use heavier weapons without a speed slowdown. Still, let's put it at a simple 1.00 damage added. Now, we have to consider how powerful the unit already is. A unit who, on average, normally deals 10 damage gets a 10% bonus. One who deals more gets less of a bonus.

Essentially, it has a 5%-15% damage bonus the majority of the time.

Magic: Ends up for the same as Strength

Skill:

-Adds a 2% displayed hit chance. This will generally mean a bit more than 2% truehit, so I'd guesstimate a 2-3% added damage from this for FE6 and out, and a 2% addition for the ones prior to FE6.

-Adds a 0.5% crit chance. A crit adds 2x the regular damage (totalling up to 3x), so a 1% addition.

- In Path of Radiance and Radiant Dawn (and FE4? I don't quite remember), it increases the chance of a skill occuring. It's generally a 0.5% to 1% addition, and the skills usually tie or outdo a crit. I'd say it gives a 2-3% addition.

So for FE1-FE5 (possibly save FE4), it gives a mere 3% bonus, in FE6-FE8 and FE11, it gives a 4-5% bonus, and in FE9 and FE10 it gives a 6-8% bonus.

Speed:

This is a tricky one.

- Can make your unit double. If so, it's a 100% damage dealt increase to certain units.

- Can make your unit avoid being doubled, if so, it's a 50% damage taken decrease.

- Gives you +2% evasion.

For a unit that already doubles everything, speed is a mere 2% addition evasion addition, and nothing else. For a unit that neither doubles nor gets doubled, it can be incredibly valuable. As in, a 30% damage increase and a 10% damage decrease.

It goes from a 2% evasion to 12% evasion, and 0% damage increase to 30% damage increase in most scenarios. It's ludicrously hard to place this stat somewhere, as it's the stat whose importance differs most from unit to unit.

For a relatively slow unit, one point could make you double 10-20% of the enemies, thus giving you a damage increase in that area.

For a very fast unit, it might merely make you double very fast opponents, giving you a 3-5% bonus, or something, as few units are that quick.

Luck:

- Adds 1% hit rate. Generally means 1% damage dealt addition.

- Adds 1% evasion. Generally means 1% damage taken reduction.

- Adds 1% dodge. Generally means 2% damage taken reduction, but a bit less in cases where the opposing unit already has 0% crit, so say 1.5%.

Total: Roughly 2.5% damage taken reduction and 1% damage dealt addition.

Defence:

- Reduces physical damage taken by 1. Generally, you take less damage than you deal. Most opponents deal damage within the 3-7 range, or something like that. This effectively means that a point of defence gives you a 20% damage taken reduction. This stat actually increases in usefullness the more you get of it, unlike any of the above.

I'd give it around 20% worthiness of damage reduction from physical units. Of course, it has no use on the ~ 1/4th of all units that are magical, so say 15% damage reduction.

Resistance:

- Reduces magical damage taken by 1. Generally, mages deal more damage to you than physical units do. Thus, the decrease in damage from 1 resistance is lower, ala 10-15%. It also works solely on 1/4th of enemy units, so it's in the 3-4% damage reduction area. It's worth a bit more for mages, and it is more valuable the more you get of it.

This gives us the following

Damage done additions:

Speed (slow unit): 10-20%

Strength: 5-15%

Skill: (Tellius): ~ 7%

Skill: (Handhelds): 4-5%

Speed (fast unit): 3-5%

Skill (FE1-FE5): 3%

Luck: 1%

Defence: 0%

Resistance: 0%

Damage taken reductions:

Defence: 15%

Speed: (slow unit): ~ 10%

Resistance: 3-5%

Luck: 2.5%

Speed: (fast unit): 2%

Skill: 0%

Strength: 0%

Magic: 0%

So if I were to put them out of a total of 179 (which you did, not sure about why you picked that number), I'd get

(I'm making averages for the speeds and skills. That's quite silly, so don't trust anything from here on out too much)

For offence:

Strength: 40-100% (70%)

Speed: 20-70% (45%)

Skill: 35%

Luck: 10%

For defence:

Defence: 97%

Speed: 32%

Resistance: 32%

Luck: 15%

If we now chose to put defence and offence as equally important (this too is quite silly), we'd get this:

Silly overall estimation:

Defence: 50%

Speed: 25-50% (38%)

Strength: 20-50% (35%)

Skill: 18%

Resistance: 16%

Luck: 13%

(This totals to 170, and I figured that the last 10% or so would go to hp, as I don't really know how to calculate that. Actually, 10% seems way too much for hp.)

My final numbers became incredibly estimate-y here. They actually do make a fair bit of sense in my head, though, so I'd really love to see your calculations for why Strength more than doubles speed in importance.

You are the one and only person who has comprehended what I'm trying to do here. I'll answer your questions instead of responding to your entire post.

My calculations are based on the average damage increase/decrease from adding one point in any stat. Yours differs in that yours is based on the percentage increase in damage, while mine is actual points of damage.

For example, 1 point of strength, on average, translates into .525 (52.5%) additional damage. I used strength values of 5-30, and hit percentages of 0-100 on a table and average all the values.

You basically noted why speed is so low, but using my calculations for points of damage, it ranks as about half as important for strength. Only a 4 point speed difference gives you a damage boost. The multiplier from a difference of 3 speed to 4 is 2 (double damage) but from 0-3 and 4-5 and 5-30 you gain no additional damage. Let's look at two characters who do 1 damage. Let's say they have 5 in each stat. We'll add 25 points of each in increments of 1 point and record damage. We'll also assume they have 100 hit and that the enemy also has 5 speed. Also note that this is just a small snapshot of all the calculations I did. It's purely for example. To get my results you would have to do this for base 6,7,8,9....all the way to 30 for each. I had help from Excel.

Str|Spd

1 |1

2 |1

3 |1

4 |1

5 |2

6 |2

7 |2

8 |2

9 |2

10|2

11|2

12|2

13|2

14|2

15|2

16|2

17|2

18|2

19|2

20|2

21|2

22|2

23|2

24|2

25|2

The average damage increase per point for strength is 1.00, but for speed it's only 0.04. Now obviously there is way more math to be done to find the actual values, but that's basically what I did. I would copy/paste my table here, but it's absolutely massive.

Now you're probably saying "Well when you do more base damage the increase the double attack is more than just one point." I'm aware of that, but the MULTIPLIER is still the same. it's still x1 if you don't double, and x2 if you do. It still comes out to the same averaged increase in damage. Now when you consider hit percentage for strength and higher base speed for both you and your opponent for speed, they eventually average out to .525 damage per point for strength (52.5%) and .239 (23.9%) for speed. Note than the value for speed is its combined offensive and defensive value. Though you did point out an oversight I believe I forgot (I don't remember), and that's defense against double attacks. I doubt though that including that will push the overall value above even 30%. Thanks for pointing that out though.

My total of 179% is just the added value of all the percents. Strength is 52.5%, which translates to .525 damage per point of strength. The other stats are the same.

Now take a character with the following stats

str-30, ski-30, spd-30, luck-30. We are just looking at damage here so we'll ignore defense for now.

How much damage would they do against an opponent with 0 in every stat (to find the 0-30 absolute average)? We will ignore their weapon for now.

65.25 damage. Now if you multiply that damage by each of my factors for str, ski, spd, and luck (the offensive stats that we are using, to find out how much each one is attributing to the total damage) you get 34.26, 14, 15.59, and 4.63 respectively. Add them together and you get 68.51. That's awfully close to to our actual damage of 65.25. Why is it higher? Because my speed and luck values also include their defensive value, so naturally they are going to artificially inflate the calculated offensive value. If you use the purely offensive values (which I can't seem to find :\) for each I'm sure you will get very, very close to our actual damage value.

Edited by Alondite
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You are the one and only person who has comprehended what I'm trying to do here. I'll answer your questions instead of responding to your entire post.

My calculations are based on the average damage increase/decrease from adding one point in any stat. Yours differs in that yours is based on the percentage increase in damage, while mine is actual points of damage.

For example, 1 point of strength, on average, translates into .525 (52.5%) additional damage. I used strength values of 5-30, and hit percentages of 0-100 on a table and average all the values.

You basically noted why speed is so low, but using my calculations for points of damage, it ranks as about half as important for strength. Only a 4 point speed difference gives you a damage boost. The multiplier from a difference of 3 speed to 4 is 2 (double damage) but from 0-3 and 4-5 and 5-30 you gain no additional damage. Let's look at two characters who do 1 damage. Let's say they have 5 in each stat. We'll add 25 points of each in increments of 1 point and record damage. We'll also assume they have 100 hit and that the enemy also has 5 speed. Also note that this is just a small snapshot of all the calculations I did. It's purely for example. To get my results you would have to do this for base 6,7,8,9....all the way to 30 for each. I had help from Excel.

Str|Spd

1 |1

2 |1

3 |1

4 |1

5 |2

6 |2

7 |2

8 |2

9 |2

10|2

11|2

12|2

13|2

14|2

15|2

16|2

17|2

18|2

19|2

20|2

21|2

22|2

23|2

24|2

25|2

The average damage increase per point for strength is 1.00, but for speed it's only 0.04. Now obviously there is way more math to be done to find the actual values, but that's basically what I did. I would copy/paste my table here, but it's absolutely massive.

Now you're probably saying "Well when you do more base damage the increase the double attack is more than just one point." I'm aware of that, but the MULTIPLIER is still the same. it's still x1 if you don't double, and x2 if you do. It still comes out to the same averaged increase in damage. Now when you consider hit percentage for strength and higher base speed for both you and your opponent for speed, they eventually average out to .525 damage per point for strength (52.5%) and .239 (23.9%) for speed. Note than the value for speed is its combined offensive and defensive value. Though you did point out an oversight I believe I forgot (I don't remember), and that's defense against double attacks. I doubt though that including that will push the overall value above even 30%. Thanks for pointing that out though.

My total of 179% is just the added value of all the percents. Strength is 52.5%, which translates to .525 damage per point of strength. The other stats are the same.

Now take a character with the following stats

str-30, ski-30, spd-30, luck-30. We are just looking at damage here so we'll ignore defense for now.

How much damage would they do against an opponent with 0 in every stat (to find the 0-30 absolute average)? We will ignore their weapon for now.

65.25 damage. Now if you multiply that damage by each of my factors for str, ski, spd, and luck (the offensive stats that we are using, to find out how much each one is attributing to the total damage) you get 34.26, 14, 15.59, and 4.63 respectively. Add them together and you get 68.51. That's awfully close to to our actual damage of 65.25. Why is it higher? Because my speed and strength values also include their defensive value, so naturally they are going to artificially inflate the calculated value. If you use the purely offensive values (which I can't seem to find :\) for each I'm sure you will get very, very close to our actual damage value.

Ooh, I see you put a lot of thought into this. That's some mighty nice work you've done here.

Well done, Alondite. I don't really have anything to say beyond that.

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Ooh, I see you put a lot of thought into this. That's some mighty nice work you've done here.

Well done, Alondite. I don't really have anything to say beyond that.

Thanks haha. I went through a few revisions before I got to these values. I wouldn't have bothered posting them if I didn't think they were at least close.

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Thanks haha. I went through a few revisions before I got to these values. I wouldn't have bothered posting them if I didn't think they were at least close.

I'm going to reply to this thread rather than the active one (which has over 10 times as many replies as this one), as that one turned into a bit of a crap-fest from both sides.

The general complaint about your numbers are that they don't fit into games. Correct? Well, here's a suggestion: let's use tier lists. Tier lists should, essentially, tell which units are better than each other. Of course, we can only use units that have the same amount of availability.

I'm not expecting your formula to be correct every time, as it's based of averages. But if we see the same mistake repeaten multiple times, then clearly something has to be changed.

For doing this properly, though, we'd kind of need to establish some sort of value for axes vs lances vs swords in the games. There's clearly fewer sword users than both axe and lance users in nearly all of the games.

So let's go with comparing Brom and Nephenee in FE9. They come in the same chapter. Brom uses axes, Nephenee uses lances. Brom has 1 less move than Nephenee.

According to the tier list, Nephenee tops "upper-middle" whereas Brom is above average in "middle".

I'm sticking to growth rates, I guess. They determine the characters most of all (well, as long as their level is less than 20/1, at least). Calculating the bases into it might be a good idea too, though.

Name / Hp / Str / Mag / Skl / Spd / Lck / Def / Res

Brom 75 45 10 50 25 20 55 25

Nephenee 55 40 20 55 55 25 35 25

Using your numbers from the OP, that turns into (I'm discounting magic completely by the way, as it's irrelevant to their fighting abilities). I'm just multiplying the hp above with the percentage below, doing the similar for Strength, and adding them up.

HP Str/Mag Skill Speed Luck Defense Resistance

10.94% 52.50% 21.50% 23.90% 7.09% 52.50% 10.50%

Brom - 8145.5

Nephenee - 7648.7

Now, this quite clearly contradict the tier list. The supposedly inferior Brom gets 6% more points on your list, despite being far lower on the tier list. (The tier list isn't perfect, but it's a good estimate, so let us assume it is for now).

Nephenee does have 1 more move in her arsenal, though, so that might be what's giving her the edge. I'd however say that axes are better than lances (because of the enemies in game), and thus debate that this evidence suggests you're overestimating heavy units. Of course, this isn't nearly enough evidence to conclude that.

Edit: Oh, and Nephenee has wrath. Blasted, I forgot that.

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I'm sticking to growth rates, I guess. They determine the characters most of all (well, as long as their level is less than 20/1, at least). Calculating the bases into it might be a good idea too, though.

FE3 DS aside, bases are always more important than growths.

Nephenee does have 1 more move in her arsenal, though, so that might be what's giving her the edge. I'd however say that axes are better than lances (because of the enemies in game), and thus debate that this evidence suggests you're overestimating heavy units. Of course, this isn't nearly enough evidence to conclude that.

I already brought up the fact that this formula doesn't account for movement at all, which is by far the most important stat in FE.

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FE3 DS aside, bases are always more important than growths.

I already brought up the fact that this formula doesn't account for movement at all, which is by far the most important stat in FE.

Yeah, you would say that.

Anyway, redoing your table so that rounds to kill is determined by hit rate rather than damage per round (since if you kill in 3 hits, it doesn't change rounds to kill at all if you do a little extra on average per round)

                          Number Rounds to Kill
Spread	|HP|    Strength| Skill|  Speed(O)| Speed(D)|   Luck(O)| Luck(D)| Defense
0	|6.00	|6.00	  |6.00	  |6.00	    |2.50	|6.00	 |6.00	  |6.00
1	|8.00	|6.00	  |5.77	  |6.00	    |2.59	|5.94	 |6.12	  |8.00
2	|8.00	|6.00	  |5.56	  |6.00	    |5.36	|5.88	 |6.25	  |8.00
3	|8.00	|6.00	  |5.36	  |6.00	    |5.56	|5.83	 |6.38	  |10.00
4	|8.00	|6.00	  |5.17	  |3.00	    |5.77	|5.77	 |6.52	  |10.00
5	|8.00	|4.00	  |5.00	  |3.00	    |6.00	|5.71	 |6.67	  |12.00
6	|8.00	|4.00	  |4.84	  |3.00	    |6.25	|5.66	 |6.82	  |16.00
7	|8.00	|4.00	  |4.69	  |3.00	    |6.52	|5.61	 |6.98	  |20.00
8	|8.00	|4.00	  |4.55	  |3.00	    |6.82	|5.56	 |7.14	  |30.00
9	|8.00	|4.00	  |4.41	  |3.00	    |7.14	|5.50	 |7.32	  |60.00
10	|8.00	|4.00	  |4.29	  |3.00	    |7.50	|5.45	 |7.50	  |Undefined (0 dmage)

Now, since you used excel (I think) I'll assume your final values are right for all the columns in which 30/damage per round = 3 * rounds per hit, and thus your final percentages would work for them, too.

hp becomes .33333 / 10 = 3.33%

str becomes .5 / 10 = 5%

skill = 3.41%

speed = 10%

speed defence = 14.49%

luck offence = 0.97%

luck defence = 2.26%

defence = 31.85%

[spoiler=defence]

1.33333

1.00000

1.25000

1.00000

1.20000

1.33333

1.25000

1.50000

2.00000

undefined (technically makes defence infinite on avearge, but we'll ignore for convenience)

sum = 11.86666

divide by 9 and you get the above

Not the biggest of changes for def, hp goes up a touch, str goes down some.

I am worried about how everything has a base of 15, though, with 30 hp. Oh, and 10 speed for the "enemy".

The "offence" has 4 stats: str, skl, spd, lck.

The "defence" has 4 stats: hp, spd, lck, def.

Using random.org, I'm going to take 7 integers between 11 and 20, and I'll use 30 for hp. I think I'll go with uniform distribution, though an argument could be made for normal distribution with an average of 15.5 and a standard deviation of 2.5, then rounding each to the nearest integer. More trouble than it's worth if I just want random numbers.

18, 16, 17, 13, 13, 17, 14

Set A:

So, offence has 18 str, 16 skill, 17 spd, 13 luck.

defence has 30 hp, 13 spd, 17 lck, 14 def.

Then I'll switch it.

Set B:

Offence will have 14 str, 17 skill, 13 speed, 13 luck.

Defence will have 30 hp, 17 spd, 16 lck, 18 def.

To get 50 hit, you would had 37 hit with offence and 35 avo. 15 skill with 15 luck for offence, 10 speed with 15 luck for defence. You needed a 48 hit weapon.

Set A has a 5 hit disadvantage. Set B has a 10 hit disadvantage. Let's use a 60 hit weapon to get 55 and 50 hit. Still 10 mt.

[spoiler=Set A]

offence has 18 str, 16 skill, 17 spd, 13 luck.

defence has 30 hp, 13 spd, 17 lck, 14 def.

Offence has 28 mt, 38 hit, 17 spd at base.

Defence has 30 hp, 43 avo, 14 def.

10 mt, 55% hit. 14 damage at base. Doubles. 3HKO to 30 hp. 55% to get a hit. 1/.55 = 1.8181... swings per hit. KO in 5.4545... swings on average. You get 2 swings per round, so 2.7272... rounds to KO. I'll use 4 decimal places for everything.

I'm not going to bother with the tougher ones to calculate. I'm not using Excel or anything, just a calculator, so I don't want to bother calculating this over and over with everything from 35% hit to 75% hit. HP, Strength, Speed(O), Defense are all easy. The rest all change the hit rate and are thus a pain.

Now, 14 damage per round 3HKOs anything up to 42 hp, so hp won't change a thing. The defender is always killed in 3 hits.

Str will only change something when it turns 3HKO into 2HKO. This happens after 1 point of strength, because 15 damage suddenly 2HKOs. You need 44 mt for a OHKO, and that's not possible with only +10 hp. So, a 2HKO only takes 1.8181... rounds on average.

Next up, speed(O) will never ever let you double, so of course it doesn't change anything either.

Finally, defence. A 3HKO is achieved on 30 hp with 14, 13, 12, 11, 10. A 4HKO with 9 and 8. A 5HKO with 7 and 6. A 6HKO with 5. An 8HKO with 4.

So, take the #HKO, * by 1.8181... to determine number of hits, divide by 2 due to doubling. Oh, and may as well say #HKO * 0.9090... due to dividing by 2.

Basically, # * 10/11, so 2.7272, 3.6363, 4.5454, 5.4545, 7.2727

                          Number Rounds to Kill
Spread	HP	Strength	Speed(O)	Defence
0	2.7272	2.7272		2.7272		2.7272
1	2.7272	1.8181		2.7272		2.7272
2	2.7272	1.8181		2.7272		2.7272
3	2.7272	1.8181		2.7272		2.7272
4	2.7272	1.8181		2.7272		2.7272
5	2.7272	1.8181		2.7272		3.6363
6	2.7272	1.8181		2.7272		3.6363
7	2.7272	1.8181		2.7272		4.5454
8	2.7272	1.8181		2.7272		4.5454
9	2.7272	1.8181		2.7272		5.4545
10	2.7272	1.8181		2.7272		7.2727

This results in HP and Speed(O) having 0% improvement.

Also Strength has the same 5% improvement it did before.

[spoiler=Defence now has]

1

1

1

1

1.3333

1

1.2500

1

1.2000

1.3333

11.1666%

Basically, def% went way way down from before. A couple others bottomed out, and strength didn't really change.

[spoiler=Set B]

Offence will have 14 str, 17 skill, 13 speed, 13 luck.

Defence will have 30 hp, 17 spd, 16 lck, 18 def.

Offence has 24 mt, 40 hit, 13 spd at base.

Defence has 30 hp, 50 avo, 18 def.

10 mt, 50% hit. 6 damage at base. No doubling at base. 5HKO to 30 hp. 50% to get a hit. 1/.50 = 2 swings per hit. KO in 10 swings on average. You get 1 swings per round at first, so 10 rounds to KO. I'll use 4 decimal places for everything that doesn't terminate earlier.

Again, I'm not going to bother with the tougher ones to calculate. I'm not using Excel or anything, just a calculator, so I don't want to bother calculating this over and over with everything from 30% hit to 70% hit. HP, Strength, Speed(O), Defense are all easy. The rest all change the hit rate and are thus a pain.

Now, 6 damage per round 5HKOs 30. 6HKOs anything up to 36 hp. 7HKOs anything up to 40 hp (42, but 30 doesn't go that high). Since I used 50% hit for this one, that's 10, 12, 14 rounds.

Str will change things from 5HKO to 4HKO to 3HKO to 2HKO. That's some sweet variance. 5HKO at 6 and 7. 4HKO at 8 and 9. 3HKO at 10 to 14. 2HKO at 15 and 16. And multiply number of hits by number of rounds, of course, to get: 10, 8, 6, 4 rounds.

Next up, speed(O) will let you double when you get +8, since there is a 4 point disadvantage at the moment. So, at 8, speed cuts it down to 5 rounds on average.

Finally, defence. A 5HKO is what you start at with 6 damage. A 6HKO with 5. An 8HKO with 4. A 10HKO with 3. A 15HKO with 2. A 30HKO with 1. And any more def than that will be invincible. 10, 12, 16, 20, 30, 60.

                          Number Rounds to Kill
Spread	HP	Strength	Speed(O)	Defence
0	10	10		10		10
1	12	10		10		12
2	12	8		10		16
3	12	8		10		20
4	12	6		10		30
5	12	6		10		60
6	12	6		10		--
7	14	6		10		--
8	14	6		5		--
9	14	4		5		--
10	14	4		5		--

hp has 10->12 and 12->14, so the rest don't help at all. hp gives a 3.667% improvement.

Str has 10->8, 8->6, 6->4, so the rest don't help at all. str gives a 10.833% improvement.

spd(0) has 10%, just like before.

As for Defence, based on what you did before, lets just look at the first 5 then divide by 5.

[spoiler=defence]

1.20000

1.33333

1.25000

1.50000

2.00000

sum = 7.28333

So 45.667% for defence.

This is basically why I advocate billions of calculations rather than simply thousands. Your answers will change drastically depending on where you start. And you can't get an accurate sense of what defence does when it frequently goes to infinity. Which is why I advocate win%. As you boost a stat, find the alteration it makes to win% from the previous amount. +4 over +3, +3 over +2, etc, just like you've been doing. You could probably cut down on the number of situations from the 610 billion I mentioned in the other topic by simply taking the 10 billion different ways unit A and unit B can compare if they each have str, skl, spd, lck, def between 11 and 20 and then finding out what +1 does for each stat (except use +10 for hp since the base value for that is a constant, preferably prime and bigger than 35). That's only 150 billion (from (1 * 5 + 10) * 10 billion). It doesn't give the info for when a stat goes above 20, but at least it doesn't overlap. My other suggestion is okay if you want to allow overlaps, since overlaps just give extra weight depending on how often it appears. But:

11	15	11	19	17
14	20	14	17	18

Take those stats for str, skl, spd, lck, def. Add 1 to str. Now add 2. Check difference in win% from 11 to 12, then do so from 12 to 13. However, 12 to 13 overlaps with the +1 str from this set:

12	15	11	19	17
14	20	14	17	18

And overlap may or may not be good. But at least when you get to +10, you have 22 str (and 23, 24, 25. up to 30 if you run the full 610 billion), which is something you'll never see if you just check the 150 billion. The difference between 150 billion and 610 billion isn't actually that much. Only a little more than 4 times as long. Of course, the time it takes to do the rest... 1 month * 4 = 4 months, so who knows how long the 150 billion can take. It's not just 150 billion calculations, since it has to go through a pretty annoying process to determine the 160 billion different win% (this includes the AvB win percentages when no changes are made to the stats), then it has to divide them to find the relative improvement from +1 to a stat, then it has to add up all 10 billion for each non-hp stat and all 100 billion for each hp stat, then it has to divide by either 100 billion or 10 billion, then you finally get it for each stat. Oh, some optimizing could be done since when it calculates the 10 billion different win%s for AvB, many of the same stat set-ups are used in the +1s. It should only have to calculate 10 billion + 100 billion for the different hp values (many of which aren't actually any different from some of the 10 billion) + the win% any time a stat is 20+1. But then you are still sitting on 150 billion numbers that need dividing by a different number. Then get added. Then have 6 massive sums get divided by 6 somewhat big numbers.

Plus I think that unit B shouldn't have the same range of stats as unit A. Depending on the game, at least. Some games the enemy is pretty close. Others like fe9 you tend to get each stat, on average, 5 lower or something. 11 to 20 for unit A and 6 to 15 for unit B could work, for example. But that won't change the number of calculations.

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FE3 DS aside, bases are always more important than growths.

I already brought up the fact that this formula doesn't account for movement at all, which is by far the most important stat in FE.

I agree with your first statement, as bases are RNG proof (unless considering Hard Mode bonuses from the GBA games, which can only help you). Growths are only reliable if they are 100% or above. They may or may not work out for you. But, Fire Emblem is based on chance quite a bit, so growths cannot be ignored.

Movement is a very important stat for those who want to clear maps quickly. And yes, an 8 Mov unit always has that mobility advantage over a 6 Mov unit, terrain restrictions aside. However, the topic creator seems to be focusing on results in battle, meaning when one unit directly engages another in combat. Movement has no impact on Hit%, Dmg, Crt%, or AS, so that is why movement is being ignored at the moment.

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Movement is a very important stat for those who want to clear maps quickly. And yes, an 8 Mov unit always has that mobility advantage over a 6 Mov unit, terrain restrictions aside. However, the topic creator seems to be focusing on results in battle, meaning when one unit directly engages another in combat. Movement has no impact on Hit%, Dmg, Crt%, or AS, so that is why movement is being ignored at the moment.

Except it does have an impact on who attacks what as well as your ability to attack archers without letting them get an attack on you first. Among other things.

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FE3 DS aside, bases are always more important than growths.

I already brought up the fact that this formula doesn't account for movement at all, which is by far the most important stat in FE.

Really, you find bases more important than growths? I suppose that makes sense. I just ran out of time (had to do something else), so I realised I only had time for either bases or growths. Of course we'll need both for the full picture.

As for movement, I'm perfectly aware you brought that up. I have absolutely no idea how we would put that into something like this, though, so we'll have to just ignore that for the moment. The only other realistic option is to give up the project entirely, and that would be dull.

Unless you have some sort of determining the value of movement accurately, Dondon, I think we'll just have to ignore it for the tier list vs OP stats for now, and then consider it after the comparison. Not a perfect way at all, but I don't see any better.

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Really, you find bases more important than growths? I suppose that makes sense. I just ran out of time (had to do something else), so I realised I only had time for either bases or growths. Of course we'll need both for the full picture.

As it has been said before, bases are RNG proof. As for which one is actually better in the long run, it really depends on the quality of the enemies (which is why I brought up FE3 DS as the sole exception to my rule - the quality of lategame enemies is really high, and as far as I know bases alone won't allow you to maintain optimal performance, so it certainly helps). For most FE games, though, the enemies are mediocre enough that better bases are always preferable to better growths.

A rough example of how it usually turns out is something like this:

We have a unit, Marcus, with good bases but terrible growths. We have another unit, Eliwood, with poor bases but good growths. Let's assume that Marcus starts with +5 on all of Eliwood's stats, that Eliwood ends with +5 on all of Marcus's stats, and that they are exactly the same at the exact midpoint of the game. (Also assume that Marcus doesn't have a movement advantage on Eliwood for the entire game.)

What generally happens is that Marcus stomps earlygame while Eliwood struggles. Eliwood catches up in midgame and they perform the same. By the end of the game, Marcus is still doing well while Eliwood is stomping. Overall advantage goes to Marcus.

Unless you have some sort of determining the value of movement accurately, Dondon, I think we'll just have to ignore it for the tier list vs OP stats for now, and then consider it after the comparison. Not a perfect way at all, but I don't see any better.

1. Please don't capitalize any part of my name (I'm really anal about this).

2. I was suggesting that if you wanted to compare the results of the formula to the tier list, you should probably select a pair of units that don't have some other determining factor such as a movement or movement type advantage.

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Bases are typically more important than growths because character growths are almost always better than enemy growths unless the unit really sucks or is intended to be a Jeigan, in addition to weapon selection and supports, in addition to skills in a few of the games. The only exceptions are FE2 (which is grindy) and FEDS2. In FEDS2, enemies get +10 hit which cancels out 2 Cs or a B support, as well as insane forges later in the game (we're talking like +5 might and +30 hit to Silvers) which further cancel out supports (as well as their 0 Luck not contributing to Hit). Your ability to critical and dodge the few enemies that don't have forges (generally Dragons) is made up for by the sheer number of enemies, as well as their competent 1-2 range (Javelins/Hand Axes got nerfed, and you don't get any Spears/Tomahawks in the main game) and 2-3 range (you get a single Longbow in 20x).

FE5 is not quite the same, its difficulty comes from the map/game design (fatigue for one) rather than individual enemies being threats (in fact, FE5 enemies are probably in the running for least threatening enemies in the entire series)

This means that Lunatic Mode provides the "early game effect" that is common in most FEs (which is usually the hardest part) through out the early game, in addition to already having a very difficult early game.

Additionally, giving an "overall power" calculation is dependent on both enemies and calculations. Skill was an excellent stat in FE5. You got 1 crit per point, weapon hit was horrible, and Pursuit Critical was around. FE6 was similar: Weapon hit sucked, and enemies had actual avoid.

Meanwhile, in FE7, it's a joke. Weapon hit is high, most supports give hit, and enemies are slowish with 0 Luck. Plus supports. Similar in FEDS: It gives even less hit, weapon hit is at an all time high, and you have plenty of money to blow on forging a bit more hit. In FE4, Luck is a joke. It just gives 1 Avoid per point. That's it. No hit, no skills, no crit avoid, nada.

For enemies, it's quite obvious. Speed becomes a very good stat in a 2RN system if you can reduce enemy hit below 50, which is dependent on *drumroll* the enemy's hit! In FEDS2, the only way to do this is to stack supports. Additionally, Move becomes weaker as enemies get stronger or more numerous. If you're forced to take defensive positioning, unless your move is so atrocious that you can't move around within a basic formation (which is basically limited to the GBA Knights and their 4 Move, or heavy terrain), it's not that bad. Meanwhile, in a game like FE9, every chapter is like playing a more successful version of the charge of the Light Brigade. Low move units suck.

I felt that FE4 handled the Move issue fairly well with class bases (the rest of the game is a different story), with a few exceptions. Mounted units have horrid bases/caps compared to unmounted units (fun fact: Lord Knight loses every stat to Swordmaster, Forrest, Warrior, and Sniper, only beating Thief Fighter by 3 Str and 2 Def, but Thief Fighter also has 7 move as opposed to 6 on the others. The other mounted classes don't do much better). The exceptions are Forest Knight (it destroys the non-Master Knight horse classes, and gets Continue and the best physical weapon type to boot), Master Knight (Male might have been okay if FE4's second gen weren't insane, but being able to circumvent "Oh noes I suck" by staffbotting makes the Princess dumb), and Dragonmaster/Falconknight (They have stats that put non Sage/Swordmaster classes to shame and get 8/9 move to boot as well as a very strong weapon selection, plus Pursuit and Continue on the 8 move one. Falconknight also gets Staves and is the best magic sword user due to its high magic. This is somewhat balanced by them not getting a road boost meaning they move about the same spaces per turn as an unmounted class, except they can ignore silly things like terrain obstructions). You can see a remnant of this in the General class caps in FE7-9 in that they crush the rest of the classes (and get WTA control in 8), as well as in 10 the mounted classes have poor caps for the most part (why the low move classes are even worse is anyone's guess).

Keep in mind that a class that wants both Strength and Magic is going to need a higher total due to hybridization. This also means that mages in FE9-11 that use the Str=Con system want a slightly higher total, although you could argue that innate 1-2 range compensates for that. Then again, mages in those games had Knight tier move so I dunno, and their bases have been almost unerringly horrendous.

Edited by Paperblade
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1. Please don't capitalize any part of my name (I'm really anal about this).

2. I was suggesting that if you wanted to compare the results of the formula to the tier list, you should probably select a pair of units that don't have some other determining factor such as a movement or movement type advantage.

1. Fair enough, I'll try not to capitalise any part of your name again. Capitalising just goes natural to me, so I might slip up once or twice in the future. Sorry about that, in advance.

2. Ah, right. Well, the problem with this is that we have to have two characters that

- Have the same availability

- Have the same move and movement type advantage

- Aren't pretty much identical on the tier list (ala most of the starter social knight duos)

Such a duo quite simply doesn't exist. Thus, we'll have to choose some characters that are close to that, but not quite that.

Edited by Pineapple
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To be fair, I think movement value is something that should be established first. It will, universally, be given more credit for swinging a character up the tier list than any weapon or stat value(which, to be honest, barely carry from game to game).

Take Gilliam vs. Franz here. Come in at the same time. Can promote to the same class with the same weapons. Franz is worth 600-900 points less. Ignoring Gilliam's base level advantage, possible flaws with the formula(speed really should be worth at least 10% more), and FE8, that would mean that Franz's 3 move is worth at least 200 points each. And while that wouldn't exactly SURPRISE me, it should be stated.

Really, though, I'd put my money where my mouth is with this sort of thing. You really could attempt to alter it from there if you could get a nice core to play it. I'd probably also consider just dropping the .04 for HP and .09 from luck

EDIT: After looking around at it, I've decided the numbers are a little odd regardless. How did you come to 178.8 as your total? And if you're not going to use a round total(100; Even 200 would be better) as a base, why have such large multipliers? No offense, but 1, 5, 2, 2.5, .5, 5, and 1 would give roughly the same results with less headaches. 10 55 25 30 10 55 15 would probably make for clearner results with similar intentions.

Edited by bunny: Now with Pancakes
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  • 2 months later...

Well, the thread is getting a bit old, but we still haven't come up with anything definitive so I though I'd post what I have been working on.

I still don't know how to incorporate movement into the formula, but I think I'm getting closer to finding realistic in-game numbers.

This time I was looking into the percent chance of killing the opponent in [x] rounds of combat.

I essentially started with what I had with a few changes that aren't really worth noting, because I found that altering the stat spread didn't do much. Damage would yield a 4 round kill with ~80% hit to start with, and then I just started playing with stats, plugging them into Reikken's "Chance to die/kill" calculator and recorded the results. I decided to record the percentage that one character will kill/be killed by the 5th round of combat. I know combat doesn't typically last that long, but fewer rounds didn't change a whole lot so I just left it for now. My results (scaled to my previous results) are as follows:

HP: 3.15%

Str/Mag: 15.6%

Skill: 14.9%

Speed: 38.16%

Luck: 13.59%

Def: 71.44%

Res:14.29%

Now to test them I plugged in some character averages from Blazing Sword...but I got some strange results. Like Matthew was rated about the same as Sain for one. I don't quite think Matthew is as proficient in combat as Sain is, he's just too weak and frail. There are some reasons for this. One being that Speed's included defensive value, specifically the ability to NOT be doubled, counts for too much. Most of your characters won't be being doubled very often.

I still believe that Strength is slightly more important than Speed, because you don't need a ton of speed to be able to double, but more Strength always translates into more damage, and more Strength plus a double translates into double the damage gains.

Skill seems a bit too high to me as well. Hit is important, but the higher it is, the less important more of it is.

So then I had an idea. What if I averaged the two sets of values? One reflects kill percentages in limited combat, and the other reflects universal damage, which is still a useful factor in combat proficiency. These are the numbers I got:

HP: 7.05%

Str/Mag: 34.05%

Skill: 18.2%

Speed: 31.03%

Luck: 10.34%

Def: 61.97%

Res: 12.39%

I haven't done much testing with these numbers yet, but they do seem more accurate than either of the previous sets of values. I'm also thinking that I might have to weigh magic according to an approximate ratio of physical/magic users in the game, or maybe of just classes in general.

As for calculating movement, the only thing I can think of is to assign a 100% value to the highest movement rating in game, considering terrain penalties. Then, assign a "percent of the highest value" to the rest of them, and then multiply that by the weighted stat total? Or maybe just the offensive values? I'm not really sure. That was the best I could come up with right now.

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I think you made a mistake somewhere. Defense can't be worth almost five times as much as strength.

The numbers for killing or getting killed heavily favor defense. The gains you get from defense are exponential. There is a chart farther up in the thread that shows that an extra 10 points of defense increase the number of turns you can survive against a given enemy tenfold, while the rest don't even double either the turns you can survive, or halve the number of turns in which you can kill your opponent (aside from speed, which exactly doubles).

Defense essentially works opposite to strength. +1 Str = +1 damage, and +1 Def = -1 damage. The difference though, is this:

Let's just say it takes exactly 3 hits to both kill the opponent, and 3 to be killed by it. Now let's say we add one to each stat. Let's just say that not our calculated rounds to kill are 2.5 for +1 Str, and we can survive 3.5 turns. Now we can't have half turns in Fire Emblem, so it will still take you 3 turns to kill the opponent, but it will now take 4 turns to kill you. That is essentially the reason defense is so valuable. Those aren't the exact values, but they are just there to demonstrate. Scroll up and take a look at the chart to see for yourself.

Now since one set of numbers is for killing/surviving, and the other for raw damage I decided to average them to get the third set of numbers. The first set doesn't work on it's own because all rounds of combat don't result in one person being killed (therefor the 2nd set's value of actual damage matters) and the second set doesn't account for how quickly you can kill an opponent. The Third set is my current set of values, and Def is only about twice as valuable as Speed and Str.

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I think one thing you are forgetting about speed is that you can (at least, for the most part) convert excess speed into strength by wielding heavier weapons. However, that means you need to take into account Constitution.

Another reason Sain is generally a better fighter than Matthew is because of his superior weapon triangle control (movement and rescue bonuses notwithstanding), which is also not factored in.

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I think one thing you are forgetting about speed is that you can (at least, for the most part) convert excess speed into strength by wielding heavier weapons. However, that means you need to take into account Constitution.

Another reason Sain is generally a better fighter than Matthew is because of his superior weapon triangle control (movement and rescue bonuses notwithstanding), which is also not factored in.

Yeah I understand all of that. For now my numbers only aim to determine pure combat proficiency. I would like at some point to find a way to include CON and MOVE, but I think it would be easier to find some acceptable numbers for the main stats before I start trying to figure out how the others factor in. Right now the numbers are simply meant to reflect killing potential and durability.

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I think one thing you are forgetting about speed is that you can (at least, for the most part) convert excess speed into strength by wielding heavier weapons. However, that means you need to take into account Constitution.

This would require a game where weapon weight is an actual problem past early game (FE9, where it hits enemies just as hard) or... ever (the others).

Another reason Sain is generally a better fighter than Matthew is because of his superior weapon triangle control (movement and rescue bonuses notwithstanding), which is also not factored in.

Matthew isn't a terrible fighter just looking at stats, so it makes sense. His real problem is that he's locked to swords, promotes super late, and his promotion doesn't really do anything for him (Assassin caps are balls).

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