Character "Overall Power" Calculation Factors.

[Narga_Rocks]

No. You consistently picked out specific situations where speed is at the advantage, so I adjusted my values to reflect that EXACT situation. My original values were designed to account for the "average" situation, not to be true for every possible situation, because that's not feasible.

Even the situations where you tried to show that str/def have an advantage, it depends solely on the weapon used. The numbers you created start leaning towards spd the moment weapon mt hit 9. I still don't see why units that have 20 str and 18 def or units that have 21 spd will be using iron lances. I've already admitted that your original values actually kinda work for the sake of low mt weapons. eg: 7 mt weapons with the high numbers I created (28 str and 16 spd compared to 30 str and 12 spd, both with 30 def) will mean that yours performs better against the enemy you created (29 str and 30 def and 14 spd). You do 7 damage. I do 5. Against 40 hp, you KO in 6 attacks and mine takes 8. The enemy KOs us in 7 attacks. Mine has serious trouble winning. Yours wins more than 50% (probably). Mine must dodge at least 1 hit whereas all yours has to do is not miss (or at least, it must not miss the enemy any more often than it dodges the enemy's attacks). Mine has to dodge at least 1 more time than it misses the enemy.

I'm not sure what you'd have to change in order to make your values work better at reasonable weapon mt values. Now, the numbers you gave result in an average of 15 per stat (we weren't looking at hp). However, your weighting system only appears to work for weapon mt values around half or less. 8 and below works, and 8 is only slightly more than half. However, by the time a typical unit starts averaging 15 per stat (ignoring hp) you will not be using weapons that weak anymore. At least, you won't use them unless you are killing a weakened enemy. There's nothing wrong with picking up an iron sword to KO something with like 5 hp left if you can cause 5+ damage with an iron sword (though if that unit will matter for enemy phase, obviously you want to be able to trade them something better after they attack).

If you are focusing on an average of 15 per stat, I highly recommend coming up with a way to balance it for, say, 10 or 11 mt weapons? Now, according to most here Raven is one of the most powerful units. Res tends to suck for many units in this game, so I'll ignore it completely. Ignoring hp and res, and giving him 8 extra points for his HHM bonuses, he needs to hit 75 for the average to be 15 each. 67 on this page. That's level 19. 19 has 67 + 8 = 75. What kind of weapons do you think are available when Raven reaches level 19?

http://serenesforest.net/forums/index.php?showtopic=21039&view=findpost&p=1183015

Even in chapter 25 (at the end of 25), a guy here playing an efficiency playthrough is hovering around level 16 for his more widely used units, and he's got a couple of units he promoted early. Given how Raven's allegedly one of the best in the game, you'd think other units would have lower totals. The player is playing a hacked "fixed mode", so stats should be close to their averages. His level 15 Kent has 51 total for str + skl + spd + lck + def. His level 15 Sain has 53 as well. And these guys are also generally placed in the top two tiers. In chapter 26 you can purchase killers. Killers are like steel only stronger with similar/same hit but less wt (and crit), so if you are looking at 15 averages then it makes sense to look at killer mt. 9, 9, 10, 11. And there are other fun things like reavers and braves that I'd assume are appearing around this time, and probably a silver or two. I really think that 10 mt is what matters. And yes, using 10 mt weapons significantly alters things for you because doubling and doing more than 3 damage a hit starts actually making a difference.

Right, but since you were using 1 singular situation, I adjusted my values to accommodate that one singular situation. Again, my original values are supposed to represent the "average" situation, which as an absolute amounts to 15 in each stat (30 HP). My values then measure the average value of one point in a stat in that "average" situation. It's a STARTING POINT as I said. I posted it here to get some constructive criticism, not "it's totally wrong and unrealistic and has no value because there's no way to calculate the average value of a stat because it is different in every situation." The numbers I got are correct for what I did, and without knowing what the "average" character actually is, it was the best solution I had: Just include them all, even if you'll never see them.

And like I said, if you want to use an average of 15, use stronger weapons. If you want to be using 7 mt weapons, then go with an average of 10 per stat or something.

Sadly, I have absolutely no idea how you are going to change the excel thing to represent the value of weapons. If you look at things the wrong way, weapons can seem to make no difference. But I think I've shown that weapons have the potential to completely change who is likely to win a confrontation. If I could tell you how to account for that, I would, but if you are trying to make units that are 50/50 against each other without having the same exact stats then weapons matter.

Ok. I'm just going to make statement here. If you consider every possible character/enemy that could ever possibly be in the game, even if you will never see them, but if they are at least possible, even only through hacking, then my values are correct (because that's what I did). Now since I included unrealistic situations, my values won't be true for some in-game situations, but they WILL be true in others. Unless my math is wrong (and since I used excel, I'm sure it's not) this is the case. If you know what the average stat spread of your characters and your opponents are, let me know and I'll use those numbers instead. My goal here is to make something of value.

Even in the case that you want to account for everything, I still see spd as undervalued because weapon mt tends to save speedy units even when they don't double. Granted for a +1 spd there are only 2 different spd values where it makes a difference, but there aren't exactly very many different values where +1 str or def makes much of a difference either, provided the weapons are strong enough.

Want to give me values I should use? I'll use game average weapon mt, overall hit%, and stat spreads and recalculate. A few things I can assure you will not change: Strength and Defense are exact polar opposites, so no matter what I do they will come out as equal, and Resistance will not be as valued as Defense because there are fewer magic users.

I have the tables and the formulas already made, all I need are the numbers.

str and def can't be polar opposites because str is going into magic. If there are 4 times as many physical weapons users as there are magic weapon users, then defence would be 4x as important, if we want to look at this as simply as possible. Count to 5, 1 of those 5 times res matters, 4 of those times def matters. However, strength matters all of those times because you don't have str and mag separated. Therefore, wouldn't it make sense that if you are going to look at this with the "polar opposites" attitude that str = def + res would make more sense? If str is given 55%, and res is given 11%, then wouldn't def be 44%?

Also, polar opposites or not, you should only be looking at what happens when you adjust unit A's stats. Giving unit A +1 str lets it do 1 extra damage on all 887 million different ways the enemies can have str, skl, spd, lck, def, res. Giving unit A +1 def lets it take 1 less damage from all 887 million different ways the enemies can have str, skl, spd, lck, def, res. (this is ignoring how 20% of the time the str goes up against res and only 80% of the time does it go against def, rather than the 100% you seem to be using.) They don't cancel each other because they act at separate moments. Now, maybe when you compare them to all the 887 million possibilities it ends up making the same difference for win%, but that's because you created enemies that will severely outrank your unit A. But enemies normally suck. A simple solution, without trying to be too perfect, would be to have unit As range from 5 to 30 in each stat and unit Bs range from 0 to 25 in each stat. Now, this doesn't actually assist with creating a Sain and Kent that will be 50/50 if they fight each other, but it does however assist in predicting how the two of them will perform on enemies. With speed going from 5 to 30 and enemy speed going from 0 to 25, you'll double more frequently and get doubled less frequently. Now you'll find that giving +1 str to unit A, on average, provides a bigger improvement to win% than giving +1 def to unit A. After all, if it is able to give more attacks than it receives over all of your comparisons (now 26⁶ ~= 300 million) then clearly the +1 str is acting more often than the +1 def, since +1 str affects things when you attack and +1 def affects things only when you take an attack. Of course, if you start looking at win% rather than absolute damage then you'll need to include hp. fe6 I'd actually say enemies should have more hp on average, but I don't know about fe7. It probably doesn't matter as much, actually.

Edited August 13, 2010 by Narga_Rocks

[Alondite]

str and def can't be polar opposites because str is going into magic. If there are 4 times as many physical weapons users as there are magic weapon users, then defence would be 4x as important, if we want to look at this as simply as possible. Count to 5, 1 of those 5 times res matters, 4 of those times def matters. However, strength matters all of those times because you don't have str and mag separated. Therefore, wouldn't it make sense that if you are going to look at this with the "polar opposites" attitude that str = def + res would make more sense? If str is given 55%, and res is given 11%, then wouldn't def be 44%?

Actually, what I was going to do is start by making Strength and Defense equal, and since Magic and Resistance depend on the ratio of physical:magic units I was going to calculate them separately. Let's just say for example that the value for Strength is 40%, Def is 40% and Res is 10% . For Magic I would do something like calculate the ratio of average Def:Res. Let's say that the average Def is 25% higher, then for Magic users I would increase the value of Strength/Magic by 25%, making it 50%. So Strength/Magic for physical units would be 40%, and 50% for magic users.

Also, polar opposites or not, you should only be looking at what happens when you adjust unit A's stats. Giving unit A +1 str lets it do 1 extra damage on all 887 million different ways the enemies can have str, skl, spd, lck, def, res. Giving unit A +1 def lets it take 1 less damage from all 887 million different ways the enemies can have str, skl, spd, lck, def, res. (this is ignoring how 20% of the time the str goes up against res and only 80% of the time does it go against def, rather than the 100% you seem to be using.) They don't cancel each other because they act at separate moments. Now, maybe when you compare them to all the 887 million possibilities it ends up making the same difference for win%, but that's because you created enemies that will severely outrank your unit A. But enemies normally suck. A simple solution, without trying to be too perfect, would be to have unit As range from 5 to 30 in each stat and unit Bs range from 0 to 25 in each stat. Now, this doesn't actually assist with creating a Sain and Kent that will be 50/50 if they fight each other, but it does however assist in predicting how the two of them will perform on enemies. With speed going from 5 to 30 and enemy speed going from 0 to 25, you'll double more frequently and get doubled less frequently. Now you'll find that giving +1 str to unit A, on average, provides a bigger improvement to win% than giving +1 def to unit A. After all, if it is able to give more attacks than it receives over all of your comparisons (now 26⁶ ~= 300 million) then clearly the +1 str is acting more often than the +1 def, since +1 str affects things when you attack and +1 def affects things only when you take an attack. Of course, if you start looking at win% rather than absolute damage then you'll need to include hp. fe6 I'd actually say enemies should have more hp on average, but I don't know about fe7. It probably doesn't matter as much, actually.

If we are going from 0-25 I think you're going to see Speed end up with a lower value. Here was my plan:

Two default units with 15 in each stat, and like 40 HP (since average of (0-60 isn't that realistic). Use a weapon with 10 Mt, and with a hit that will give an overall hit% of 50%. I know that seems low, but 50% is the average of 0-100%, all of which you're likely to see in-game (either by players or enemies). Plus if I used 100% hit, than it would be impossible to calculate Skill's true value since it wouldn't be effecting hit percentage. I would then use stat spreads of 10, since that seems about the largest spread between players and enemies that you'll see on average. I'm torn though on How I want to calculate. If I want to calculate average #HKO, or something like percentage damage increase.

Edited August 13, 2010 by Alondite

[Charpig]

Most players on this site are probably more concerned with actual results than simply having a higher displayed Mt. So, I would suggest you go with #HKO, since that is very useful and people on this site frequently use it to determine how strong a character is in battle. Increasing 12 dmg to 18 dmg (a 50% damage increase) is useless in battle if it doesn't change the number of hits I need to KO an enemy.

Edited August 13, 2010 by Charpig

[Alondite]

Most players on this site are probably more concerned with actual results than simply having a higher displayed Mt. So, I would suggest you go with #HKO, since that is very useful and people on this site frequently use it to determine how strong a character is in battle. Increasing 12 dmg to 18 dmg (a 50% damage increase) is useless in battle if it doesn't change the number of hits I need to KO an enemy.

Alright, that's what I did, and here's what I got. Values are in "Number of Rounds to Kill," and a double attack counts as one "round." The values in each column correspond to to the spread of stats (how much I added to each stat). I'm not sure how the chart is going to come out on here, but it may still be readable.

Keep in mind, 10 mt weapon, 15 base stat for each character with a 50% hit rate (average of 0-100%, I already explained why) I used a 10-20 spread instead of 15-25 spread to calculate speed defense so it would include defending against the double attack.

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 |6.20 |5.45 |5.77 |6.00 |2.59 |5.94 |6.12 |6.67

2 |6.40 |5.00 |5.56 |6.00 |5.36 |5.88 |6.25 |7.50

3 |6.60 |4.62 |5.36 |6.00 |5.56 |5.83 |6.38 |8.57

4 |6.80 |4.29 |5.17 |3.00 |5.77 |5.77 |6.52 |10.00

5 |7.00 |4.00 |5.00 |3.00 |6.00 |5.71 |6.67 |12.00

6 |7.20 |3.75 |4.84 |3.00 |6.25 |5.66 |6.82 |15.00

7 |7.40 |3.53 |4.69 |3.00 |6.52 |5.61 |6.98 |20.00

8 |7.60 |3.33 |4.55 |3.00 |6.82 |5.56 |7.14 |30.00

9 |7.80 |3.16 |4.41 |3.00 |7.14 |5.50 |7.32 |60.00

10 |8.00 |3.00 |4.29 |3.00 |7.50 |5.45 |7.50 |Undefined (0 dmage)

As you can see, defense has a massive effect on how many rounds it takes to KO someone. 31.43% more rounds to KO for +1 defense on average.

Here are all the average percentages, in the same order if anyone cares.

2.92% 7.19% 3.41% 10.00% 14.49% 0.97% 2.26% 31.43%

*edit* as expected the chart is out of alignment, but it shouldn't be too hard to read.

Also Magic and Resistance require the other values to be correct first to calculate, so I'm doing those after.

Edited August 13, 2010 by Alondite

[Narga_Rocks]

Actually, what I was going to do is start by making Strength and Defense equal, and since Magic and Resistance depend on the ratio of physical:magic units I was going to calculate them separately. Let's just say for example that the value for Strength is 40%, Def is 40% and Res is 10% . For Magic I would do something like calculate the ratio of average Def:Res. Let's say that the average Def is 25% higher, then for Magic users I would increase the value of Strength/Magic by 25%, making it 50%. So Strength/Magic for physical units would be 40%, and 50% for magic users.

You could perhaps use that.

If we are going from 0-25 I think you're going to see Speed end up with a lower value. Here was my plan:

At this point I'm more concerned with getting str > def because that's the case in the game for a player. Perhaps for the enemy def > str, but the PCs use str so much more often than def that if they are placed equivalent by you then you are saying that on a per-use basis def is >> str.

If you have PCs with 5 to 30 and Enemies with 0 to 25, then you can calculate the importance of stats for PCs and Enemies separately.

for speed values of 5 to 30 compared to 0 to 25, there are 26 * 26 different arrangements. Of those 676 different possibilities, the PC will double in:

(2 + 3 + ... + 26) + 26 different scenarios, since 5 doubles 0 and 1, 6 doubles 0, 1, and 2, 7 doubles 0, 1, 2, 3, ... 29 doubles 0 to 25, 30 doubles 0 to 25.

2 + ... + 26 + 26 = 376.

The PC will get doubled in:

17 + 16 + 15 + ... + 1 different scenarios, since 5 is doubled by 9 to 25, 6 is doubled by 10 to 25, 7 is doubled by 11 to 25, ... 21 is doubled only by 25, and anything above 21 isn't doubled by anything the enemy can do.

17 + ... + 1 = 153

double 376, nobody doubles 147, get doubled 153.

As a result, in all the different possible combats that speed generates (with everything else being equal), the PC attacks 1052 times while the enemy only attacks 829 times.

Since the PC uses strength more often than it uses defence (only uses defence 829 times but uses strength 1052 times), strength is likely going to end up more important.

For the enemy, the reverse is true: the enemy uses defence more often than it uses strength.

What effect this may or may not have on speed I neither know nor care at the moment.

Two default units with 15 in each stat, and like 40 HP (since average of (0-60 isn't that realistic). Use a weapon with 10 Mt, and with a hit that will give an overall hit% of 50%. I know that seems low, but 50% is the average of 0-100%, all of which you're likely to see in-game (either by players or enemies). Plus if I used 100% hit, than it would be impossible to calculate Skill's true value since it wouldn't be effecting hit percentage. I would then use stat spreads of 10, since that seems about the largest spread between players and enemies that you'll see on average. I'm torn though on How I want to calculate. If I want to calculate average #HKO, or something like percentage damage increase.

I think the bold is one of the biggest problems I have with what you are doing. PCs and Enemies are completely different entities despite the stats doing the same thing. There are two reasons:

1: the player chooses advantageous battles. It arranges to attack in situations where it can't be countered and you can set up your units to prevent the enemy being able to do the same thing.

2: the player will be able to attack enemies that are one hit away from death and thus the enemy can't counter. The enemy won't be able to do this if the player is intending to prevent deaths.

3: with a different stat spread, different stats have more or less importance

Maybe more reasons, but basically the importance of a stat is different depending on the situation, and the player will mainly use favourable situations. Now, when you look at all potential situations, things average out over time. However, when the PCs are taking one set of situations and the Enemies are taking a different set of situations, if you calculate the importance of stats separately you'll see different results for PCs from what you get with Enemies. If you want to apply your weightings to the PCs to compare their power, your conclusions will be better if you don't let enemies affect the weightings for the PCs, and your weightings for enemies will be better if you don't let PCs affect the weightings for enemies.

Oh, and you could get away with 20 to 60 hp, but yeah 0 to 60 doesn't seem as likely. Also, can't you just use 70% hit on the weapon and let the chips fall where they may from what the stats create? Hit ranges from 55 to 100 in fe7. Even fe6 has hit range from 45 to 95. If you are hung up on using the same stat spread for unit A that you use for unit B, on average hit will certainly be better than 50. Even taking into account how luck only gives luck/2 for hit, since 30 luck is the most you can have and at worst that starts units off at a 15 hit disadvantage against equal-stat opponents: it's still going to mean at least 55 hit at equal stats.

*edit* as expected the chart is out of alignment, but it shouldn't be too hard to read.

use tags. Specifically, code

                          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	|6.20	|5.45	|5.77	|6.00	|2.59	|5.94	|6.12	|6.67
2	|6.40	|5.00	|5.56	|6.00	|5.36	|5.88	|6.25	|7.50
3	|6.60	|4.62	|5.36	|6.00	|5.56	|5.83	|6.38	|8.57
4	|6.80	|4.29	|5.17	|3.00	|5.77	|5.77	|6.52	|10.00
5	|7.00	|4.00	|5.00	|3.00	|6.00	|5.71	|6.67	|12.00
6	|7.20	|3.75	|4.84	|3.00	|6.25	|5.66	|6.82	|15.00
7	|7.40	|3.53	|4.69	|3.00	|6.52	|5.61	|6.98	|20.00
8	|7.60	|3.33	|4.55	|3.00	|6.82	|5.56	|7.14	|30.00
9	|7.80	|3.16	|4.41	|3.00	|7.14	|5.50	|7.32	|60.00
10	|8.00	|3.00	|4.29	|3.00	|7.50	|5.45	|7.50	|Undefined (0 dmage)

As you can see, defense has a massive effect on how many rounds it takes to KO someone.

Edited August 13, 2010 by Narga_Rocks

[Alondite]

You could perhaps use that.

At this point I'm more concerned with getting str > def because that's the case in the game for a player. Perhaps for the enemy def > str, but the PCs use str so much more often than def that if they are placed equivalent by you then you are saying that on a per-use basis def is >> str.

If you have PCs with 5 to 30 and Enemies with 0 to 25, then you can calculate the importance of stats for PCs and Enemies separately.

for speed values of 5 to 30 compared to 0 to 25, there are 26 * 26 different arrangements. Of those 676 different possibilities, the PC will double in:

(2 + 3 + ... + 26) + 26 different scenarios, since 5 doubles 0 and 1, 6 doubles 0, 1, and 2, 7 doubles 0, 1, 2, 3, ... 29 doubles 0 to 25, 30 doubles 0 to 25.

2 + ... + 26 + 26 = 376.

The PC will get doubled in:

17 + 16 + 15 + ... + 1 different scenarios, since 5 is doubled by 9 to 25, 6 is doubled by 10 to 25, 7 is doubled by 11 to 25, ... 21 is doubled only by 25, and anything above 21 isn't doubled by anything the enemy can do.

17 + ... + 1 = 153

double 376, nobody doubles 147, get doubled 153.

As a result, in all the different possible combats that speed generates (with everything else being equal), the PC attacks 1052 times while the enemy only attacks 829 times.

Since the PC uses strength more often than it uses defence (only uses defence 829 times but uses strength 1052 times), strength is likely going to end up more important.

For the enemy, the reverse is true: the enemy uses defence more often than it uses strength.

What effect this may or may not have on speed I neither know nor care at the moment.

I think the bold is one of the biggest problems I have with what you are doing. PCs and Enemies are completely different entities despite the stats doing the same thing. There are two reasons:

1: the player chooses advantageous battles. It arranges to attack in situations where it can't be countered and you can set up your units to prevent the enemy being able to do the same thing.

2: the player will be able to attack enemies that are one hit away from death and thus the enemy can't counter. The enemy won't be able to do this if the player is intending to prevent deaths.

3: with a different stat spread, different stats have more or less importance

Maybe more reasons, but basically the importance of a stat is different depending on the situation, and the player will mainly use favourable situations. Now, when you look at all potential situations, things average out over time. However, when the PCs are taking one set of situations and the Enemies are taking a different set of situations, if you calculate the importance of stats separately you'll see different results for PCs from what you get with Enemies. If you want to apply your weightings to the PCs to compare their power, your conclusions will be better if you don't let enemies affect the weightings for the PCs, and your weightings for enemies will be better if you don't let PCs affect the weightings for enemies.

Oh, and you could get away with 20 to 60 hp, but yeah 0 to 60 doesn't seem as likely. Also, can't you just use 70% hit on the weapon and let the chips fall where they may from what the stats create? Hit ranges from 55 to 100 in fe7. Even fe6 has hit range from 45 to 95. If you are hung up on using the same stat spread for unit A that you use for unit B, on average hit will certainly be better than 50. Even taking into account how luck only gives luck/2 for hit, since 30 luck is the most you can have and at worst that starts units off at a 15 hit disadvantage against equal-stat opponents: it's still going to mean at least 55 hit at equal stats.

use tags. Specifically, code

I think 70% hit will keep the relative differences between stats the same. In effect it will probably just raise each one by a proportionally equal amount (like 20% more for each or something), which changes the numbers, but not how they relate to each other.

Oh and I used 30-40 HP, since that's probably where the "average" HP falls when considering the entire game. Like minimum 15 or so, maximum 60.

Edited August 13, 2010 by Alondite

[Narga_Rocks]

I think 70% hit will keep the relative differences between stats the same. In effect it will probably just raise each one by a proportionally equal amount (like 20% more for each or something), which changes the numbers, but not how they relate to each other.

That's unlikely. then again you aren't using true hit and you aren't looking at win% and you are comparing stats as if they are equivalent, so who knows?

But I can tell you that earlier when we were comparing the damage per round of character A and character B, the hit rate changes who is likely to win significantly. With a unit that does 5x2 against a unit that does 12, high hit weapons favour the unit that does 12 damage and lower hit weapons favour the unit that does 5x2. At least, it did when there was a 19 hit difference between our units.

Edited August 13, 2010 by Narga_Rocks

[Alondite]

I can try, but I don't think it's really going to change a whole lot. Defense is going to go up even more, since higher chance to get hit = more need for defense.

[Narga_Rocks]

I can try, but I don't think it's really going to change a whole lot. Defense is going to go up even more, since higher chance to get hit = more need for defense.

Like I said, since you are apparently going with 30 hp, 15 in each stat, and then simply, what, raising an individual stat 1 at a time? You may not get much change.

Oh, and when you calculate rounds to kill, are you calculating average damage per round and then going 30/that number to get number of rounds to KO? Can you see if that gives you the same result as taking number of hits to kill and then multiplying by "rounds per hit" or something like that? Basically, determine the average number of rounds it takes to make a successful hit.

If you have a 64% hit rate, that results in a hit every 1.5625 rounds (if you aren't doubling). So, if you need to hit 3 times, that means you would have an average of 4.6875 rounds to win.

Or, you cause 6.4 damage per round (10 hits). 30 / 6.4 = 4.6875.

Now, this appears to work all fine and dandy for what you did. However, things change when you start considering numbers that don't give perfect kills (drop to precisely 0 hp).

16 str gives you 11 damage per hit. With a 50% hit rate, that gives you 5.5 damage per round. 30/5.5 = 5.4545... rounds. But that's not the whole story. It takes 3 hits to kill whether a unit causes 10 damage or 11 damage. You have a hit rate of 50%. In order to get 3 successful hits, 3/.5 = 6. It takes, on average, 6 rounds to kill the enemy regardless of whether or not you do 10 damage or 11 damage. This is because 10 or 11 doesn't make a difference for the number of hits, and it is the number of necessary successful hits that matter. It takes 6 rounds on average to deliver 3 successful hits, and thus it takes 6 rounds on average to kill. Strength won't actually do anything until you get to +5, and it won't make a difference at any other value. +0 to +4 all take 3 hits to kill the enemy, and +5 to +10 all take 2 hits to kill the enemy. The number of rounds it takes to get 3 hits doesn't change one bit if you have a little more strength. Ditto 2 hits.

Recalculate with that in mind and see what happens. Yes, I'm aware that this will make defence valued more and strength valued less. A single point of defence will now make it take 4 hits rather than 3 hits, and 4 hits takes 8 rounds on average. And as you change the #HKO it gets worse and worse. Oh well.

Oh, and again, I'd go with win% rather than simply looking at rounds to kill. Granted, rounds to kill is better than straight up damage, but it's still not perfect.

In theory, two units with the exact same stats would have a 50% chance of winning. With equal speed, you can assume they each go first half the time. Since they are identical, unit A going first should have a win% = unit B going first's win %, and similarly for win% when not going first, resulting in 50% each. As you increase individual stats, the chance of victory will change as well, obviously.

Now, the reason for win% being more helpful is defence and speed (D) and luck (D). I assume these are how those stats affect the defensive unit. The only stats you should be altering is unit A. You are currently altering unit A or unit B depending on which stat. That's a problem. However, if you use win% then you can give unit A more defence and it will mean something for unit A's win %. Obviously giving unit A more defence doesn't change the number of rounds it takes unit A to kill unit B, and that's why you made your chart the way you did. Oh, and yes, the first point of defence will have a pretty large affect on the win%, since it changes unit A from being 3HKOd to being 4HKOd while he still manages to 3HKO the enemy.

Anyway, when units don't have the same speed, the one with more speed should always go first (may as well go arena-style, ABABABABAB. And with doubling, ABAABAABAABA. This is different from the Goldie videos for fe10, but considering how arenas exist in fe7 and they don't use the Goldie method, it's fine). Yes, this will give a pretty big boost for the first point of speed, but it probably should.

Anyway, I'll take a really simple example to show how this works. Each unit does 10 damage and has 10 hp, and unit A has 1 more speed than unit B. We'll give unit A a 50% hit rate, and unit B a 48% hit rate (due to the speed differential).

Unit A goes first. If he hits, he wins. 50% chance of victory.

Unit B goes. He has a 48% chance of winning, but only if unit A didn't win already. 48% * (chance A didn't win) = .48 * (1 - .5) = .24 = 24%. A has 50%, B has 24%.

Unit A goes first in round 2. 50% chance of victory, but there is only a 26% chance the battle is still happening. 13% chance of victory. A has 63%, B has 24%.

unit B goes. 48% chance, but only 13% chance battle is still going on. 6.24% chance of victory. A has 63%, B has 30.24%.

Unit A goes first in round 3. 50% chance, but only 6.76% chance of battle still happening.

etc, etc.

A will probably end up around 68% and B around 32%. One point of speed changes the battle from 50/50 to 68/32. Obviously the rest of the speed points won't make as big of a difference (until you get to the point where A doubles B, of course). In this case, more strength is meaningless because everyone already OHKOs, so this isn't a good test for strength (need more hp). 1 point of defence also changes things drastically since unit B now needs to hit unit A twice.

If I do +1 def, unit A and unit B each go first half the time since they have the same speed.

A causes 10 damage each hit and needs to cause 10 total.

B causes 9 damage each hit and needs to cause 10 total.

Since they have the same spd/lck/skl, they each have 50% hit.

50%: A is first.

A has 50% to win, so 25% total

B has 50% to cause 9 damage.

A has 50% to win. 25% chance to get the opportunity, 50% chance to win with it, product = 12.5% to win.

B has 50% to cause 9 damage. He previously might have caused 9 damage, so 50% * 50% = 25% chance to kill. Only 12.5% chance of this battle occurring, so 3.125% chance of victory)

50%: B is first.

B can't win, but causes 9 damage 50% of the time.

A has 50% to win, so 25% total.

B has 50% to hit, 50% to have hit in the first round. 25% to win, but only 25% for this opportunity to occur. 6.25% to win.

A has 50% to win, but only 18.75% to get this opportunity. 9.375% to win.

So far, after 2 rounds,

A wins .25 + .125 + .25 + .09375 = 71.875%

B wins 12.5%

There is a 15.625% chance that the battle will go on to round 3. If we assume that the ratio doesn't change too much (it probably won't change drastically), then we can extend our current results to make:

A wins 71.875/84.375 = ~85%

B wins 15%

Of course, if you start with 30 hp then it gets a lot more complicated since nobody can even win until the third round. Going first shouldn't have such a dramatic effect, and neither should being 1 extra HKOd. 1HKO vs. 2HKO is considerably different from 3HKOd vs. 4HKOd. Now, they will both still have a pretty big effect, but it shouldn't be quite so extreme. Also, strength won't change anything until +5. 3HKO to 3HKO makes no difference. 3HKO to 2HKO makes a difference, though, and that won't happen until +5 strength. Now, to reduce the whole def changes things immediately and drastically, you could either go with 27 hp to start or make an 11 mt weapon. This would make the first point of def matter less, and it starts going crazy at the second point of defence. Up to you.

Oh, and one other advantage to win% is you don't have any columns that are undefined. If unit B can't damage unit A, then unit A has a 100% chance of victory provided that it can hit successfully and cause damage while hitting.

Also, I still say that if you truly want to get an average over time, you'd need to do a lot more starting situations. Even if you just look at stats starting between 11 and 20 (keeping hp a constant, say, 30), that's still 1 hundred thousand different possibilities for str, skl, spd, lck, def. And since both unit A and unit B can start that way, that gives you 10 billion different initial comparisons. And since you need to add 1 to 10 to each stat (and hp), each unit A v unit B will give you 61 comparisons for your chart (going by win%. If you go with your current method that makes 81 comparisons). Basically, you've got your untouched stats, where you just look at A v B. That's 1. Then you've got the comparisons where you have added to a stat. You add 1 to 10 to each stat, and there are 6 stats. Hence, 61 comparisons. In total, you would have 610 billion comparisons. 100 billion for each stat + the 10 billion base comparisons. You can average out each stat over those 100 billion different values and then you'll get a much more accurate idea of how much each stat helps you out. To tell you the truth, I'm not sure precisely how best to do this part. Each of the 10 billion unit A and unit B combinations would have a different base win%. Perhaps for each of the 66 comparisons resulting from a single AvB combination, you could take the new win% and divide it by the old win% to get a %increase/decrease in win% (positive is increase, negative is decrease). Then if you add up all your different values, you'd get the average increase in win% for +1 in each stat. This reintroduces the potential for undefined values, as it is possible some base unit As will be incapable of beating a unit B. It also introduces the possibility for heavy skewing. A unit A that does 1 damage to a unit B will likely have a win% that is extremely low. Like, 0.1%. But certain additions could bring it up to 50%. This would be 500x improvement. However, since you have 100 billion different win% for each stat, I don't think it will skew your results too heavily because it isn't exactly a common occurrence. To avoid the potential 0% problem, all you have to do is use 10 mt weapons. At most, there is a 9 point difference between initial strength and initial defence, since both unit A and B start between 11 and 20 str/def. Thus there will never be a unit A incapable of beating a unit B.

I really don't think Excel is capable of this, by the way, but various programming languages should be able to pull it off.

Also, using the 610 billion different values should help strength a little bit. At 10 damage to 30 hp, there's only so much up to +10 strength can do. At most, it changes a 3HKO into a 2HKO. However, some of the unit A's will only do 3 damage to 30 hp. +7 str makes a 3HKO instead of a 10HKO. Even +1 str turns a 10HKO into an 8HKO. It might still be advisable to use a base of 37 hp (it's prime and higher than 35. Another good number is 43), or even to add hp to the altering of the initial stats of unit A and unit B. This takes things from 10 billion AvBs to 1 trillion AvBs, but oh well.

Edited August 13, 2010 by Narga_Rocks

[bunny: spider bitten]

Link

Funsies.

Edited August 16, 2010 by bunny: Now with Pancakes

[Alondite]

Like I said, since you are apparently going with 30 hp, 15 in each stat, and then simply, what, raising an individual stat 1 at a time? You may not get much change.

Oh, and when you calculate rounds to kill, are you calculating average damage per round and then going 30/that number to get number of rounds to KO? Can you see if that gives you the same result as taking number of hits to kill and then multiplying by "rounds per hit" or something like that? Basically, determine the average number of rounds it takes to make a successful hit.

If you have a 64% hit rate, that results in a hit every 1.5625 rounds (if you aren't doubling). So, if you need to hit 3 times, that means you would have an average of 4.6875 rounds to win.

Or, you cause 6.4 damage per round (10 hits). 30 / 6.4 = 4.6875.

Now, this appears to work all fine and dandy for what you did. However, things change when you start considering numbers that don't give perfect kills (drop to precisely 0 hp).

16 str gives you 11 damage per hit. With a 50% hit rate, that gives you 5.5 damage per round. 30/5.5 = 5.4545... rounds. But that's not the whole story. It takes 3 hits to kill whether a unit causes 10 damage or 11 damage. You have a hit rate of 50%. In order to get 3 successful hits, 3/.5 = 6. It takes, on average, 6 rounds to kill the enemy regardless of whether or not you do 10 damage or 11 damage. This is because 10 or 11 doesn't make a difference for the number of hits, and it is the number of necessary successful hits that matter. It takes 6 rounds on average to deliver 3 successful hits, and thus it takes 6 rounds on average to kill. Strength won't actually do anything until you get to +5, and it won't make a difference at any other value. +0 to +4 all take 3 hits to kill the enemy, and +5 to +10 all take 2 hits to kill the enemy. The number of rounds it takes to get 3 hits doesn't change one bit if you have a little more strength. Ditto 2 hits.

I get what you're saying. Fortunately, I think it's easy to do. By the sound of it, just rounding each number up to the next whole number will accomplish the same thing haha.

Recalculate with that in mind and see what happens. Yes, I'm aware that this will make defence valued more and strength valued less. A single point of defence will now make it take 4 hits rather than 3 hits, and 4 hits takes 8 rounds on average. And as you change the #HKO it gets worse and worse. Oh well.

Oh, and again, I'd go with win% rather than simply looking at rounds to kill. Granted, rounds to kill is better than straight up damage, but it's still not perfect.

In theory, two units with the exact same stats would have a 50% chance of winning. With equal speed, you can assume they each go first half the time. Since they are identical, unit A going first should have a win% = unit B going first's win %, and similarly for win% when not going first, resulting in 50% each. As you increase individual stats, the chance of victory will change as well, obviously.

Now, the reason for win% being more helpful is defence and speed (D) and luck (D). I assume these are how those stats affect the defensive unit. The only stats you should be altering is unit A. You are currently altering unit A or unit B depending on which stat. That's a problem. However, if you use win% then you can give unit A more defence and it will mean something for unit A's win %. Obviously giving unit A more defence doesn't change the number of rounds it takes unit A to kill unit B, and that's why you made your chart the way you did. Oh, and yes, the first point of defence will have a pretty large affect on the win%, since it changes unit A from being 3HKOd to being 4HKOd while he still manages to 3HKO the enemy.

Anyway, when units don't have the same speed, the one with more speed should always go first (may as well go arena-style, ABABABABAB. And with doubling, ABAABAABAABA. This is different from the Goldie videos for fe10, but considering how arenas exist in fe7 and they don't use the Goldie method, it's fine). Yes, this will give a pretty big boost for the first point of speed, but it probably should.

Anyway, I'll take a really simple example to show how this works. Each unit does 10 damage and has 10 hp, and unit A has 1 more speed than unit B. We'll give unit A a 50% hit rate, and unit B a 48% hit rate (due to the speed differential).

Unit A goes first. If he hits, he wins. 50% chance of victory.

Unit B goes. He has a 48% chance of winning, but only if unit A didn't win already. 48% * (chance A didn't win) = .48 * (1 - .5) = .24 = 24%. A has 50%, B has 24%.

Unit A goes first in round 2. 50% chance of victory, but there is only a 26% chance the battle is still happening. 13% chance of victory. A has 63%, B has 24%.

unit B goes. 48% chance, but only 13% chance battle is still going on. 6.24% chance of victory. A has 63%, B has 30.24%.

Unit A goes first in round 3. 50% chance, but only 6.76% chance of battle still happening.

etc, etc.

A will probably end up around 68% and B around 32%. One point of speed changes the battle from 50/50 to 68/32. Obviously the rest of the speed points won't make as big of a difference (until you get to the point where A doubles B, of course). In this case, more strength is meaningless because everyone already OHKOs, so this isn't a good test for strength (need more hp). 1 point of defence also changes things drastically since unit B now needs to hit unit A twice.

If I do +1 def, unit A and unit B each go first half the time since they have the same speed.

A causes 10 damage each hit and needs to cause 10 total.

B causes 9 damage each hit and needs to cause 10 total.

Since they have the same spd/lck/skl, they each have 50% hit.

50%: A is first.

A has 50% to win, so 25% total

B has 50% to cause 9 damage.

A has 50% to win. 25% chance to get the opportunity, 50% chance to win with it, product = 12.5% to win.

B has 50% to cause 9 damage. He previously might have caused 9 damage, so 50% * 50% = 25% chance to kill. Only 12.5% chance of this battle occurring, so 3.125% chance of victory)

50%: B is first.

B can't win, but causes 9 damage 50% of the time.

A has 50% to win, so 25% total.

B has 50% to hit, 50% to have hit in the first round. 25% to win, but only 25% for this opportunity to occur. 6.25% to win.

A has 50% to win, but only 18.75% to get this opportunity. 9.375% to win.

So far, after 2 rounds,

A wins .25 + .125 + .25 + .09375 = 71.875%

B wins 12.5%

There is a 15.625% chance that the battle will go on to round 3. If we assume that the ratio doesn't change too much (it probably won't change drastically), then we can extend our current results to make:

A wins 71.875/84.375 = ~85%

B wins 15%

Of course, if you start with 30 hp then it gets a lot more complicated since nobody can even win until the third round. Going first shouldn't have such a dramatic effect, and neither should being 1 extra HKOd. 1HKO vs. 2HKO is considerably different from 3HKOd vs. 4HKOd. Now, they will both still have a pretty big effect, but it shouldn't be quite so extreme. Also, strength won't change anything until +5. 3HKO to 3HKO makes no difference. 3HKO to 2HKO makes a difference, though, and that won't happen until +5 strength. Now, to reduce the whole def changes things immediately and drastically, you could either go with 27 hp to start or make an 11 mt weapon. This would make the first point of def matter less, and it starts going crazy at the second point of defence. Up to you.

Oh, and one other advantage to win% is you don't have any columns that are undefined. If unit B can't damage unit A, then unit A has a 100% chance of victory provided that it can hit successfully and cause damage while hitting.

Also, I still say that if you truly want to get an average over time, you'd need to do a lot more starting situations. Even if you just look at stats starting between 11 and 20 (keeping hp a constant, say, 30), that's still 1 hundred thousand different possibilities for str, skl, spd, lck, def. And since both unit A and unit B can start that way, that gives you 10 billion different initial comparisons. And since you need to add 1 to 10 to each stat (and hp), each unit A v unit B will give you 61 comparisons for your chart (going by win%. If you go with your current method that makes 81 comparisons). Basically, you've got your untouched stats, where you just look at A v B. That's 1. Then you've got the comparisons where you have added to a stat. You add 1 to 10 to each stat, and there are 6 stats. Hence, 61 comparisons. In total, you would have 610 billion comparisons. 100 billion for each stat + the 10 billion base comparisons. You can average out each stat over those 100 billion different values and then you'll get a much more accurate idea of how much each stat helps you out. To tell you the truth, I'm not sure precisely how best to do this part. Each of the 10 billion unit A and unit B combinations would have a different base win%. Perhaps for each of the 66 comparisons resulting from a single AvB combination, you could take the new win% and divide it by the old win% to get a %increase/decrease in win% (positive is increase, negative is decrease). Then if you add up all your different values, you'd get the average increase in win% for +1 in each stat. This reintroduces the potential for undefined values, as it is possible some base unit As will be incapable of beating a unit B. It also introduces the possibility for heavy skewing. A unit A that does 1 damage to a unit B will likely have a win% that is extremely low. Like, 0.1%. But certain additions could bring it up to 50%. This would be 500x improvement. However, since you have 100 billion different win% for each stat, I don't think it will skew your results too heavily because it isn't exactly a common occurrence. To avoid the potential 0% problem, all you have to do is use 10 mt weapons. At most, there is a 9 point difference between initial strength and initial defence, since both unit A and B start between 11 and 20 str/def. Thus there will never be a unit A incapable of beating a unit B.

I really don't think Excel is capable of this, by the way, but various programming languages should be able to pull it off.

Also, using the 610 billion different values should help strength a little bit. At 10 damage to 30 hp, there's only so much up to +10 strength can do. At most, it changes a 3HKO into a 2HKO. However, some of the unit A's will only do 3 damage to 30 hp. +7 str makes a 3HKO instead of a 10HKO. Even +1 str turns a 10HKO into an 8HKO. It might still be advisable to use a base of 37 hp (it's prime and higher than 35. Another good number is 43), or even to add hp to the altering of the initial stats of unit A and unit B. This takes things from 10 billion AvBs to 1 trillion AvBs, but oh well.

That would require a monstrous bit of math methinks, and since speed doesn't determine who goes first in-game it makes things even trickier. I have an idea that involves comparing the #RTK for each unit, and that should net a similar outcome without all the tedious, time consuming calculations.

I increased the hit percentage to 70%, and I also noticed that currently the critical bonus is 0, so I'm thinking of adding 5 base crit to take into account the crit bonus from skill, and crit defense from Luck.

Edited August 16, 2010 by Alondite

[bunny: spider bitten]

If anything, it should be assumed that all player characters are attacking second. Most battles will occur during the enemy phase. Also, if your goal is to balance the games, suggestions I'd have to make would be taking one move away from mounted classes at least, and an increase value of resistance(If only because the natural magic user layout in 6-8 will have a higher resistance and, as such, this can serve as a minor balance regardless.

EDIT: Also consider the standard 'STR as CON' patch. This will give your proposed layout more strength early on.

Edited August 17, 2010 by bunny: Now with Pancakes