While I like statistical analysis, and you obviously know your stuff in that regard, I don't think this particular test shows much of anything.
As you said in your paper, the stat generation system used is not orthodox, meaning this isn't going to tell us much about actual characters (who will not have their scores placed in order). It doesn't tell us much about the system, as one party is built to purpose (the Orc), while the other is a random pile of numbers poured into an often ill-fitting mold. It doesn't even tell us much about ability scores, as the character is not designed to utilize them to any particular extent.
That Strength is king is no surprise, both because this is the common wisdom and because of the test parameters. The lack of Weapon Finesse and choice of weapon and armor severely reduce the value of Dexterity. I also saw no mention of Initiative or flat-footedness, which would alter the results. Additionally, Figure 4 is incorrect. A character's first hit die is maximized, meaning your numbers are totally off. This will likely change the relative value of Constitution.
I really like the idea of this, and hope you do other examinations in the future. However, going forward, I'd recommend looking at very specific propositions, with a greater attention to how things will be going in terms of actual gameplay. For example, a more specific test on the relative value (in relation to survival) of placing the 2nd and 3rd highest scores in Dexterity or Constitution could be quite enlightening.
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Interesting read! Was the Orc you used the same Orc out of the Bestiary? Did you change anything with the Orc (no feats or racial scores)? While the fighters used no feats or ability modifiers, the Orc does. The orc's AC, HP, and strength (plus the Orc ferocity ability) would show an unfair bias towards the Orc.
Perhaps you could run a test with 1,000,000 random stat fighters fighting 1,000,000 random stat fighters (all with standard gear) to see how ability scores affect the outcome.
The other thing is that tactics make a huge difference. E.g., does the player setup ambush and get a couple of rounds of arrow fire off before the Orc closes? What about allies and assistance? What about fighting defensively vs. not, or moving to gain tactical advantage on the battlefield?
The Orc wasn't built to purpose, it was randomly generated - I could have generated one randomly for every battle but then I'd probably need to analyze its stats too, so I figured it was simpler to standardize the orc (in any case standardization just means rolling hit points once - the rest of an Orc's stats are fixed).
I don't think I explained particularly well. When I say "Built to purpose," I mean it is designed for combat. The standard Bestiary Orc has its ability score array placed in a way that emphasizes combat, with a high Strength and at least moderate Dexterity and Constitution. That it slaughters Fighters with ability scores placed in order should be no surprise, at it has had its ability scores placed purposefully for advantage in this situation. That is why I don't think the analysis shows much about the deadliness of the system as a whole, and makes the line in your conclusion ("and in the absence of feats it appears that Pathfinder is an extremely nasty environment for solo adventuring") less supported.
The results surprised me - I thought that dexterity would be more important. A dex of 18 vs. a dex of 3 means your AC differs by 8 (40% reduction in hit chance) and your initiative increases by 8. I would have thought that would make a huge difference even without any special feats, but it doesn't.
Slight error: your AC will only differ by 6 in this scenario. Chainmail Armor has a maximum dexterity bonus of +2. Or did you mean a Chain Shirt (+4 AC and +4 Max Dex)? Regardless, I'm not incredibly surprised about Dexterity. Going first doesn't matter as much as successfully hitting and the chance to take the enemy out in a single swing, which is all Strength in this scenario. With the randomized hitpoints the Orc has a even better than normal chance of taking out the Fighter in a single swing, reducing the number of times it will have to break through AC to win (and thus reducing the value of Dex/AC compared to maximized hitpoints).
I'll update that in a subsequent post.(The main reason constitution is a weak stat in this analysis is that the random variation in hps washes it out - so this finding is valid for D&D 3.5 rather than Pathfinder).
It will be interesting to see the results. I'd imagine Constitution will still not be particularly important, but at least more important than it currently is.
First, though, I want to add feats. With hps maximized at level 1, toughness would be more important than I expected. My guess is that power attack will be a thorough dud. I'm not going to test the full range of feats, of course (I only have one life), but any predictions or suggestions would be appreciated.
Power Attack will be interesting. I'd imagine, at this level, it would be most important to those with moderate Strength, as the bonus damage will increase the likelihood of taking out the enemy in a single swing (though using a one-handed weapon makes this more questionable). Remember, though, that it has a minimum Strength requirement of 13. I'm not sure how that can be integrated into the current system of ability scores, but from the rest of this I'm confident you'll find a mathematically acceptable way.
Though I don't think their is enough data to create a true statistical model, you could speculate. Which is always fun.
1. I'm a little curious about why you're bothering to roll up the stats at all, rather than just creating an array of fighters of all possible starting stats. Does the fact that you only have 745 Str 3 fighters limit the significance of findings? Especially since those fighters are spread over 256 values of Con & Dex? Why not just make 250 fighters of each of the possible stat arrays from 3/3/3 to 18/18/18 so as to get adequate sampling within each?
2. Your Footnote 2 does provide a good explanation of why to do it the way you did it, rather than the way I suggest in 1, supra.
3. I notice that you're not considering any racial stat bonuses here: would it make sense to expand the test range to 3-20, assuming for example that a goodly number of Human or Half-Orc fighters would apply their +2 to a physical stat?
4. As you pursue future research grants, I might suggest a panel study to do followups on the subjects of this research and their descendents. I might hypothesize that since high strength fighters are much more likely than high dexterity fighters to return from battle triumphantly, and therefore to attract the attention of the most comely of village lads or lasses, that the baby boom resulting from your study is likely to produce a high ratio of Paladins to Bards, through the inheritance of a high Str/high Cha combo as much more likely than a high Dex/high Cha combo. (This study would be complicated by the fact that RAW, as far as I'm aware, lacks any rules for heredity of ability scores.)
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HangarFlying, the Orc is just a basic bad guy from the online bestiary. I didn't do anything except roll the HPs. I did some initial testing with a Goblin (same CR) and it was completely useless, I think because its attack stats are weak. I guess if I gave the fighters a falchion things might have gone better for them, the poor fools.
As I mentioned to Mort, the random fighter vs. random fighter thing makes the stats much harder to do. At this stage I'm more interested in just randomizing one side of the battlefield. It restricts the questions one can ask but at least makes the results comprehensible.
tonyz, I doubt I'll ever be incorporating much in the way of tactics. I'm not going to write a whole computer game and run a million simulations with it while I have a day job!
Goblins are weak compared to orcs, but then again goblins are built for stealth not brute force. But you do have a good point regarding making it against one opponent rather than varying opponents.
A few things to keep in mind for future tests. The PCs, being fighters, get full hp (as someone else already astutely pointed out. The Orc, as a warrior, would have hp, though I believe common practice uses average hp (don't know if it would be easier on you to use average hp or not - or if it would give a more accurate representation because that is what would be most likely encountered). Finally, orcs have "ferocity" which means they can still keep fighting (though they are staggered) until their hp falls to a negative amount equal to their constitution score. This last part might skew the numbers even farther in favor of the Orc.
This analysis is interesting, but I don't think it provides much in the area of usable information.
Nobody is going to create a fighter with a str and dex of 5 and try to fight an orc. To model the effectiveness of such a fighter is a waste of time.
To make this approach more statistically viable and get results that are more usable, you should instead randomize a 15, 20 or 25 point buy and use some reasonable boundaries for str, dex and con. Then you'll end up with some usable results.
If I am understanding your system, you have a tremendous amount of "noise" in your data in the form of fighters who would never actually exist and are not viable no matter what their str, dex or con is.
For the sake of gaining usable info, you should also randomize their armor, going from leather armor up to plate armor, so that you can pull out data where dex does or does not factor into armor selection.
How are you running this simulation? Is it in java? Are you using a spreadsheet?
Whilst I don't think randomising the stats over the entire range matters much, it seems to me that randomising hit points (for the fighter) is an error. The impact of con on the survival of a fighter with 1hp is negligible and will be dragging down the overall impact, I suspect.
I wonder what the average damage the Orc inflicts is? Whatever this value is, any fighter with HP below this value dies immediately.
This is where the CON stat is important. The average bestiary Orc is using a falchion, doing 2d4+4 damage. That is averaging 8.5 damage a hit. That is enough to kill any fighter with a lower than normal con. I would think if the fighter had enough hit points, that would allow a second swing to kill the Orc and survive the battle.
I'm eager to see what if the fighter was using the same weapon, or if the Orc wasn't using the (arguably) most powerful melee weapon.
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great post. However as was pointed out to me by the group I played with today-there are two things that can drastically cut the life span of your character.
1. Painting the miniature
2. typing up a back history
as soon as you do either of these, you character will die much faster
while statistical analysis is always interesting, I doubt those results are relevant when in real play. On the other hand I don't know how one would conduct a valid test, it's probably even more awefully conditioned than the stock market.
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Well, the guy admitted that these tests were being run using flat stats, no racial adjustments, nor including any feats. And while he admits to a procedural error regarding first HD full hp, I don't think his hypothesis is invalid. I think it's interesting to note that STR more than DEX or CON is a determining factor for survivability.
...I think it's interesting to note that STR more than DEX or CON is a determining factor for survivability.
Until you get hit by an Disintegrate or singing for the great Bogawuus pleasure is the only way to prevent death in the stake pits of Muzmuz ;-)
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Morty
might I suggest "the power gamers 3.5 Warrior Strategy guide" by goodman games.
They break down the two weapon fighter Two handed weapon fighter, and sword and shield fighters statistically. They also break down lots of other stuff as well. with your interest in statistics, you might find this book interesting.
Elyas
Faustusnotes, there are no meek orcs. Ferocity is a racial trait. Humans are DOOOOOOOOOOOOOOOOOMED! Unless humans procreate at a faster rate than orcs, in which case, humans can counter with numbers).
Orcs are by far the absolute meanest brute enemies at low levels. Primarily due to their built in diehard, but the +4 strength racial makes them very dangerous as well. I've had CR 1/4 naked berserker orcs (that is, 1st level orc warriors who wear no clothing and fight with sticks and stones) who are terrifying.
However, even against equal numbers, they can be taken down by humans and other core races. A big part of it is equipment and preparation, and sometimes a good matchup. Focus firing can bring an orc apart easily enough. Using terrain can make it difficult for an orc to close. Fire-bombing is brutally effective at low levels (4 PCs vs 3 orcs = throw 4 alchemist fire on orc #1, he dies, repeat for orc #2 and #3, they die, loot the bodies for 260 gp worth of gear each, pays for the alchemist fires with loot left over).
Then there's just good old fashioned running. Pop some caltrops and take off. Consider hit and run tactics. Goblins are physically weaker than PC classes but excel at hit and run tactics. PCs can do the same versus enemies who are stronger than themselves. There's also the fact once an orc has been staggered, they are incredibly easy to kite.
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My play experience has been that having good combat stats will *decrease* a characters life expectancy.
The reason for that is that the better your combat stats, the more likely you are to actually engage in combat. Actually engaging in combat will decrease your character's life expectancy by more than having good stats will increase it.
The most survivable character is the one with either the Charisma to defuse the combat, or the Dexterity to successfully avoid being hit while they run away.
Once you assume that the combat will take place, you've already wiped out the most important variable.
This looks really cool, and I gotta take a bettwer look, but have 2cp to throw at this...
Question, how are you determining AC? How would the value of dex shift in the case of a tank? If a character has a longsword/bastard-sword and shield, can the character's ac be brought up to the point where a higher dex makes a bigger difference? Or taking into account finesse, can a high dex granting ac and boosting accuracy make up for strength? What effect does a boost to con have on a character like that? Lower damage, but has the high AC to avoid more hits and the HP to take an extra hit. Does that grant decent survivability?