Post/Author/DateTime	Post
zoneout 12-27-06, 09:01 PM	Please forgive me but it has just been too long since I had this in school for me to remember what I need to do. I am trying to work out some basic numbers on a 1st level fighter (12hp, AC 17, Atk bonus +5, dmg d8+3) being attacked by 4 goblins (5hp, AC 15, Atk bonus +3, dmg d4). Based on the above numbers I have guessed that it would take 6 hits for the goblins to bring down the fighter at average damage (12/2 = 6). I have also guessed that it would take the fighter 4 hits to bring down the 4 goblins at average damage (4 + 3 = 7 > 5, so one hit per goblin, 4 goblins). In addition I have guessed that the fighter has a 40% chance to hit on any attack and a goblin has a 30% chance to hit on any attack: chance to hit = (20 + atk bonus - opp AC ) / 20 Finally I have guessed that it would take 10 attacks for the fighter to likely get 4 hits on the goblins (7 if he has cleave) and 20 attacks for the goblins to get 6 hits on the fighter: no. of attacks = no. of hits needed / % chance to hit (i.e., 4 / .4 = 10) So...how many rounds will it take for each to acheive its objective? I can guess 10 on the fighter (or 7 if he has cleave), but the number of rounds for the goblins to get 20 attacks in depends on how many are left standing as the rounds go by. I figure a .35 probability that on any attack the fighter will hit and kill any goblin (7/8 * .4 = .35). Thanks for any input and I appologize if I have mangled the science of probability and / or if the answer is too simple for me to remember.
Jaxgaret 12-27-06, 10:08 PM	Average d4 roll = 2.5 Average d6 roll = 3.5 Average d8 roll = 4.5 etc. Thought this might help you :)
Ilion 12-27-06, 10:25 PM	First off, I think your numbers are basically sound. Jaxgaret is right about the averages, and in fact that small difference means that the goblins should need only 5 hits on average (rather than 6) to take down the fighter. Now, in an actual game there are a lot of variables. Does the fighter have the Cleave feat? He could theoretically even have Great Cleave if he's a human, and get 'em all in one round. :) If the goblins flank him their chance to hit goes up significantly and our hero is in trouble. I would say ignore it, but if all 4 goblins attack him in one round they really can't avoid flanking. Let's say the goblins have to attack single file along a narrow bridge or something. The fighter hits on a 10 or less (55% of the time). So let's say he takes out a goblin every other round. That's 8 rounds of single-goblin attacks. Clearly the fighter will be fine barring really lucky goblin rolls. If they surround him and ALL get flanking bonuses, their chance to hit goes from 35% to 45%. Again let's just round to 50% for simplicity and say they'll do 5 points of damage (2 hits at 2.5 points each). So if they win init, they'll get 5 points of damage in the first round. If they fighter misses his attack, they'll do another 5 the second round before he knocks one off. After that it gets more complicated, but I think our boy has had it. So to answer your question: It depends! :)
Jaxgaret 12-27-06, 10:28 PM	Please forgive me but it has just been too long since I had this in school for me to remember what I need to do. I am trying to work out some basic numbers on a 1st level fighter (12hp, AC 17, Atk bonus +5, dmg d8+3) being attacked by 4 goblins (5hp, AC 15, Atk bonus +3, dmg d4). Okay, the Fighter has a 55% chance of hitting a goblin with each swing, and does an average of 7.5 damage without crits. More importantly, unless the Fighter rolls a 1 for damage, he is dropping a Goblin each time he hits them. So the Fighter will drop a Goblin 7 out of 8 hits. So he'll pretty much drop a Goblin every other round, so it will take on average 8 rounds to take out the Goblins, if he doesn't have Cleave. If he has Cleave, then it'll take on average 5-6 rounds. The Goblins have a 35% chance of hitting the Fighter with each swing, and do an average of 2.5 damage per swing without crits. This is an average of a little less than 1 damage per round each, say .9 damage. Since there are 4 Goblins, this means that they will do about 3.5 damage the first round, and if the Fighter doesn't have Cleave, almost half a damage less per round, due to Goblin deaths. So, on average, they'll do 3.6 + 3.15 + 2.7 + 2.25 + 1.8 + 1.35 + .9 + .45 damage, dropping the Fighter in the 4th or 5th round. If the Fighter does have cleave, then the Goblins will die more quickly, doing roughly 3.6 + 3 + 2.4 + 1.8 + 1.2 + .6 damage on average, dropping the Fighter in the 5th or 6th round, which makes for about an even fight. These are all very rough estimates. Anyone got a better shot at it? EDIT: Darn it, forgot about flanking. Yeah, the Fighter pretty much bites it if you include flanking bonuses, barring a Great Cleave.
highbulp 12-27-06, 10:40 PM	Fighter with +5 to attack hits an AC 15 55% of the time. So fighter hits 55% of the time for an average of 7.5 (4.5+3), meaning the fighter is dealing an expected damage of .55*7.5 = 4.125dmg a round. The goblins each have 5hp, so it is expected that the fighter will take 2 rounds to down each goblin, or a total of 8 rounds to kill all the goblins. The goblins with a +3 to attack hit an AC 17 35% of the time, for an average of 2.5dmg, so do an expected damage of .35*2.5=.875damage a round (each). There are 4 goblins, so they do a total expected damage of 3.5damage a round, meaning they will be able to deal 12 damage to the fighter in 4 rounds. This assumes a number of things: that the fighter does nothing other than attack (factoring in Feats like Cleave or Power Attack change the numbers of course). It also doesn't consider how each time the fighter takes out a goblin, it reduces the amount of damage the goblins are taking, which depends on who goes first (does the first goblin die before he gets his second attack?). It also does nothing with flanking, critical hits, or any other of the literally hundreds of variables, including DM ones (like, what happens on a natural 1?). And of course, these are just averages--a particular fight make go better or worse for the fighter depending on the rolls.
Fallenangel359 12-28-06, 06:16 PM	Remember, the more goblins the fighter drops, the less damage per round the goblins will be doing.
zoneout 12-28-06, 06:34 PM	Thanks for your help. Boy I really missed the boat on the flanking and average damage issues and I thank Jaxgaret and Ilion for bringing that up. Thanks to Highbulp as well. Fallenangel: Exactly! Hope to find a decent answer! I guess I should tell y'all what I am up to. Basically, the challenge rating system doesn't make sense to me. When I throw an encounter at some of my players, who are experienced, they usually chew them up and spit them back...or they die horrible, horrible deaths, nothing in between. It is even worse when the CR is less than one. So I devised this idea: Create an index on the number of creatures (in this first case goblins) that it takes to match up with a Mr. Vanilla first level fighter. They will fight to their maximum abilities (i.e., if they have the sense to flank, they will flank) and the number I am looking for would allow for the the fighter to win 50% of the time and the goblins to win 50% of the time. The dynamics of combat enter into this and tactics, perhaps something I layout on the map for my players would be their edge, their way to win vs lose. The numbers might even help plan out a combat as a villan would to max out chances of an opponent, and parties thinking they might have an easy time would find instead they are in a tight spot! Once I can get the math right, I hope to have a matrix of PC classes (again all at first level) to see what each class adds to the party. Even healing potions or other available healing would make a difference. And then expand to other creatures or NPCs as well. An ambitious project I know. Below is my first level fighter, done with the DMG point buy method. Let me know what you think. Mr. Vanilla STR 16, Dex 12, Con 14, Int 10, Wis 10, Cha 9, Skills: Climb 7, Jump 7, Swim 7, Tumble 3, Longsword, shortbow, light mace, scale mail, large wooden shield, power attack, cleave, weapon focus (longsword), 38 gp. Dinner is NOW, will update to standard stat block soon.
highbulp 12-28-06, 06:53 PM	Theoretically, this is what the CR system has done (though how well it has done it's job is obviously debatable). Trying to create any kind of "standard" for an encounter is inherantly impossible, because each party is different. So all you're doing is designing your own CR system, which may or may not work any better than the normal one. I use CR as a guideline for finding encounters. If I'm looking through a book and see a CR10 creature, I know that my 3rd level players probably won't be able to take it on. But I tend to look for anything in the range from CR 0 to twice to party level (so for a 3rd level party, I'd even consider creatures listed as CR6, though they would only be bosses likely). Then, rather than trying to compare only two numbers (the PCs level to the CR), I compare a bunch of things. I look at the creature's average/max damage. How fast will that down one of the players in my campaign? I then look at the creature's AC. Will my players be able to hit it ever? I look at the number of hitpoints. Will this battle take way too long? Are my players going to kill this thing in one hit before it gets off it's special fun attack? Basically, you want to look at the entire creature, compare it to your particular group, and then decide how challenging it would be. CR is simply a guideline. Nothing more.
BW0222 12-28-06, 09:44 PM	zoneout, Combat almost never works out that way. First, there is always movement and position involved. This makes it extremely difficult to guess on the numbers and types of attacks. For example, the fighter might move up and attack a single goblin next to a wall. The other goblins might never be able to all get next to the fighter. They might need to rely on ranged weapons -- bringing cover, firing into melee, and ammunition into the equation. Second, there is often lighting conditions, surprise, critical hits, terrain, furnature, equipment (oil, tanglefoot bags, etc.) etc. to consider which can dramatically affect combat, yet is not factored into simple hit and damage numbers. Third, there are often various tactics which either side could employ. Flanking and cleave was mentioned. There is also fighting defensively, total defense, jumping on a table to get a height advantage. Forth, there is often psychological factors to consider. The goblins don't know that one is a 1st-level fighter -- nor does the fighter know what the goblin are (they could be warriors, commoners, or 4th-level fighters). The goblins aren't suicidal and may flee or surrender rather than fight to the dead. If the fighter killed two goblins in two rounds, or the last six goblin attacks missed, most goblins would be assuming that they can't win the fight and considering fleeing. If you surprised them, or are yelling back down the hallway, they might assume more of you are coming and their only thought might be to flee. Even if you didn't kill one -- chances are he'd flee (or move back and use less affective missile weapons) if reduced to 1hp anyway. On the flip side, if you missed six times and they hit twice... you'd likely switch tactics -- drinking a potion, fleeing, moving back to a doorway and getting them one at a time. What would you do if they pulled out whistles and started blowing them?
Mogofeiden 12-28-06, 10:23 PM	zoneout, BW0222 is right. However, the CR system is geared for a 4 man party where the EL equals the average lv of the PCs. Meaning that, barring exceptional circunstances, the PCs win as their enemies are always at 1/4 strenght. A 50/50 situation means if the PCs lose its a TPK. With the CR system they might lose 1 member but they'll win the fight. Players know this so, it might take a few TPKs before they're in the same page as you. If you want a 50/50 or 1:1 situation think if the PCs were NPCs what would be their EL? 4 lv1 PCs @1cr per lv per PC = EL4 (DMG guidelines)
zoneout 12-29-06, 07:56 PM	Thanks again to all who have taken the time to consider this issue. I see everyone's point and agree. However, a 50 - 50 matchup on the basic points may be a good one, letting the combat turn on tactics and combat choices, forcing the players, once in a while, to outsmart what they are facing. Knowing my luck I'd probably kill every PC on the first try...and have to call up a troop of 10th level clerics, resurection scrolls in hand, to get the PCs up an going.