Rapid Shot analysis by Sean Reynolds

[mmu1]

Excuse me? But what are you talking about? As the SRD says right above, Shield and Armor enhancement bonuses DO stack. If you have a +5 Shield and +5 Armor, you get an armor class of 10 (base)+ 10 (enhancement +5/+5) + 2 (Large Shield Bonus) + 8 (Plate Armor bonus) + 1 (dex).

I'm talking about the fact that armor and shield stacking has a single benefit (increases AC) and bow and arrow stacking has a double benefit - it increases both the chance to hit and the damage.

And, again, there is no real equivalency between armor and shield stacking and bow and arrow stacking, no "archer vs. non-archer" issue. Using a shield involves a trade-off. It is not a flat-out bonus for everyone that doesn't use a bow, not a freebie like the bow and arrow stacking. In other words, the former is an example of good design (and bad nomenclature, shields should simply give a "Shield" bonus to AC, that way this whole ridiculous argument wouldn't even exist), the latter isn't. Any similarity between them is semantic, and it proves nothing, but you've latched onto it blindly.

 

[Ondo]

Sean calculated the percentages correctly and, in fact, does take hitting with both shots into account. Here's an example:


BAB Odds/Each Hit Odds/Any Hit Difference
-3/-3 35% 58% +8%


To calculate the chance of each hitting you simply multipy your chances of hitting (7 out of 20) times 5% and arrive at 35% for any one, single hit. So far, so good.

To calculate the chance of any hit you must calculate the following situations:
First Hit/ Second Miss = (35%)*(65%) = 22.75%
First Miss/ Second Miss = (65%) * (35%) = 22.75%
First Hit/ Second Hit = (35%) * (35%) = 12.25%

Add together and you get 57.75% which rounds to 58%. Or the easy way is 100% - [the chance of both attacks missing (65%) times (65%%)= 42.75%] = 57.75%. Either way, Sean learned his Statistics 101 well...As for Rapid Shot being too powerful at -2; for me, it's a game and if this gives a slight advantage to the PCs, no big deal. Making sure they can do the math to calculate their AC and to hit bonuses, that's another story... (But then again, I am a math teacher)

The very, very significant fact that you and Sean miss is that hitting with two arrows is twice as good as hitting with one. Your both treating it as though it were the same. Double that percantage to get the average number of times you hit and you get 70%, exactly double the original 35% and a far, far more relevant number.

Think about it. If you had a 100% chance to hit with one shot, or you could shot 2 with still a 100% chance, shooting two would be twice as good. Sean's analysis says it would be no benefit at all.

 

[Morpheus]

The very, very significant fact that you and Sean miss is that hitting with two arrows is twice as good as hitting with one. Your both treating it as though it were the same. Double that percantage to get the average number of times you hit and you get 70%, exactly double the original 35% and a far, far more relevant number.

Think about it. If you had a 100% chance to hit with one shot, or you could shot 2 with still a 100% chance, shooting two would be twice as good. Sean's analysis says it would be no benefit at all.

I'm still trying to figure out what this is saying and I read it over three hours ago. 35% + 35% = 70%? That's how probability works? I'm going back to get a refund on my master's because I never learned that.

I know that has to be the point because in an earlier post:


Let's take a look...

Using AC 15 and -2 for each shot, we got:

Chance of any, one Single Hit: 20%
Chance of Both Hits 4%
Chance of Both Missing: 64%
Chance of Hitting at least Once: 36%

AC 17 and -2 for each shot:

Chance of any, one Single Hit: 10%
Chance of Both Hits 1%
Chance of Both Missing: 81%
Chance of Hitting at least Once: 19%

Which very clearly states the percentage for both arrows hitting. Now, I admit, this is a somewhat simplistic view without the myriad of possibilities (iterative attacks, Dex. bonuses, etc), but I think that the point Sean was making was that it seemed to increase the PCs chances to hit more so than other feats or abilities. Do I agree with him? I don't really care. What I do care about is that people understand where and how he arrived at his conclusion using math (which he did correctly).
Others may argue that the Expected Value of damage done is a more accurate measure of this debate. Again, I could care less. Just make sure the math is right and let others come up with their own conclusions.

 

[Elder-Basilisk]

I think that the point he's making is that rapid shot does much more than increase the possibility of hitting with ONE arrow. It also grants the possibility of hitting with two arrows (and in most situations I've experienced as a player, it's more like a foregone conclusion than a possibility). Thus it has an exponential effect on average damage per round which is different from the effect of a simple increase in the possibility of hitting once that doesn't hold out the possibility of hitting twice (weapon focus is an example of this).

To use a simple example, take
A. a single attack which hits 60% of the time for an average of 10 points of damage. Compare that to the following:
B. 2 attacks that deal an average of ten points of damage each--both of which hit 50% of the time. (equivalent to rapid shot)
C. A single attack which hits 75% of the time for an average of 10 points of damage. (equivalent to a +3 bonus to hit in this case)

Hit frequency
A. Hits 60% of the time
B. Hits at least once 75% of the time; hits twice 25% of the time.
C. Hits 75% of the time

Average Damage Per Round
A. 6 points
B. 10 points
C. 7.5 points

Both options B and C increase the chance of hitting to 75% of the time but because option B offers the chance of hitting twice, it yields 33% more average damage per round than option C.

My understanding of the criticism is that Sean's analysis focusses on the chance of hitting and doesn't adequately deal with the exponential increase of average damage per round.

Unlike Sean, it appears that the previous poster and I both believe that average damage per round rather than chance of hitting is the relevant factor WRT balance. You appear to understand this distinction but I thought I'd spell the criticism of Sean's position out more clearly.

Which very clearly states the percentage for both arrows hitting. Now, I admit, this is a somewhat simplistic view without the myriad of possibilities (iterative attacks, Dex. bonuses, etc), but I think that the point Sean was making was that it seemed to increase the PCs chances to hit more so than other feats or abilities. Do I agree with him? I don't really care. What I do care about is that people understand where and how he arrived at his conclusion using math (which he did correctly).
Others may argue that the Expected Value of damage done is a more accurate measure of this debate. Again, I could care less. Just make sure the math is right and let others come up with their own conclusions.

 

[Ondo]

I'm still trying to figure out what this is saying and I read it over three hours ago. 35% + 35% = 70%? That's how probability works? I'm going back to get a refund on my master's because I never learned that.

If you flip a coin twice, you'll get heads once on average. If you shoot two arrows with a 50% chance to hit, you'll get 1 hit on average, not 3/4 of a hit, even though you'll only get at least one hit 75% of the time.

What I do care about is that people understand where and how he arrived at his conclusion using math (which he did correctly).

Doing the math correctly is far less important than knowing what math to do, which he failed at miserably. If Rapid Shot let you roll twice and take the best result his math would be appropriate. It doesn't, it gives you another attack.

 

[green slime]

While we are griping about archers:

The REAL REAL problem I have with archery is this - That GMW affects FIFTY arrows.

I don't mind arrows and bows stacking attack bonus and damage; If you purchase magical arrows, they cost the earth, and are single shot weapons. I mean if you are prepared to blow 100,000 gp to purchase a +5 Bow with 50 matching +5 arrows, then go ahead stack it all on.

IMO is GMW shouldn't affect 50 arrows on a single casting. ONE arrow. That would put an end to that abuse, and cause players to carefully harbour the use of their magical arrows.

And then Rapid Shot becomes far less of a problem...

 

[Bagpuss]

Okay heres another table.

D20 Roll is the roll need to hit with a normal attack
% change in damage is the average expected increase for using rapid shot so 100% would be the same damage, 200% would be double, 50% half a normal attack, etc. The number in brackets is the penalty for Rapid Shot.

[color=white]
D20 Roll     % change in      % change in      % change in
                damage (-2)      damage (-3)      damage (-4)
 2                178.95%            168.42%           157.89%
 3                177.78%            166.67%           155.56%
 4                176.47%            164.71%           152.94%
 5                175.00%            162.50%           150.00%
 6                173.33%            160.00%           146.67%
 7                171.43%            157.14%           142.86%
 8                169.23%            153.85%           138.46%
 9                166.67%            150.00%           133.33%
10                163.64%            145.45%           127.27%
11                160.00%            140.00%           120.00%
12                155.56%            133.33%           111.11%
13                150.00%            125.00%           100.00%
14                142.86%            114.29%            85.71%
15                133.33%            100.00%            66.67%
16                120.00%             80.00%            40.00%
17                100.00%             50.00%            50.00%
18                 66.67%             66.67%            66.67%
19                100.00%            100.00%           100.00%
20                200.00%            200.00%           200.00%
[/color]

Now considering that if a balanced encounter you often need at least a roll of 8 to hit the target with your primary attack, so really you need to be looking at the lower end of that table.

If you increased the penalty for Rapid Shot to 3, then for about a 3rd of encounters Rapid Shot is either no help or a penalty, actually reducing the damage you are likely to cause.

 

[mmu1]

If you flip a coin twice, you'll get heads once on average. If you shoot two arrows with a 50% chance to hit, you'll get 1 hit on average, not 3/4 of a hit, even though you'll only get at least one hit 75% of the time.

Actually, you're wrong. You'll get heads once 50% of the time, and at least one head 75% of the time. Your average chance of doing something at least once in a series of attempts is never one (100%) unless you also have a 100% chance of suceeding on every individual attempt.

If you shoot two arrows with a 50% chance of hitting with each, you'll on average do one hit's worth of damage, because of the 25% chance of hitting with two arrows.

But the average to hit probability is 75%.

 

[mmu1]

While we are griping about archers:

The REAL REAL problem I have with archery is this - That GMW affects FIFTY arrows.

I don't mind arrows and bows stacking attack bonus and damage; If you purchase magical arrows, they cost the earth, and are single shot weapons. I mean if you are prepared to blow 100,000 gp to purchase a +5 Bow with 50 matching +5 arrows, then go ahead stack it all on.

IMO is GMW shouldn't affect 50 arrows on a single casting. ONE arrow. That would put an end to that abuse, and cause players to carefully harbour the use of their magical arrows.

And then Rapid Shot becomes far less of a problem...

One arrow is probably going a bit far in the other direction... I think one arrow / caster level would be a better way of doing it.

Although personally, I'm flat out in favor of removing stacking... Have bows add to both to hit and damage, and bypass damage reduction, and be done with it.

 

[Rel]

This has been a very interesting thread to read. Interestingly, not a single player in any of our campaigns has taken Rapid Shot. I think this is largely because we have a fairly small group (3 Players + GM) so it is hard to have a dedicated archer.

Along those lines, I had one point to mention about the feat expenditure comparison with melee fighting. I think that Precise Shot should be factored in to the equation.

My reasoning is this: There are a few likely encounter scenarios that parties tend to run into. A small number of powerful enemies, a few (or a single) powerful enemy and some mooks, or a bunch of mooks.

If there are only a few (or a single) enemies, the melee fighters will engage them fairly quickly and the archer will be forced to fire into melee. This means that without Precise Shot they will suffer an extra -4 on top of any cover that their own team is providing to the enemy. If there are a bunch of bad guys, it is likely that they will be able to maneuver around the "front line" and penetrate into the group deep enough to attack the archers in melee. This means that archery itself is going to become a less optimal tactic.