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2 years ago ::
Jun 09, 2008 - 5:39PM
#1
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I created a spreadsheet to compare rolling twice and taking the largest (Danger Sense), and just adding 4 to your initiative (Improved Initiative).
Improved Initiative had an average of 14.5, while Danger Sense had an average of 13.8.
If initiative matters to you and you need to choose between these, it looks like Improved Initiative, which is available in the Heroic Tier, is the preferable one.
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2 years ago ::
Jun 09, 2008 - 6:13PM
#2
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Incorrect, because the distribution for Danger Sense isn't uniform -- it's heavily slanted towards the higher numbers. For example, 20 is the most common result.
Sometimes mean ≠ mode.
That said: take both, or take Quick Draw and Danger Sense.
Cheers, -- N
Want your forums to look like forums? Use FireFox + Stylish + this Stylish script. UPDATED September 9, 2009.
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2 years ago ::
Jun 09, 2008 - 10:56PM
#3
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However, Danger Sense gives you zero results above 20, while Imp. Init. has 21-24 each occurring equally as often as 5-20.
Consider it this way: at what N added to a single roll, will the result be statistically higher than the maximum of two rolls? 1? 4? 10? 20?
I don't have the math to calculate that formally. But experimentally, with 10,000 trials in Excel, +1 and +2 are lower than the max of two, +3 is almost equal (within about 3%), and +4 gives greater results around 25% of the time, or a ratio of 0.8:1 in favor of I.I.
Improved Initiative is the better deal of the two.
You're right that the bare average isn't necessarily informative: I found that at +3, the average for the high value is slightly higher than that of the single roll, but the single +3 still "beat" the other method a slight majority of the time. Without knowing how to calculate the odds, the experimental method consistently reveals which is actually more benefit.
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2 years ago ::
Jun 10, 2008 - 12:01AM
#4
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Ziana, the point is that while Improved Initiative is clearly better for getting a higher initiative roll most of the time, Danger Sense is (for obvious reasons) better at preventing a low roll. Some people think that's important, and there's been an ongoing discussion as to how much it matters. In any event, taking both is clearly the right call. 
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2 years ago ::
Jun 10, 2008 - 12:15AM
#5
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Danger Sense is (for obvious reasons) better at preventing a low roll.
DS will statistically skew to 20, but it's still possible to roll a 1. With II you can't roll lower than 5.
Some people think that's important
Isn't statistically having the higher roll more of the time of the most value? That's what II offers.
taking both is clearly the right call.
Only if you consider initiative that essential, and you're willing to give up two feats to maximize. If someone only has room for one, then if they want to be higher on the initiative list, more often, then II appears to be the way to go.
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2 years ago ::
Jun 10, 2008 - 12:31AM
#6
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The average for 2dK drop lowest is:
SUM (n*(2*n-1), n, 1, K) / K^2
which works out to: (K+1)*(4*K-1)/(6*K), for any die size K.
d20+4, avg = 14.5
2d20, drop1, avg = 13.825
Here's how you can work it out yourself:
Use 2d4, make a grid:
....1 2 3 4
1| 1 2 3 4
2| 2 2 3 4
3| 3 3 3 4
4| 4 4 4 4
The top row is the result of die 1, the column is die 2. The number in each grid represents the value of the roll. If you rolled a 2 and a 3, you drop the 2 and have 3. The odds of getting any grid result is 1/16. So, just add up all 16 numbers in the grid and divide by 16.
You can figure out the formulas for 3dK drop 1 etc this way, it just takes some time.
Cheers,
The Hanker Chief
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2 years ago ::
Jun 10, 2008 - 6:54AM
#7
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DS is better if you already have a high initiative modifier (relative to enemies).
II will be better if you have a low modifier.
..but people spending a Feat here will often already have a high modifier or want both.
It doesn't help that you apparently usually fight enemies that have a couple of levels on you.
Initaitive is a lot more important to some classes than others. The main one to care that won't have a massive Dex is Wizards.
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2 years ago ::
Jun 10, 2008 - 7:24AM
#8
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DS will statistically skew to 20, but it's still possible to roll a 1. With II you can't roll lower than 5.
Isn't statistically having the higher roll more of the time of the most value? That's what II offers.
Only if you consider initiative that essential, and you're willing to give up two feats to maximize. If someone only has room for one, then if they want to be higher on the initiative list, more often, then II appears to be the way to go.
The only thing initiative boosters are good for is getting a higher result than your enemies. Pretty obvious, but necessary to point out.
The only stats you're looking at are min roll, mean roll, and max roll. That's a good starting point, but it doesn't tell the whole story. Improved Initiative is a better feat when the number you need to roll to win initiative is between 2 and 6 or 16 and up. In between that, DS is better.
Does anyone have numbers on what sort of init bonuses you're looking at from monsters at various ranges? If we have that we can compare average rolls from monsters and how likely a character with each is to win initiative.
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2 years ago ::
Jun 10, 2008 - 8:00AM
#9
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While you're at it you might look at how important winning initiative is to those monsters.
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2 years ago ::
Jun 10, 2008 - 4:04PM
#10
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The only thing initiative boosters are good for is getting a higher result than your enemies. Pretty obvious, but necessary to point out.
The only stats you're looking at are min roll, mean roll, and max roll. That's a good starting point, but it doesn't tell the whole story. Improved Initiative is a better feat when the number you need to roll to win initiative is between 2 and 6 or 16 and up. In between that, DS is better.
Does anyone have numbers on what sort of init bonuses you're looking at from monsters at various ranges? If we have that we can compare average rolls from monsters and how likely a character with each is to win initiative.
I worked out the math for a few cases and then did a numeric simulation using matlab at work to check (a million opposed rollls for each initiative value from 20 above to 20 below the character's) and I found that II is always better than DS. By better I mean a higher probability of beating a monster's initiative.
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