Improved Initiative is objectively better than Danger Sense

[Flipguarder]

So I think we landed on a quick saying that informs people interested in the topic.

"If you wanna go sooner, get danger sense, if you're tired of going last, take improved initiative. If you want to go first, take both."

 

[Stuntman]

I enjoy the chance of rolling the dice twice, but even if Stuntman's math is correct, dont you think the diference is all too small?

The difference between II and DS is that the person choosing II will beat the person choosing DS 55.5% of the time. DS is really close to a +3 Initiative modifier. An initiative modifer of +3 will beat DS by only 50.7% of the time.

A paragon feat should be better tham a heroic one, and it does not seems to be, unless...

The way I see it, Improved Initiative is probably the feat most players are familiar with. It's exactly the same as the 3E feat. Danger Sense seems like a feat you can take in addition to II. II allows you to win initiative more at the heroic tier and then if you want an even bigger boost, you have to wait until paragon teir to take DS. The exact values are close enough anyway that it doesn't make much of a difference.

I do agree that if a player does not take II at all and then reaches paragon tier, that player may be mislead into believing that DS is better for him than II. In any case, the difference is not that great and it may even be the case that DS may be better for the player in question.

If we consider all that powers/feats that allow a friend to reroll dice and/or add something to the result? Would that change the math balance?

I am under the impression that things get even worse for Danger Sense...

I would say that the more other bonuses you get to initiative, the more likely DS is better for you compared to II. The exact nature of the bonus would change the calculations. A strict +2 to +10 bonus to initiative will make DS a slightly better feat than II. I'm not sure about rerolls, though as I haven't made those calculations. Rerolls for rerolls will make the calculations more complex than bonuses.

 

[Mad Hamish]

The other thing to consider is Danger Sense and Quickdraw as a combination.

 

[Eldorian]

The statistics in this thread are misleading.

Danger sense decreases variance of your initiative, meaning that you're less likely to get a lower roll. This means that if there are several competing monsters, you're less likely to lose to all of them, and less likely to beat all of them, than with improved initiative.

 

[DracoSuave]

The statistics in this thread are misleading.

Danger sense decreases variance of your initiative, meaning that you're less likely to get a lower roll. This means that if there are several competing monsters, you're less likely to lose to all of them, and less likely to beat all of them, than with improved initiative.

Actually, it does increase your likelyhood of higher initiative, while decreasing your variance--it doesn't act on a bellcurve like you think.

You have 39 outcomes where you roll a 20, 37 where you roll a 19, etc. The median for this would be 15, as opposed to on a bellcurve which would be 10. This means that you have ~50/50 shot of rolling higher than 14, give or take a trivially small number of outcomes. Normally that median is between 10 or 11.

As well, with a bell curve, the mode is the same as the median, 10 or 11, and the average is 10.5. With Danger Sense, your mode is 20, which is what causes a straight linear curve rather than a bell curve.

It -does- add consistancy: You consistantly roll higher.

 

[Stuntman]

The statistics in this thread are misleading.

Danger sense decreases variance of your initiative, meaning that you're less likely to get a lower roll. This means that if there are several competing monsters, you're less likely to lose to all of them, and less likely to beat all of them, than with improved initiative.

The +4 you get from Improved Initiative also means you're less likely to get a lower roll. Your old lower rolls become medium rolls and your medium rolls become higher rolls and your higher rolls become extremely higher rolls. Also, you will not get extremely low rolls. Also, the +4 to initiative means you will more likely win the tie breaker in the event of a tied initiative. Initiative modifier is one of the tie breakers that Improved Initiative modifies, but Danger Sense does not.

 

[bonus]

Ah, I didn't consider that you have to just beat the other guys, yeah. Great analysis! Very cool stuff.

 

[Eldorian]

Actually, it does increase your likelyhood of higher initiative, while decreasing your variance--it doesn't act on a bellcurve like you think.

You have 39 outcomes where you roll a 20, 37 where you roll a 19, etc. The median for this would be 15, as opposed to on a bellcurve which would be 10. This means that you have ~50/50 shot of rolling higher than 14, give or take a trivially small number of outcomes. Normally that median is between 10 or 11.

As well, with a bell curve, the mode is the same as the median, 10 or 11, and the average is 10.5. With Danger Sense, your mode is 20, which is what causes a straight linear curve rather than a bell curve.

It -does- add consistancy: You consistantly roll higher.

Why must a bell curve have a mean of 10.5 for it to be a bell curve? Also, where did I claim it was a bell curve? Where did I claim that it didn't increase expected value?

All I claimed was that it reduced variance. Consistency is not a defined term in regards to statistics, as far as I know.

 

[Ferret]

The +4 you get from Improved Initiative also means you're less likely to get a lower roll. Your old lower rolls become medium rolls and your medium rolls become higher rolls and your higher rolls become extremely higher rolls. Also, you will not get extremely low rolls. Also, the +4 to initiative means you will more likely win the tie breaker in the event of a tied initiative. Initiative modifier is one of the tie breakers that Improved Initiative modifies, but Danger Sense does not.

But if you get a low roll, say a 1, then II makes that 5. If you have DS and you roll a one then you get another go, 75% chance of beating that 5. So there is a 25% chance you'll not win that tie.

Like everyone says, DS is reduscing the chance of a low roll. II is boosting your low roll, but that's no guarantee it will be high (granted 75% isn't a guarantee, but it's good!).

Roll a ten, and you get a 14, with DS you get a ten and then re roll, 35% chance to win.

Say you now roll a twenty, Woo! You now have a score of 24. Wow, Roll a twenty with DS and you don't win.

As you can see, II relies on you getting a good roll, you have to roll well for it to pay off. Not as well as without it, but still well, i.e rolling a 5 is still as likely as rolling a 10, or ten. Granted you'll never roll a one... DS on the other hand gives you consistently better rolls, regardless of the first one, a 20 is 4 times more likely than a 5. And with DS a roll of 5 or less is 6.25% likely, which is negligible.

 

[Minigiant]

DS keeps you from going last. II lets you go first.

With DS, there a very low chance you will be the last or second to last person in a normal fight due to rerolling. With II, there a high chance you will be one of the first 3 persons in a normal fight due to your higher potential initiative result.