Why so hostile? Why do you think I'm having trouble evaluating advantage?Yes it is. But against a variable target you can take the average. But obviously you don't know how math works and such. Compare it against a static number and you know what is better. Too bad it was lost but we had it calculated. I won't do it for you again.
Actually what is your problem understanding that you can compare a bonus against advantage and look what is better?
And why do you think I was asking for your calculations? I don't need your calculations, I just said what the benefit of advantage is: it's not a static number like +4, it's variable.
If you have a 50-50 shot at making your roll (that is, you need to roll an 11 or better), advantage is at its most advantageous and you get a +25% (percentage points) increase, which, translated to a d20 means +5.
That is, your chance goes up from 50% to 75% = +5
At the other end is the situation where you only miss on a 1, or only succeed on a 20. In this case advantage gives you a second chance of rolling that specific number (which is 5%) - so you get about a +1.
That is, your chance goes up from the chance of rolling a 20 on a d20 on a single try (5%) to the chance of rolling one 20 on two tries (nearly 10%) = +1
In no way is it helpful to try to boil down this range (a bell curve from +1 up to +5 and back down again to +1) to a single number. +2, +3 or +4 doesn't matter; they're all correct.
And they are all wrong too.
Have a nice day
Edit: Do note that none of this is specifically tied to initiative. The above is true for any roll involving what D&D calls "advantage".
As for initiative, I haven't seen your numbers, but since every campaign is different, there really is no useful way of calculating an "average" here, unless you do it after the campaign is finished. You certainly can't just sum up the bonus for all monster/NPC initiatives from +0 to +10 (say) and calculate how much adventage helps you, and then divide by ten. Nor can you calculate the average from all the MM monsters, since no real-life campaign contains one specimen of each monster race.
In the end, the conclusion must be that no single number is actually helpful. The only thing you can say is stuff like "against monsters with the same initiative bonus as you, advantage is incredibly helpful" and "if you're especially slow, advantage on initiative is not going to change much, I'm afraid - you're much better off looking for Dexterity bonuses instead".
And still, it doesn't paint a complete picture. When you have advantage you no longer have any reason to hunt for advantage. This impact of this - in how actual play changes - cannot be underestimated.