Actually, while the repeated 20s may not actually be complained about, they have been noted as an example of the bias being spoken of.
For a median, are you talking about introducing a bell curve towards the median of results? That would be just a repeat of the same problem, though with a differing trend.
As to the potential problems with my open line suggestion, I don't see there being significantly more issues than we already face with people making mistakes, but perhaps I am wrong there.
I have not received feedback so I just went ahead and did two things that apply only to the Dice related to the Quick Reply box within Topics:
1. The Dice box is much smaller with no scrolling. On small mobile devices you may need to scroll on the X axis to see the last option for the "Amt." Drop down menu but it is far better than loads of scrolling as it was before.
2. There is a new "Shall I Tweak Rolls?" checkbox that is already checked by default. If it is used then your Dice rolls will be slightly tweaked based on my description above though to what level or how it is done I will not mention here so I can get more unbiased feedback. When a line of rolls is tweaked then "+ tweaked" will show for that line but there will be no indication as to which number was tweaked only that one of them within that line was tweaked.
Feel free to use in your games and see if it better serves your purposes. If it does I will port it over to the "Add Reply" page and add in some conditions for its use.
Extra Bonus: Since I was on a roll (Pun intended) I added something that Dungeon Masters / Game Masters may like which is the ability to see all Dice rolls, made within their games, without delay.
There are some things to consider, for instance a Player still has 30 minutes to edit (Redo) their rolls if they think they forgot something. Therefore, if you rush to use their rolls then you might end up with a problem if they change it later. Even so, this will be great for the Dungeon Master / GM because they will not have to wait to see their own rolls and can make calculations right away.
Okay, I'm not sure how you thought the tweaks, as described, would actually help the issue. That just covers it up with a new one.
Introducing a new bias away from the extremes would reduce the occurrence of said extremes, but it does not actually get you closer to the goal of an unbiased data set.
I will say that I much appreciate the ability to see rolls ahead of when they're unveiled to everyone else.
I will repeat what I said…
We break from Embedded Dice Support to share correct from past times:
Today is: 30th March (GMT), in history on the 30th of March, 1986 AD the following event happened:
5th NCAA Women Basketball Championship: Texas beats Southern California 97-81