You need to be aware of the possibility, but to assume it's nothing but confirmation bias is pretty insulting.
That depends a lot on the assumptions being made by the person doing the back of the envelope calculations.
But ultimately, I trust the DM's assessment of the mood at the table and their assessment of the pacing of the adventure over back of the envelope calculations of someone who isn't there.
See, I don't. The DM is far too involved to be anything but biased. That was the point of my little anecdote a few pages back where no less than six other people at the same table as me couldn't see past their own gut feelings, despite being shown pretty clear math beforehand until such time as I had to actually track the damage and present it after the session. People playing are far too involved to be an unbiased observer. [MENTION=23751]Maxperson[/MENTION] pretty much admits that he isn't tracking things very closely - he doesn't know how many monsters he's using, he doesn't know how many rounds combat usually takes, he doesn't know a lot of the actual details - just his gut feeling that he needed to adjust the math 2-4 times/campaign (a still very nebulous concept since he hasn't defined what a campaign is for him) to avoid a TPK.
In my experience, this shouldn't be needed. I've never needed to adjust the numbers to avoid a TPK in the last ten years. That's through 3e, 4e AND 5e. So, we have two anedotal bits of evidence - one claims that you need to adjust the numbers to avoid TPK's and another that says, nope, the numbers are fine the way they are.
Woohoo, dueling anecdotes. Absolutely meaningless and totally unuseful. If you cannot back up the claims with a bit of math, then the claims can't actually be reproduced and are therefore meaningless.
The fact that 40% of the people responding in this thread feel that fudging is something they do without any qualifiers, means to me that there are a lot of DM's out there who really need to brush up on some statistics classes. That or they are defining fudging really, really broadly. My question to anyone who does fudge is, why do you feel the need to fudge? Are the numbers coming up that often? Why are these outlier numbers coming up so often?
Look, for my group, we generally play about 50x3 hour sessions per year (probably a bit less, maybe 45, but, work with me here, this makes the math easier). Now, we run fairly short sessions, so, generally, in 5e, we're getting in about 3 combats per session. That's 150 combats per year. Figure 4 rounds/combat, which is about right for 5e. That's 600 rounds of combat/year. Again, presume 10 attacks from the baddies per round, giving us 6000 attacks per year.
Anything that is less than 1 in 6000 might occur in that space, but, is increasingly unlikely. A TPK from a standard encounter (since an overwhelming encounter is SUPPOSED to kill PC's and we don't have to worry about that according to [MENTION=23751]Maxperson[/MENTION]) requires that the PC's miss more often than usual and the baddies hit more often - right? Standard encounter means that the PC's have about a 50-60% hit chance. The baddies should hit about the same, maybe less, say 30%. Now, work out the chances that the PC's will miss so often and the baddies hit so often that it results in a TPK. That's a heck of a lot less than 1 in 6000.
Now, [MENTION=23751]Maxperson[/MENTION] is saying he needs to step in 2-4 times per campaign. He still hasn't stated how long that is. How many hours of gameplay are we talking about. For my back of the envelope calculation, 1 year of gaming is about 150 hours of play. So, we need to know how many hours of play he considers to be a campaign so we can do comparisons. If a campaign is 10000 hours of play, then fair enough, 2-4 times to fudge probably isn't a big deal - it's just such a huge sample size that it's very likely to come up. But, if a campaign is closer to 200 hours of play, then it would be extremely unlikely that, barring changes to the rules or possible user error, you would need to step in that many times.
So, to sum up, no, I don't trust DM's perceptions of the game over the math. I've seen far too many posters try to pass off incredibly unlikely events as "evidence" to prove their point. And, just like always, when you point out that the odds of their events actually occurring are extremely remote, they get all annoyed that I'm trying to "disprove their experience." Sorry, just because you say you experienced something is not good enough. I refuse to play duelling anecdotes. Back up your point. Time after time after time, people try to pass off anecdote as proof. The plural of anecdote is not data.