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Summary (with a couple extras), of chance of being mid-tier with choice to play up or down:
Random table, Season 0-3: 41%
Random table, Season 4: 55%
Random 6 player table, Season 0-3, : 16%
Random S4 table, "play w/friend" chance*: 45%
*: 1 in 3 chance of each subsequent player to have a character w/in 1 level of the previous player.
Fromper: I'm mostly addressing the initial state when people sit down, assuming that most people have some idea of what character they wish to play. There are certainly things that can be done to reduce the issue, though saying it's 20% or lower is inaccurate. However to address your points:
1) Groups of friends can be: a) too small to affect the balance significantly, or b) not the exact same level.
2) Bigger cons are rare. Scheduling multiple tables of one scenario at a gameday can be very frustrating (from experience). Local organization can help.
3) Game day is new - very valid point, though when new you tend to grow quickly, and then potentially split the experienced group due to random attendance changes.
4) You have an interesting point here. However, it's somewhat likely that the L.3 players will gravitate to the 3-7, and the level 5 players will gravitate to the 1-5, so as not to be mid-tier.
5) When you bring your 3rd, 4th, and 6th level PCs to Rivalry's End, which are Shadow Lodge? If it was just the 6th, you'd be heavily inclined to play that one I imagine. Ignoring specific scenarios like this, it again goes to the "initial state" vs "negotiated end".
Non-hypothetical example: I played my L.7 character in a 3-4 tier Shadow's Last Stand, part II, because I had played him a year and a half earlier in part I. I could have switched to a L.3 that fit the table better, but didn't want to. If the rest of the table had been a little higher, that could have pushed us to a L.5 average (we had 6 players) and resulted in a choice. For me, it didn't matter up or down, so most likely we would have stayed 3-4, but the choice is there.

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But just because the player is demanding that they do something they aren't allowed to do (as the APL clearly falls squarely within subtier 4-5, even with a season 4 scenario)
…
The correct response is "I'm sorry, but with the characters we have at this table, the party must play subtier 4-5; we literally cannot play down."
You DO realize that when those VC are talking about the choice to play up or down within the guidelines, they MEAN FOLLOW THE APL RULES RIGHT?!? If the party APL is not an average of 3, there is no option to choose in a 1-5 scenario. No if and or buts about it. The GM in your example flat out ignored the APL rule.
The way we calculate average party level is broken, it should only include the four highest level PCs. Example is with a tier 1-5 scenario.
Example #1: Four level 4 PCs = APL 4 and they play at subtier 4-5.
Example #2: The group in example #1 is joined by a level 1 PC. APL 3.4, the table can now decide to play up or down. Level 1 guy decides he doesn’t want to play up. GM is concedes and tells the table they have to play down to subtier 1-2.
Apparently, the consensus is that this is a fair outcome, but I don’t think so.
Guys, while I appreciate your response, I did present the example above which you ignored multiple times.
Four level 4 players (which is clearly APL 4 and therefore subtier 4-5) are then joined by a level 1 PC, which makes the table APL 3.4, which gets rounded down to 3. Then it’s the player’s choice to play up or down and this is where we get into situations where one player can veto an entire table of players, thanks to some help from some GMs that automatically make a table play down if only one player wants to play down.
Also, please consider the other subtiers (3-7, 5-9, 7-11). If you had a 4 player table at subtier 10-11, would you really appreciate a level 7 player joining and demanding the table play down and because of that, the GM automatically appeases the player and forces everyone to subtier 7-8?

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I understand that. I have never seen anyone be a jerk over this. However, this is anecdotal and evidently it is common? Sorta common?
Maybe I've just had a disproportionately high amount of tables where there was no question.
I'm with you on this David. I've hardly ever seen it. That's why I said it was less than 20%... maybe for the tables I've been at, maybe less than 10%.

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I understand that. I have never seen anyone be a jerk over this. However, this is anecdotal and evidently it is common? Sorta common?
Maybe I've just had a disproportionately high amount of tables where there was no question.
I've only seen an actual pressuring come up once, at Paizocon last year, where I believe there was exactly one table of each of a huge variety of scenarios, which made it trickier than at Gencon where there would always be so many that it was hard not to muster an obvious low or high table. From that observation at Paizocon and other smaller cons (though the players didn't really pressure, it was still a question many times at Totalcon this year, maybe three quarters of tables had the choice), I'm guessing it might be fairly common at cons like that, where there are one or two tables of the same scenario at most. I pretty much never see any issues at local gamedays because our players mostly know each others' limitations and capabilities, and they choose accordingly. That and they tend to be clumped in such a way that the subtier is evident. To be fair, I'm pretty open with my opinion as to which subtier a group could play, and I'm a good judge of which is correct to challenge a given group. People usually choose to follow my advice on which subtier, and despite suggesting playing up at least 75% of the time, there's never been a time that I suggested playing up and then the party walked out with less gold than they would have playing down (that is to say, once or twice a character would die who may or may not have survived at the lower tier, we'll never know, but the extra reward pooled across the party was greater than the full cost of raise and restorations, and the players all chose to make such a pool for their brave comrade). The only wipes or near wipes I've ever seen have been at the low subtier every time. The only two TPKs I GMed were a table of entirely new characters in one of the hardest 1-2s around and a table of new characters with a very hardworking wizard trying to cover for extreme stupidity of his allies in First Steps 2, which still would have been only a single death if the inquisitor hadn't rolled a natural 1 on his true strike attack.
The pressuring at Paizocon was pretty much Jason S's example incarnate. Except we had a slightly different spread, and the one who refused to play 4-5 was level 2 and not 1. It was a total and complete cakewalk apparently (according to my friend who stayed there, and with whom I didn't get to play), even after I left the table to look for another game because I didn't want to cake through it so they had one fewer character. The GM allowed the one level 2 to dictate for the whole group (to be fair, two of the other players just generally didn't seem to care one way or the other and my friend and I definitely wanted to play up with such a strong group).