If we want to go with just anecdotal evidence, let's take the team we know the very most about: the Boston Red Sox.
Rotations: focus on 1-2 punches and how many GS outside the top 4-5 SP'ers.)
1967: Lonborg "and 3 days of rain." (He started 39 games in a different era.)
Lee Stange 2.77 is awesome, but he pitched in relief for 11 of his 35 games.
Gary Bell 3.16 for 24 starts was awesome, too.
Darrell Brandon 4.17 (19 GS and 20 RP gms)
56 GS by 8 others (including 11 Bennett & Santiago, 9 Morehead, 8 by Rohr & Waslewski)
By the stats, it looks like they had 2-3 solid SP'ers, but in that era, it was really only 1.
1972 (missed the ALCS by 0.5 games in the unbalanced games played strike year)
35 Pattin 3.24 (looks like an ace in today's game, but not then.)
30 Siebert 3.80 (a decent #2)
22 McGlothen 3.41
21 Curtis 3.73
19 Tiant 1.91
(27 GS by others, including 16 by Culp and 7 Krausse)
This was a decent rotation, and we don't know how they might have done had they made the 4 team playoffs.)
(The '73 team won more games than '72 but finished 6 games out: Tiant 35/3.34, Lee 33/2.75, Curtis 30/3.58, Pattin 30/4.32, 15 Moret 15/3.17 and only 19 GS by others.)
Here is where I feel "the era" changed...
1975 Does not checked either box, but Tiant, Wise and Lee were a better 1-2-3 than surrounding years.
35 Tiant 4.02 (Hero in the playoffs)
35 Wise 3.95
34 Lee 3.95
20 Cleveland 4.43
16 Moret 3.60
20 by others: 11 Pole 4.42
I'd argue this was a deeper rotation than previous seasons, but it still lacked a serious 1-2 punch.
1977 team won more games than 1975, but finished 2.5 out.
4 of the top 4 SP'ers by GS had ERAs over 4.26. (Tiant was at 4.53 and Jenkins was #2 at 3.68)
1978 won 99 games and missed playoffs due to 163 game loss to NYY
36 Torres 3.96
35 Eck 2.99
31 Tiant 3.31
24 Lee 3.46
16 Wright 3.57
(11 Ripley 5.55 & 10 by others.)
This team seemed to have the formula to win. A nice 1-2-3 punch with Lee as the #4.
1986 lost WS in 7 games to NYM
33 Clemens 2.48 (perhaps the best SP the Sox have ever had, along with Pedro.)
30 Boyd 3.78 (nice numbers, but I'm not sure we can say he was a solid #2 punch.)
26 Nipper 5.38 (Yikes!)
25 Hurst 2.99 (could be viewed as a solid #2)
16 Seaver 3.80
31 by others (10 Sellers 4.94/ 6 by Brown 5.34)
1995 finished first in 3 division AL
29 Erik Hanson 4.24
27 Wake 2.95
23 Clemens 4.18
21 Z Smith 5.61
14 Eshelman 4.85
32 by others (12 Cormier 4.07)
1998 a 92 win team that made the playoffs as a WC team thanks to Pedro
33 Pedro 2.89
33 Wake 4.58
31 Saberhagen 3.96 (a decent #2, that year)
23 Avery 5.02
10 Lowe 4.03
32 by others (8 by Wasdin 5.25, Schourek 4.30 and Rose 6.93)
1999 a 94 win team that lost in the ALCS
29 Pedro 2.07 (WOW!)
27 Portugal 5.51
26 Rapp 4.12
22 Saberhagen 2.95
18 Rose 4.87
40 by others (17 Wake 5.08)
(2002 won 93 games and missed the playoffs: (32 Lowe 2.58, 30 Pedro 2.26 was a great 1-2 punch! Then, 29 Burkett 4.53, 23 Castillo 5.07, 15 Wake 2.81 w 30 gms as RP) 33 GS by others (12 Fossum 3.46)
2003 We all know the story of 2003
33 Wake 4.09
33 Lowe 4.47
30 Burkett 5.15
29 Pedro 2.22
That's a lot of starts from the top 4, but no solid 1-2 punch)
14 Fossum 5.47
23 by others is low. (10 Suppan 5.57)
2004 First Ring in over 8 decades! Checked both boxes: Great 1-2 punch and minimal starts outside the top 4-5 in the rotation:
33 Pedro 3.90 124 ERA+ in this hitter's era
33 Lowe 5.42
32 Schill 3.26 148 ERA+
30 Wake 4.87
29 Arroyo 4.03 (120 ERA+)
Only 5 GS outside the top 5! Lowe and Wake did not have great seasons.
2005 won 95 games but lost in ALDS (No Pedro & Lowe)
33 Wake 4.15
32 Arroyo 4.51
32 Clement 4.57
30 Wells 4.45
16 W Miller 4.95
19 by others (11 by Schill 5.69)
It's amazing we won so many games with this rotation, but we did not get far in the playoffs.
2007 World Champs, again! (Beckett & Schilling as the solid 1-2 punch, but not much support beyond them.)
32 Dice-K 4.40
31 Wake 4.76 (almost 400 IP from our 3-4 SP'ers)
30 Beckett 3.27
24 Schilling 3.87
23 Tavarez 5.15
22 GS from others (11 by Lester at 4.57 and 7 by Gabbard at 3.73)
(2008 won 95 games and lost in the ALCS: 33 Lester 3.21, 30 Wake 4.13, 29 Dice-K 2.90- maybe a good #2, that year, 27 Beckett 4.03, 15 Buch 6.75) 29 by others. Once could argue this rotation had a pretty solid 1-2-3 and they should have gone farther.)
(2009 also won 95 games but lost in the ALDS: 32 Beckett 3.86, 32 Lester 3.41, 24 Penny 5.61, 21 Wake 4.58, 16 Buch 4.21 but 37 by others w 12 by Dice-K 5.76 and 8 by Smoltz at 8.33.) We had a decent 1-2 punch but not much more.)
2013 was the 3rd ring! 97 win team: Had a 1-2 punch but 28 GS outside the top 5.
33 Lester 3.75
29 Lackey 3.52
29 Dempster 4.57
27 Doubront 4.32
16 Buch 1.74 (WOW!)
Added Peavy 10 GS with a 4.04 ERA
(2016 won 93 games and lost in ALDS: 35 Price 3.99, 33 Porcello 3.15 was a solid 1-2, but then... 24 Wright 3.33, 21 Buch 4.78, 20 ERod 4.71 and 29 by others w 13 by Pom at 4.59.)
(2017 also won 93 games, but Price was hurt: 33 Porcello 4.65, 32 Sale 2.90, 32 Pom 3.32, 24 ERod 4.19, 15 Fister 4.88 and 26 by others w Price at 11/3.38)
2018 was the 4th ring year! It had a very decent 1-2-3 and even 1-2-3-4 punch- 5 with Nate added.
33 Porcello 4.28
30 Price 3.58
27 Sale 2.11 (WOW!)
23 ERod 3.82
11 Nate 3.33
38 by others does not "check the second box, but the trade for Nate explains some of this. 13 GS by Johnson 4.17, 11 by Pom 6.08, 8 Velezquez 3.28)
(2021 won 92 games and went farther than many imagined: 32 Nate 3.75, 31 ERod 4.74, 31 Pivetta 4.53, 22 Richards 4.87 some as RP, 22 Perez 4.74 some as RP, 25 by others w 13 by Houck at 3.52. Erod did not really provide the 2nd "punch.")
It's my contention that having a solid 1-2 (or 1-2-3) punch with fewer GS outside the top 4-5 best SP'ers does not guarantee a ring, but with very few exceptions, every ring year we had checked both boxes. Many seasons we came close also checked both boxes or checked one box with emphasis.
There are other ways to win rings. The Sox have not been very good at winning rings without 2-3 solid SP'ers in the rotation. This does not mean we cannot win, unless we have 2-3, but to me, pitching has always been the best key to winning. Not the only one, but the best.