I'm not sure, if those numbers include the pre-1994 seasons. I'm going by recent years. The playoffs changed in 1995, and team budget disparities ballooned almsot exponentially in the early to mid 2000's. When budgets were more bunched, it was likely more random.
Opening Day Team payrolls:
2000: NYY 93K, LAD 88K, ATL 85K, BAL 81K
#15 58K
#30 17K
2001: NYY 110K, BOS 110K, LAD 109K, NYM 93K
#15 $63K
#30 $24K
2002: NYY 126K, BOS 108K, TX 105K, AZ 103
#15 61K
#30 34K
2003:NYY 153K, NYM 117, ATL 106, LAD 106
#15 71K
#30 20K
2004: NYY 183, BOS 125, LAA 101, 101
#15 65K
#30 28K
2005: NYY 206, BOS 121, NYM 105, PHI 95
#15 69K
#30 30K
...
2019: BOS 205, CUBS 205, NYY 205, SFG 178
#15 125K
#30 53K
Where we can pick the starting point matters, but let's say in 2003:
(League Ranking by Wins- 1 to 4 per league)
2003: FLA 3> NYY 1
2004: BOS 2> STL 1
2005: CWS 1> HOU 3
2006: STL 4> DET 3 (2 wins from #1)
2007: BOS 1> COL 1
2008: PHI 2> TBR 2
2009: NYY 1> PHI 2
2010: SFG 2> TX 4
2011: STL 4> TX 2
Play-In Game Starts (12 teams make POs, so 1-6 in each league):
2012: SFG 3> DET 6
2013: BOS 1> STL 1
2014: SFG 4> KC 4
2015: KC 1> NYM 6
2016: Cubs 1> CLE 2
2017: HOU 1> LAD 1
2018: BOS 1>LAD 3
2019: HOU 1 vs WAS 3
5 of the last 17 World Series Champs were NOT top 2 in their league. If it were random, we'd expect 8-9.
13 out of 34 League Champions were NOT top 2 in their league. One would expect 16-18, if it were random.
World Series Champs Rankings in their league - last 17 years:
1st: 9 wins if HOU wins, 8 if not
2nd: 3 wins
3rd: 2 wins if HOU wins, 3 if not
4th: 3 wins
1st: 8-9
All Others combined : 8-9
1st or 2nd: 11-12
All Others: 5-6
The 4 years from 2011 to 2014 looked random. The rest: not even close.