The Home Run Derby is tonight so I jumped on Pine to do some research.  I pulled up some key numbers, ran some Monte Carlo simulations, and here's what I found...

I first looked at each player's total home runs this season and total at bats.



I then looked at the average "Park Factor - Home Run" for each player this season.



This got me the home run % per at bat for each player as well as whether, on average, they were in stadiums that were easier or harder to hit home runs in.  Here's a chart with all this info:

SeedBatter NameHR/ABHR/AB %Avg PF-HRAdj. HR/AB%
1Kyle Schwarber29/3368.63%98.68898.70%
2Pete Alonso24/3347.19%98.65227.25%
3Corey Seager22/3466.36%98.45456.42%
4Juan Soto20/3126.41%103.07696.18%
5José Ramírez19/3305.76%1035.55%
6Julio Rodriguez16/3464.62%98.09894.68%
7Ronald Acuña Jr.8/2303.48%102.94923.36%
8Albert Pujols6/1494.03%90.188684.41%


As you can see, the seedings are relatively good, with the potential exception of Albert Pujols who could be 7th seed.  Armed with these percentages, I did a Monte Carlo simulation (simulating 100 pitches with these HR rates) where each bracket was played 10,000 times.  Here's what I got:

No. 1 Kyle Schwarber vs. No. 8 Albert Pujols

Kyle Schwarber  won 8571 times (91.3%)
Albert Pujols  won 816 times (8.7%)

No. 2 Pete Alonso vs. No. 7 Ronald Acuña Jr.

Pete Alonso won 8591 times (91.7%)
Ronald Acuña Jr.  won 778 times (8.3%)

No. 3 Corey Seager vs. No. 6 Julio Rodriguez

Corey Seager  won 6534 times (73.11%)
Julio Rodriguez  won 2403 times (26.89%)

No. 4 Juan Soto vs. No. 5 José Ramírez

Juan Soto won 5179 times (58.72%)
José Ramírez won 3641 times (41.28%)

No. 1 Kyle Schwarber vs. No. 4 Juan Soto 

Kyle Schwarber won 7092 times (77.64%)
Juan Soto won 2043 times (22.36%)

No. 2 Pete Alonso vs. No. 3 Corey Seager 

Pete Alonso won 5344 times (60.04%)
Corey Seager won 3557 times (39.96%)

No. 1 Kyle Schwarber vs. No. 2 Pete Alonso

Kyle Schwarber won 6016 times (66.42%)
Pete Alonso won 3041 times (33.58%)

This is just a rough estimate.  Hope it helps!  It does match the Pine Parlay of the Day... BOL!!