Is it fair to expect  a 1911-Ty Cobb, 1921- Babe Ruth,  1908-Nap Lajoie, etc will perform better in a $180 mill cap vs a $255 mill cap.  Or even better in a $160 mill cap ?? 

In a nutshell, yes, for the reason that in a $255 mil cap league, they'll be facing 95 Maddux and 00 Pedro in practically every series.

Yes, but marginally so. The difference in players at $180m and $255m is mostly relegated to the benches, so they'll be facing mostly the same pitchers, but there might be a few slightly lower quality pitchers around the league. There is a bigger difference, I think, between $160m and $180m than between $180m and $255m. As the lower quality of players is almost entirely relegated to starters between $160m and $180m.

Thanks ... I would like to see what a 1911 Ty Cobb or a 1921 Babe Ruth would do in a $160 mill cap league.  Would they exceed their real stats ?  I know you would eat up much of your cap for 1 guy.  But, very interesting.  I presume the '95 Maddux ... '00 Martinez would do real well also ?

Has anyone tried to put together a team ... in a low cap league ... with a high dollar HOF'er or two ?  If so, what were the overall results them and your team.

I've run a few $60m leagues where I've required owners to have either two $9m+ players or one $12m+ player, but that's a league where everyone is doing that.

In an OL I once entered a team with both the '04 Bonds and the '20 Ruth. That team won 89 games and missed the playoffs.

Anything 80M and over is a better league than a RL league (for example last years WS winners come in at 66M).  Therefore, even super players are more likely to underperform.  The only things that would pump their stats is being in an OL with owners who have very bad teams, or by putting them in stadiums that magnify their strengths.