I like the three paths thing, I think it's fairly accurate.
I also think we all use (And in some cases invent) stats to attempt making difficult comparisons. So the old stats sort of work, and newer ones like WAR also work. The relative success of teams using newer stats seems to support those stats, most of which I haven't really gotten into.
All stats have some failings, things they don't and in many cases can't account for.
One of the things that's come to fascinate me about sports are what are usually called the "intangibles" Stuff that just can't be readily handled by stats.
My impressions of some of the players mentioned- all without resorting to stats, just how I recall them being a fan.
Kaat - Solid pitcher with some really good days and seasons. Lasted a long time I think because he was a reasonable negotiator who would take decent pay in return for being a player pretty much as long as he wanted.
Shilling - Also pretty solid, and a throwback who pitched a lot more innings than most modern pitchers.
Mussina- Decent pitcher, especially on a good team, and I don't really recall him pitching for a bad team, sure, the Orioles weren't the Yankees, partly because they had to play the Yankees fairly often. Could he have carried a bad team? Hard to say.
Rice - I'll admit bias here, one of my favorite players. He took a lot of heat from the press, some with reason some not. Pretty much every player in Boston does. His later years were not great, but weren't horrible. Even the better years some said he was disappointing simply because the season he had wasn't 78 (A really good maybe great season by most standards)
Glavine- Another dependable occasionally brilliant pitcher. Also a guy who kept pretty low key and went for the long view of things.
Trammell - Again, solid, durable, reliable, and constantly outshone by flashier players.
Many of the others I didn't see in their prime, or at all.
Some examples of intangible stuff?
Don Baylor - Went to the WS four straight years for four diferent teams all when he was older, and easily cut loose in favor of a younger cheaper player. But he must have had some positive effect right?
Tim Wakefield - Spotty, as most knuckleball pitchers, amazing sometimes, horrible at others. But a number of times he was asked to go out and take whatever happened over several innings to give the bullpen some rest. And hardly ever a complaint about that despite it wrecking his individual stats. How can you figure what the value that is to a team?
The modern stats I think need to be balanced with a bit of the old. The best example I can think of is the As right when modern stats were getting popular. They regularly fielded entire teams of inexpensive slightly above average players with a handful, usually pitchers who were a good deal better. And they did very well even with a lack of budget. But.......They weren't generally all that exciting. So the fans stayed away, and that's a piece of why they were stuck in the small budget category. Spending on a couple hitters who might be about the same by the numbers but might be more entertaining to watch would have served them a bit better.
Steve B
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