I think what you are missing here is the fact that attributes are THE numbers that express true ability of a player in this game. The fact that you still see variations in stats (e.g., every time you simulate a season), is purely due to sampling effect due to natural random variation; if you fix player attributes, keep repeating the simulation, and accumulate enough sample size, and do appropriate analysis, then you will actually find there are pretty clear and (somewhat simple) relations between attributes and the stats that the simulation engine produces.
And it is actually true that something like Contact = 65 is meant to produce a .260 hitter at the MLB level. I lost the exact mappings B Ma revealed long time ago, but there are relations like this for all attributes. Sure, you will actually see Contact = 65 hitter hitting .230 or even .290 in any given season, but that's not because the game internally modules his ability to hit for a .260 any given time... it's only because he got (un)lucky, and the sample size isn't big enough within a season for his stats to equilibrate to .260 closely.
In such a case, you should always make your plan using attributes over stats, because only thing stats tell us is how the player over/under-performed to that point in season, relative to his expected performance level (which attributes accurately describe).
To me, that really robs us of one of the most fascinating aspects of appreciating baseball... all those imaginative elements between stats and baseball action itself. I think baseball stats are interesting because, while they are extensive and have come a long way with sabermetrics, they are still mysterious in a lot of ways, and when you look at basic stats and how players perform, there are still many "why is this?" moments. (Not to mention baseball stats look aesthetically beautiful... but that's just me.)
Players highly touted by scouts have often failed... great minor-league stats often not translating to MLB performance... players mysteriously upping their game all of sudden and vice versa.
All these fun stuff happens largely because we don't have access to complete information of player ability in real life.
Unfortunately, console video games tend to reduce all that imaginative exercises to simple numbers like OVR and non-obscured attributes.
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