If you are rolling 1d20+50 vs a DC of 80 then of course you're hosed. But the size of the modifier doesn't determine that - I mean, you'd be hosed if you were rolling 1d20+5.At the first few levels, one d20 did just fine, but in time, you get some hefty DCs, like an Escape Artist check at a DC of 80 allows you to fit your head into a space thats way smaller than it for example, and one 1d20 will have to mave a modifier of at least 50 for it to be reasonable to do.
Of course I can change some of the math, but as written, 50 dwarfs 1d20 by a longshot in my humble opinion.
Whereas if you're roling 1d20+50 vs a DC of 60 then the die roll is just as important as rolling 1d20+5 vs a DC of 15. In either case, you succeed 55% of the time.
Hence my point - it's not the size of the modifier that determines the relevance of the d20; rather, it's the difference of modifier and DC. If that difference lies outside the interval of 2 to 20 then we have either auto-success or auto-fail. If not, then the die roll matters.
I'm not 100% sure what you mean here, but there is absolutley no difference, mathematically speaking, between rolling 1d2+50 against a DC of 60 and rolling 1d20+5 against a DC of 15. In neither case does the die or the modifier contribute differently to the result - in both cases the modifier brings it about that the die roll needs to be at least 10 for the check to succeed, and in both cases the actual rolling of the die then determines whether or not the roll equals or exceeds that requirement.At very low levels, because modifiers are so small, the d20 is a much bigger contributor to your final score; at very high levels, the d20 is a relatively small component of the whole, with the modifier being the thing.
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it feels better if the die and the modifier are contributing about equally to the result.
If the game doesn't have DCs, and so it's simply all about rolling as high as possible, then of course a bigger modifier will contribute more to the total, compare to the die roll, than does a smaller modifier. But as far as I know there is no version of D&D which is simply about rolling as high as possible and then having the GM arbitrate that. There's always a target number (whether from the matrices charts in AD&D, or the DCs that are set out in 3E and 4e).
Now this I do understand, and I agree it's an important issue. 4e takes a two-pronged approach - take some steps to keep numbers close together, and have rules that systematically produce a spread of DCs to be reached.That, and the difference between the modifiers of a character who is 'good' at something vs one who is 'poor' at that thing. The "Epic Level Handbook" spends quite a lot of time discussing it, but the big takeaway is that it's quite easy to have one character who can save on a '2' and another who needs a '20'.
In combat, in my current 4e campaign the lowest bonus on a character sheet is the invoker/wizards's +18 to hit on oppy attacks with his sceptre, and the highest bonus is +25 for some of the martial PCs. At their level average ACs are around 35-ish, so the invoker/wizard has little chance of hitting, while the martial PCs have quite a good chance, especially with advantage or modest buffing.
With skills the spread is much wider (and I would think that this is pretty common, given the way the designers have patched and repatched to cope): skill bonuses go as low as +7 (the fully armoured paladin trying Acrobatics or Stealth) and as high as +36 (the invoker-wizard using History, or using Religion to perform a ritual); and the typical "good" skill bonus is around +25. The system tries to cope with this by having Easy, Medium and Hard DCs for each level, and by then encouraging encounter design that builds in DCs at all levels (either directly, or as unlockable via good play). The +36 is auto-success even against a Hard DC for that character, but that is a class feature - the Sage of Ages, instead of a stat boost at 21st level, gets +6 to all knowledge skills - so this is a player who has traded off combat ability for out-of-combat skill. (The notion that 4e does not permit this is a mere rumour not warranted by the actual design of the game!)