I agree a 1d60 would have a higher potential but a low chance of getting high numbers. Which is why there will be +1s to it. So far the dice in my mind is the potential one has and the + is your actual base level of skill. Weight lifters can have a 1d20 to strength potential and can roll a 1 on strength feats but the +10 will assure they at least get 11. Another example is a sniper. He can have the potential from his experience to have a 1d10 in overall accuracy and a +5 as his/hers skill set that doesn't dip any lower (unless considerable factors hinder him/her) than a even 6. 

So the dice is the potential to max out for higher feats but the +1s count for the persons earned natural status. Im contemplating a 1d2+1 being newbie level. With it going up by 1 for every 2 levels. So a 1d4+2 then 1d5+2, then 1d6+3, 1d8+4, 1d10+5 etc.