One of the first things I noticed about monsters in 13th Age (which is still available for preorder as far as I know, but there are something like less than 20 Escalation Edition orders left) is that the monster stat blocks, while wonderfully simple (a GM's dream come true!) lacks any reference to a monster's attribute scores. What happens when it makes sense in the fiction for a character to make an opposed Dex, Str, etc. check against a monster?
Rolling against the DC for your environment is perhaps the simplest solution, but there's something about opposed rolls that really captures the feel of "this guy vs. that guy." Besides, what about opposing the Int of a really dumb ogre, or the Str of a tiny kobold? The normal DCs might be a bit too high for that (though opposing the ogre's Str or the kobold's Dex could easily work by boosting the DC to the hard value for the environment). Perhaps it's an aesthetic thing, but I'd really prefer that the numbers come from the monster than the environment. And it's not that complicated to derive these scores.
For Str, Dex, Con checks, roll 1d20+(PD-10)
For Int, Wis, Cha checks, roll 1d20+(MD-10)
Depending on which attribute your modified defense is standing in for, feel free to apply a +4 or -4 bonus/penalty (if it's worth adjusting the effect should be big enough to be noticeable, so just stick with +/- 4). For example, a kobold is agile but small and fragile, so a Dex check modifier might be [PD-10+4], whereas a Str check modifier might be [PD-10-4], or you might simply not apply the penalty. The goal here is simplicity, since attribute checks probably won't come up too often for monsters.
Why This Works
Think about how a player's MD/PD are determined. You use the base value for your class (10-12, which once the 10 is subtracted out will correspond to a 0 to +2 "background" point value). Then you add the median of your 3 relevant ability scores, and of course your level gets added as well. Monster PD/MD is quite a bit simpler to determine (one only has to look at the chart), but the numbers are fairly consistent with what you might expect compared with the method used for PCs.
So in summary, PD/MD is essentially 10+[better/lesser bonus]+[attribute]+[level]
Similarly, a skill checks boils down to 1d20+[background]+[attribute]+[level]
All you really have to do is substitute a d20 roll for 10 (which itself is a substitute for an assumed average d20 roll; think of it as turning an opposed attack vs defense roll into a single roll (attack) compared against a target number). The better/lesser bonus baked into the defense numbers is roughly comparable to the bonus a PC might get from a background (even if not exactly, it's not worth further complicating matters since this proposed system has the benefit of simplicity). Attribute modifier and level are already both accounted for. Finally, the optional modifier allows a GM to very easily tweak the numbers on-the-fly when the final results don't quite match up with expectations.
Now let's apply this to a monster from EE6 - the Kobold Hero. His bonus for opposed Str/Con/Dex would be +6, while Int/Wis/Cha would be +2.
So what kind of challenge is this little kobold supposed to present to a party of heroes? The agility of kobolds is pretty well-established, so he should be pretty comparable to a 2nd level Rogue. The Rogue would get a +6 (assuming an 18 Dex) even without any backgrounds, which he would probably have if a Dex check is involved. Depending on the reason for the roll, that +4 optional bonus might be worth applying. After all, Kobolds are already Evasive and good with traps, so they deserve a boost when it comes to tasks that require quick reflexes or when dealing with traps.
On the other hand, kobolds are known to be pretty weak, relying on overwhelming numbers and craftiness instead of physical strength. Plus they're small, probably even smaller than Halfling PCs. A +6 for opposed Str checks doesn't seem quite right, so we'll apply that -4 penalty without much hesitation.
The mental attributes probably aren't worth messing around with too much, but I'd definitely apply the +4 bonus if the roll involved traps or dirty tricks of some kind, and I might apply a +4 bonus to Cha rolls when dealing with kobolds (since the kobold hero is a leader), but a -4 bonus when dealing with almost everyone else (since few folk like kobolds).
This system has the advantages of using the monster's own existing statistics for opposed rolls without crowding up the stat block with ability scores, as well as being extremely simple to apply. As a GM you're doing 2 things: subtracting 10 from either PD or MD, and then tweaking that result with a +/- 4 to ensure the end result is consistent with expectations.
How I love transparent math.
Cross-posted to 13th Age Homebrews, an awesome resource still in its infancy that seeks to collect a lot of fan-created material in one place. Check it out for more ideas!