A Look at the Probabilities of a Power Roll in Draw Steel

 Draw Steel's central die-roll uses 2d10. While this is like the d20 in that the maximum result is a 20, it actually changes up the probabilities quite a lot. Not only does this bump the average up by half a point (an average roll of 11 versus an average of 10.5,) but it also skews things closer to the center.

Draw Steel's rolls also don't have moving targets: from level 1 to level 10, the best result is a total of 17 or higher, and the worst result is an 11 or lower. Classes gets a boost to their primary characteristic(s) automatically at certain levels, starting off with a 2 and ending up with a 5, so you'll genuinely wind up rolling better the higher level you get.

That being said, your average power roll on an ability that uses your main characteristic is still always going to land in the tier 2 territory. At level 1, you have a 2 in that stat, and so your average will be 13, and at level 10, you'll have a 5 in the stat, which will give you an average roll of 16, both in that tier 2 range.

But what about the probabilities of rolling tier 3 results?

The math is somewhat trickier than it is on a d20 - if it used that, you'd just roll a 17 or better 4 out of 20 times, or 20% of the time. Your stat would boost that, as you could get a total result of 17 on a 15 or higher at level 1.

But rolling 2d10 instead creates a bell curve. (EDIT: actually, I think it's more of just a peak.) If we (for the sake of clarity) imagine rolling percentile dice, treating one of our d10s as the tens place, it becomes clear that the total number of possible rolls is 100.

Eleven is the most likely result, because for every number we roll on the die, there's another number on the die that we can roll to get a total of eleven - 1 and 10, 2 and 9, etc. 12 becomes less likely because if we roll a 1 on either die, even with the highest result we can get on the other, a 10, doesn't get us there.

Now, let's say we want to see how likely we are to roll a 17 (again, we're talking about "natural" numbers on the dice here). The lowest either die can roll is a 7. We have the pairs of 7 and 10, 8 and 9, 9 and 8, and 10 and 7. So, 4 out of 100 possibilities, or 4%.

But we're not worried about landing on 17 itself - we're fine if we get 18, 19, or 20. We can get an 18 3% of the time (8 and 10, 9 and 9, 10 and 8,) and then 19 2% of the time (9 and 10, 10 and 9) and finally a 1% chance of rolling 20 (10 and 10).

This appears to be demonstrating a very simple pattern: that the chance of any given number (on its own) is basically 1 to 10%, with pairs on either end of the die's range the least likely on the outside and the more likely as they approach 11. Is that right? (Somewhere a high school math teacher - or even a middle school math teacher - is disappointed without knowing why.)

Let's figure this out:

In theory, 2 and 20 should have a 1% chance, 3 and 19 should have a 2% chance, 4 and 18 should have a 3% chance, 5 and 17 should have a 4% chance, 6 and 16 should have a 5% chance, 7 and 15 should have a 6% chance, 8 and 14 should have a 7% chance, 9 and 13 should have an 8% chance, 10 and 12 should have a 9% chance, and then 11 has a 10% chance of being the result.

(Ok, I realize I screwed up with the calculator, but this logic was right).

Now, our chance of rolling a tier 3 result is thus anything that gets us 17 or higher, so 4+3+2+1%, or 10%. If we have a 2 in that characteristic, though, we only need to roll a total of 15 or higher, so we can actually add the chances of rolling 16 or 15, giving us an additional 5 and 6% chance, so we're now looking at a 21% chance to get our tier 3 result. Twice as likely! (Wow, turns out James Introcaso wasn't lying when he said that that 2-point bonus was a big deal!)

Now, let's consider what happens if we have an Edge. An Edge (which plays a role similar to Advantage in 5E) gives us a +2 bonus to our roll. As we've seen, that +2 can be a huge deal. But how good is our roll going to be if we are making a power roll for one of our abilities (and thus have a +2 to start with as early as level 1) and then also have an Edge? That means a total of +4 (which is also what we'll have without an Edge at level 7). Getting a tier 3 result thus now only requires us to roll a 13 or higher, which is a 36% chance. Still not a guarantee, but a significant statistical boost.

What about a double edge? As a reminder, when you have multiple edges, rather than stacking, they transform into a double edge - you no longer add a number to the result, but just take one higher tier result. (I'll note that this is one mechanic that, while it seems mathematically effective, might take a while to get players to understand instinctively). In other words, our +2 bonus from our Characteristic is still in effect, but rather than making it +4, we're just upgrading our total result.

Effectively, this changes our range dramatically: now, any result of a 12 or higher is a Tier 3 result, and thanks to our stats, we've only need to actually roll a 10 or higher on the dice. Thus, this becomes a 64% chance. In other words, you're more likely than not to get a tier 3 result if you have a double edge on a power roll for one of your abilities, even at level 1.

By level 10, when you have a 5 in your primary characteristics, a double edge using it will require you only to roll a 7 or higher on the dice, meaning an 85% chance that you're going to get that maximum result.

As a point of comparison: in a d20 system like D&D, if you're just trying to hit a DC of 17, you have a 20% chance to do so. Having a +2 bonus to your roll turns this into a 30% chance. If you add another +2 (like from your proficiency bonus,) it goes up to 40%. It's not entirely dissimilar, but Draw Steel's system skews toward the middle, which means that adding a higher characteristic is shifting the window to make a tier 3 result closer to that middle, and pushing tier 1 results farther away from it.