In the 4th edition DMGs (DMG p42, DMG2 p80), recommended DCs for easy, moderate, and hard situations are provided in tables. What's interesting is that the levels in the left-hand column are grouped by 3's.
I thought maybe this had to do with 1/2 level modifier, but that goes up every two levels. I thought maybe it had to do with increasing ability scores, but those go up every four levels. It seems like the number 3 is arbitrary here.
What is the motivation for putting DCs in groups of 3's?
With the updated chart, by Stephen Schubert, the reasoning is actually provided (emphasis added). It presents DCs reverse engineered from the possible breakpoints at each level solved for the desired odds of success. The lumpy fashion is due to half-level scaling + attribute scaling at 4,8,11 (repeat per tier), and the every five level bonus from expected items.
Easy: ... These are the simplest checks and should represent a reasonable challenge for characters that have no training in the skill (an untrained character). An untrained character is typically adding half his level to the skill and probably doesn’t have an ability score that helps him out. He might get another +1 by Epic tier, since all his ability modifiers have increased by 21st level. ...
Moderate: A moderate check requires a bit of training or innate ability, or a bit of luck. These checks are aimed at skilled characters who have training in the skill, though there are other options for getting a similar skill modifier, such as having a high ability score (18+) in the skill’s key ability or combining a racial bonus and a moderate (14+) ability score. These DCs scale a little faster than easy DCs, which accounts for ability score increases or adding a feat or path feature if the key ability isn’t your primary or secondary class stat. ...
Hard: ... Without additional assistance (such as a power bonus or another character’s aid), the expert PC will succeed against these DCs around two out of three times. The expert PC typically has training in the skill, and his or her primary ability score is the skill’s key ability (or secondary ability score along with a skill focus feat or racial bonus). As the character increases in level, we expect feat and item selection to provide an extra boost along the way, as well as ability score increases. ...
My analysis is part speculation, but at least tells you why it's groups of 3 rather than 4 or bigger. Why it's not level by level or groups of 2 keeps being a mystery to me.
D&D 4e has characters go from level 1 to 30. 30 can be divided by 1, 2, 3, 5, 6, 10, 15 or 30, so groups of 4 was never a viable option to begin with.
Groups of 5 or more would have certainly been too wide: having the same DC at level 6 and 10, while the modifiers to the roll go up quite fast, wasn't good enough.
I wonder why they did not group them by two, since 3 makes groups cross the tiers (at 10-12 and 19-21) and I can only speculate that they wanted the table to fit the space on the page or to avoid a lenghtier, bulky list.
Either way, I don't believe there's anything in the game justifying the choice of that 3.
