I've recently started playing 4th edition Dungeon and Dragons, and my inner math geek has some commentary about how things have changed from 3.5 math, particularly with regard to:

## Experience

A lot has changed here, obviously. The table in the PHB now goes to 30, and 30 is the official ascension to godhood. "You win D&D!" and all that.

The table itself has changed as well as the basic open-ended nature of leveling. Fourth edition, despite its generally more mechanics-based approach to rulemaking than 3.5, threw out a perfectly rational table in favor of something which appears to have been made up. The 3.5 table was generated from a nice combinatoric function. The 4.0 table lurches along in fits and starts and matches no formula I can come up with. There is no polynomial or exponential function which fits the curve properly. The best approximation I know of is an exponential, 1840 * 1.24^x, which comes fairly close with a correlation coefficient of 0.98. But it's still off by 20% at level 30, and puts the difference between level 1 and level 2 at a mere 442 XP.

## Hit Points

A lot has changed here too. Hit points are now entirely deterministic, and quite frankly I don't know what has taken so long. At low levels, starting constitution and feats can make a big difference, percentage-wise. Yet by the time your character is having an epic effect on the world, the fact that she's a 25th level paladin is far more important than five points one way or the other on her con score. That seems far more in keeping with the feel of the genre: no matter how you were born, you're a hero now and that's what counts.

## Attribute Points

Attribute points have gone the same way as hit points, having been made deterministic in fourth edition than in third. These never really stop being important at higher levels the way con and feats do with respect to hit points. Per-level increases in defenses are matched by per-level increases in the to-hit rolls to attack these defenses, so someone who starts out ahead will stay ahead by roughly the same amount as the levels tick by.

One interesting change in fourth edition is that there are more stat bumps per level on average, and there are mandatory stat bumps for everything. This means that by epic level, even a character's dump stat will be at or above the population norm, and a player who chooses more balanced attributes can have a character with an 18 and all other attributes at 17. Plus, of course, the expected accumulation of stat-boosting magical geegaws.

## Skill Checks

Kevin Sullivan has great info about skill checks on his site. It relates primarily to third edition, but the basic mathematics are just as applicable to fourth edition.

## Weapon Damage

There's a lot to say about weapon damage, which is fitting considering the central role it plays in many campaigns. My friend Alan has a great page about weapon damage with average damage taking into account auto-miss and crits and the d20 result required to hit (essentially opponent's AC - attacker's to-hit).

Weapon damage scaling with size continues to make no sense in D&D. The left column is the damage done by a medium-sized weapon of a given type. To the right is the damage done by the same weapon in different sizes. Percent of medium damage is based on the average die roll for each size weapon.

Medium damage | Tiny damage | % of med. | Small damage | % of med. | Large damage | % of med. |
---|---|---|---|---|---|---|

1d2 | 0 | 00.000% | ? | ?% | 1d3 | 133.33% |

1d3 | 1 | 50.000% | 1d2 | 75.000% | 1d4 | 125.00% |

1d4 | 1d2 | 60.000% | 1d3 | 80.000% | 1d6 | 140.00% |

1d6 | 1d3 | 57.143% | 1d4 | 71.429% | 1d8 | 128.57% |

1d8 | 1d4 | 55.556% | 1d6 | 77.778% | 2d6 | 155.56% |

1d10 | 1d6 | 63.636% | 1d8 | 81.818% | 2d8 | 163.64% |

1d12 | 1d8 | 69.231% | 1d10 | 84.615% | 3d6 | 161.54% |

2d4 | 1d4 | 50.000% | 1d6 | 70.000% | 2d6 | 140.00% |

2d6 | 1d8 | 64.286% | 1d10 | 78.571% | 3d6 | 150.00% |

2d8 | 1d10 | 61.111% | ? | ?% | 3d8 | 150.00% |

2d10 | 2d6 | 63.636% | ? | ?% | 4d8 | 163.64% |

This table shows two distinct types of oddness. First, a medium weapon that does 2d? damage does twice as much damage as a medium weapon doing 1d? damage. However, this relationship does not hold for tiny, small, and large variants. A tiny 1d8 weapon does 1d6 damage, but a tiny 2d8 damage does 1d10 damage rather than 2d6. Likewise, a large 1d8 weapon does 2d6 damage but a large 2d8 damage does 3d8, rather than 4d6 damage.

Also, weapon size categories do not demonstrate even scaling relative to medium. Tiny, small, and large weapons do not do (approximately) a set percentage of the damage that a medium weapon does. For example, large weapon damage ranges from 125% to 165% of corresponding medium weapon damage. This variation is not due to the lack of convenient die combinations to yield the desired percentage. Again using large weapons, note that most hover around 150% of medium. However, 1d2, 1d3, and 1d6 are all notably low, and 1d10 and 2d10 are notably high. If we assume 150% is the target, 1d3 should become 2d2 (150%) or 1d3+1 (150%), and 1d6 should become 1d10 (157%); 1d10 should be 1d8+1d6 (145%) or 1d10+3 (155%), and 2d10 should either be 2d8+2d6 or 2d12+1d6 (150%) or 3d8+3 (150%). The point is that these numbers seem to have been arrived at more by virtue of their nice patterns than by virtue of any meaningful numerical relationship.

## Feats and Damage

I will eventually put some more meaty content here but in general, fourth edition has made feats much more straight forward in this respect. Feats tend to grant small bonuses in specific situations which as a readily-predictable effect on average damage output. This sharply contrasts with the 3.5 feats which often dramatically changed the cost/benefit equation of particular weapons and strategies.