It was mentioned in the comments that damage per round does not matter much since there are many methods of taking foes down without actually damaging them. And even more of that, a character can be highly beneficial to the party even if he doesn’t take out foes effectively. Opening locks, disabling traps, negotiating NPCs, identifying magic items and many more things can be very important out of combat.
Moreover, many abilities may be more or less beneficial depending on the style of the campaign. Will you spend more time under open sky or in a dungeon? In the first case fly is valuable, in the later meld into stone is more preferable. Will it be an urban or wilderness adventure? In the first case skills like diplomacy or gather information will work well, in the later gather information is virtually useless while survival is almost a must. The clue to making a good character is working with the party and with the GM. Working with the GM will help you to get some hints on what type of challenges your character will face. Working with other players will help chosing your role in the party in order to form an effective team (if the style of the campaign is cooperative).
If you still want the DPR, which is not completely useless, I suppose, here are some guidelines.
DPR as it is.
If you want to have an average damage your character is able to deal, you can calculate it.
First thing you need is the average roll for each die. It is the sum of all numbers you can roll divided by the number of die sides. (Dice average is useful in many other situations)
- 1d2: (1+2)/2 = 1.5
- 1d3: (1+2+3)/3 = 2
- 1d4: (1+2+3+4)/4 = 2.5
- 1d6: (1+2+3+4+5+6)/6 = 3.5
- 1d8: 4.5
- 1d10: 5.5
- 1d12: 6.5
So, replace the dx in your damage entry by the corresponding average and you’ll have your average damage per hit. For example, if you are playing a fighter with strength score 18 fighting with Greatsword you’ll have your damage entry 2d6+6. Greatsword damage for medium character is 2d6, your strength bonus +4 multiplied by 1.5 for two handed weapon gives a total of +6. In this case your average damage per hit will be
2d6+6 = 2 × 3.5 + 6 = 13 hp.
To get the damage per round you’ll have to account for your chance to hit. It, basically, depends on two numbers: your Attack Bonus and the target’s AC. Since the distribution of target’s AC highly depends on the monster selection, it is too difficult to estimate your average DPR, but it is quite easy to estimate your DPR vs a fixed AC. Subtract your Attack Bonus from target’s AC, and you’ll get the minimum score you need on a natural d20 roll.
Thus all the rolls smaller than that (AC - Attack Bonus - 1) will be a miss, and 20 - (AC - Attack Bonus - 1) will be a hit. As each point on d20 represents a 5% (or 0.05) chance, your chance to hit will be
(20 - (AC - Attack Bonus - 1)) × 5%
For example, if your target’s AC is 16 and your Attack Bonus is 10, then
(20 - (16 - 10 - 1)) × 5% = 75% (or 0.75)
I.e. you’ll hit 3 times per 4 attacks on average.
If we assume the fighter from above example has BAB +6, which gives him two attacks per round at +10/+5 (for his +4 strength), his DPR vs AC 16 will be:
0.75 × 13 hp + (20 - (16 - 5 - 1)) × 0.05 × 13 hp = 1.25 × 13 hp = 16.25 hp
This calculation does not take into account critical hits. It can be calculated, but I wouldn’t bother you with more math, since DPR is not so important for the game.