This is an app useable on all mobiles, tablets and desktops that calculates the mean damage done per round in D20 RPG systems and Generates Random Encounters
The app has the following features:
Calculates mean damage per round for different numbers of attacks per round with different attack bonuses, damage dice, damage bonus and critical threat ranges and multipliers
Takes into account opponent damage reduction and critical hit immunity. Damage is calculated accurately using polynomials for multiple dice. Estimating by multiplying average dice gives errors especially when there is damage reduction.
Export a table of damage per round for different opponent armour classes or save bonuses into an Excel spreadsheet
Sign up to the app to save your calculated rounds and settings.
Use the Encounter Generator to create random encounters for Pathfinder 2e rules, using most of the creatures from the Bestiary and Bestiary 2, specific for different locales. Included are area descriptions, creature behaviour, hazards and treasures. Underground Encounters have more detailed area descriptions so each one is likely to be unique.
Signing up requires submitting a user name and email address. Also required is an activation key code currently provided on the sign up page. An email is sent to the submitted email address with an activation link. Clicking this link activates the account. Lost and retrieved passwords are sent to the submitted email account.
All comments are visible to all logged-in users. Users' profiles (their previous comments, not their emails) are visible to other logged-in users by clicking the Users tab but not editable. The Site Admin can remove a user at their discretion.
If the user is not logged in, this brings up the default home screen. To log into an existing account, click 'Log in' to the right of the top menu bar.
If the user is logged in, the Home page shows a live feed of recent comments from all users, and a form to send a new comment. If desired, the user can upload a picture with the comment. To the top left of the screen is the user's name and gravatar. To view the comments of a particular user, click the Users tab on the top menu bar, then select the user from the list.
When a user logs in, this brings up their User page. This shows their previous comments. (The Home page shows the comments of all users.)
A user can also view their User page by clicking 'Profile' under 'Account' on the navigation bar at the top of any page, or by clicking Users on the navigation bar and selecting the User's name from the list of all users. The last method also allows the user to view the profiles of other users.
After a user has signed up to RPG Online Tools, they may change their password or Gravatar image on this page. (The Gravatar is a third party facility to associate an image with an email account so that the user's chosen custom image is displayed typically with their user name in many different apps.) Upon changing password, a confirmation message is sent to the email address the user employed to sign up to the App.
Ever wondered whether you should go down the dual wielding route to DPR Heaven, or stick with a massive weapon in two hands? Does the Barbarian's Rage beat the Fighter's Expert Weapon Proficiency? Is it better to choose a weapon with higher base damage or more critical damage?
This page calculates the average amount of damage dealt per round when attacking with a weapon or using spell attacks. Obviously, it takes into account the chance that you will actually hit. You may include all the attacks you would make in a round by adding attacks. You can even include Pathfinder 2e spell attacks. For spells requiring saving throws rather than rolling to hit, refer to the page "Spell Saves DPR Calculator".
For example, in Pathfinder 2e a STR 18 1st level Fighter wielding a Greatsword performing 3 basic attacks against a Goblin Commando AC 17, HP 18 will deal a massive average DPR of 15.23, thus sometimes killing the Goblin outright. The same Fighter with a Longsword and Shortsword, using the Agile Shortsword for the last two attacks, does only 12.8. It then depends on what particular feats you take to enhance that style. Comparing the Greatsword with a Greatpick, the latter does 15.9 damage and, with an average damage per critical hit of 27.5, I would say is more exciting to use! "Greatswords are impressive, but now DPR leads... Greatpicks for everyone!"
Enter the attack bonus of this attack, and select the damage dice and the total damage bonus for the attack. Also select the appropriate critical hit range (the natural dice rolls that yield a critical threat with that weapon e.g. 20, or 19 to 20) and critical hit multiplier (the number of times the normal number of damage dice are rolled).
For variable damage bonuses, e.g. sneak attack, either add damage dice by e.g changing 1d6 to 2d6 or, if the extra damage dice are different size from the base damage die, use the second variable damage column. If there are two types of damage, e.g. flaming sword, and the opponent has different DR for the two types, one could calculate two separate DPRs for two different target damage reductions with the same attack bonus and AC and then add them together. If one damage reduction is zero or low, however, it may be easier simply to ignore this one.
To add stats for another attack in the same round, click the "Add Attack" button, and to remove the most recently added attack, click the "Remove Attack" button.
Enter the opponent's Armour Class (AC) and any Damage Reduction for that attack. Damage Reduction has a complicated effect on calculating damage per round so that it is not possible simply to take mean damage on damage rolls. If the damage reduction is greater than the attack's damage bonus, the attack may do zero damage but never negative damage; to do any damage now is a less than 100% probability even with a hit, a probability that varies according to the relative sizes of the damage reduction and attack damage bonus.
Some opponents will be immune to critical hits. This will obviously reduce the Damage per Round (DPR).
In most D20 systems a critical hit occurs only on a natural high die roll. So if the critical hit range is 19-20, a critical threat occurs if the unadjusted die roll is a 19 or 20.
In Pathfinder 2nd Edition, a critical hit occurs on a natural high die roll or if the natural die roll is lower but the attack roll after all the normal to hit adjustments is at least 10 greater than the minimum to hit.
In most D20 systems a critical roll is only a threat not a guaranteed critical hit. A second roll is made and a critical occurs only if that second roll would have been enough to hit or if the second roll is a natural 20 even if a natural 20 would not normally hit.
In other systems, e.g. D&D 5th Edition or Pathfinder 2nd Edition, a successful critical on the attack roll is an automatic critical hit.
Note that in most systems an initial natural 20 roll is always a hit, even if the opponent AC is so high that the adjusted roll is insifficient to hit. But even though the critical threat range may be more than natural 20, e.g. 19-20, rolling a 19 does not automatically hit. So it is possible to score a critical threat on a natural roll and still not hit.
In some D20 systems there are no critical outcomes for rolling a Natural 1 or a Natural 20 on a Saving Throw, except that a Natural 20 is always a success and Natural 1 always a fail.
In Pathfinder 2nd Edition, there are critical successes when rolling, counting the save bonus, 10+ greater than the Difficulty Class (DC), with Natural 20 improving the outcome by one level (usually from a success to a critical success). Similarly, a critical failure results from a bonus adjusted roll worse than 10 less than the DC and a Natural 1 makes the outcome one level worse than the total would give.
In most D20 systems, critical damage is determined by rolling more damage dice. So if a hit does 1d8 + 4 damage a x2 critical hit will be determined by rolling 1d8 and adding 4 and then another 1d8 and adding 4, and if the critical multiplier is x3, 1d8 is rolled 3 times and 4 is added three times.
Also, only the basic variable damage dice gets rolled multiple times, not additional damage e.g. fire from a flaming sword, or the strength bonus damage.
In Pathfinder 2nd Edition, the numbers of dice were getting out of control so critical damage was changed to roll just as for a normal hit, and then the final result is multiplied by the critical multiplier. Additional damage dice, and the fixed damage bonus from strength are also doubled, but not the extra fatal or deadly dice.
You may say that this does not alter the mean damage for DPR calculations; adding dice instead of multiplying one die just narrows the standard deviation about the mean total roll. Wrong! If there is damage reduction, the possibility of scoring zero damage but never negative skews the distribution and the chance of scoring zero damage will be different for two low dice rolls versus one low roll multiplied by 2.
Clicking this button calculates the total mean Damage per Round (DPR) for all the attacks or spells in the round. If the user is logged in, a table of DPR for all Armour Class (AC) of Saving Throw Bonus values is saved to the user's profile.
When the user is not logged in, clicking this button from the calculations page downloads an Excel worksheet file with a table of Damage per Round (DPR) values for all Armour Class (AC) or Saving Throw Bonus values, not just the entered AC or Saving Throw Bonus value.
When the user is logged in, clicking this button from the Show Rounds page downloads an Excel worksheet file with a table of all the saved rounds, with attacker/caster and target stats and Damage per Round (DPR) vs Armour Class (AC) or Saving Throw Bonus tables.
This is also graphically represented, so the user can instantly min-max different strategies for different targets. For example, at a point where one round's DPR crossed above the value of another round's, it would be at this AC or Saving Throw Bonus value where that strategy should be used. Now you know when to use flurry, or whether to attack with two weapons or one!
The graphs throw up some interesting (to a nerd) results. In Pathfinder 2e, the Saving Throws graph has kinks in it because of Natural 1's and Natural 20's. The Saving Throw Bonus point where a Critical Fail occurs only on a Natural 1 is different from that where a Critical Success requires less than Natural 20, producing a shallow slope between these points. For example, with DC 15, a saving Throw Bonus of +3 means only a Natural 1 will critically fail for double damage (2+3=5, which is not more than 10 less than 15); at +4, there is an unreduced critical fail chance, so the damage with increasing bonus does not decrease much. But it is at +6 where a Natural 19 rather than Natural 19 or 20 results in a Critical Success, making the slope steeper again thereafter.
Aside from these kinks, one can appreciate that the slope of DPR vs Saving Throw Bonus is steepest when the target critically fails on more than Natural 1, and shallowest when the target is failing rather than critically failing on a natural 1 (because even a 1 plus the Saving Throw Bonus would match the DC). So on offence it is best to put the best magical boost on the best PC, but on defence it is best to put the best Saving Throw boost on the worst PC to avoid those critical fails.
When the user is logged in, clicking this button brings up a page listing, most recent uppermost, all the saved rounds with caster or attacker and target stats and the associated tables of Damage per Round (DPR) vs Armour Class (AC) or Saving Throw Bonus.
This page calculates the average amount of damage dealt per round when casting a spell that requires a basic saving throw rather than a spell attack.
A standard saving throw (Fortitude, Reflex or Will) is made by the target against the caster's Spell DC. A critical success results in no damage, a success in half damage rounded down, a fail in full damage and a critical fail in double damage (multiply dice rolls and damage bonuses by 2).
Now a caster can directly compare the average damage from a spell requiring a save versus a spell requiring an attack roll. For example, in Pathfinder 2e a goblin warrior has an AC of 16, a Will save of +3 and a Ref save of +7. A 1st level PC with spell DC of 17, and spellcasting ability modifier of +4 casting an Electric Arc cantrip does 1d4 + 4 damage requiring a basic reflex save, which is an average of 4.88 damage, but it affects two goblins.
A Ray of Frost cantrip, using the spell attack calculation on the other page, has an attack bonus of +7 and the same damage of 1d4 + 4. The average damage is only 4.55 to one goblin.
A crossbow, that lower edition staple of low level wizards, which deals 1d8 damage, only does 3.15 damage per round even if the caster had a dexterity of 18!
The reason for the difference, despite Reflex being the goblin's best saving throw and only having to meet the DC not beat it, is mainly the half damage on a successful save.
A Daze spell on the goblin, which requires a Will save, only does 4 damage, but the average is 3.8 damage because of the high chance of a critical fail and some damage on success. And the goblin has a 15% chance to lose an action next turn through being stunned!
You can also compare attack damage and spell damage for melee characters. Say you are a STR 18 CHA 18 1st level Champion wielding a longsword with a free hand, and you took some cantrip-bestowing feat. Do you make 3 longsword attacks, or use Electric Arc for your last 2 actions, knowing that AOO is unlikely? The average damage for longsword combinations is 10.63. (This would be 14.02 for a Fighter expert in longswords.) The average damage for 1 longsword attack is 5.95, and the Electric Arc is 4.88 to two goblins, giving a total DPR of 15.71, better than a Fighter! Even a shield-bashing Champion with no weapon will outclass a Fighter for damage per round, with the added AC bonus and Shield Reaction. Of course, circumstances will vary - you might want to concentrate your damage on one opponent, for example.
These cantrips also scale quite well with level - an 11th level Champion would do an average of 29.5 damage to each of two goblins with a single infinite-cast Electric Arc. The only question is whether free Force Lightning would tempt your Champion to the Dark Side...
Enter the caster DC for the spell or other damaging effect that requires the target to make a saving throw and select the damage dice and the total damage bonus.
To add stats for another spell in the same round, click the "Add Spell" button, and to remove the most recently added spell, click the "Remove Spell" button.
This tool generates random encounters according to the PCs' level and locale and using a selected encounter difficulty.
Underground locales ("dungeons") have randomly generated entries, area descriptions, exits and hazards. Using a 5-ft square grid or dungeon tiles, you could generate a whole rogue-like dungeon on the fly with your own geometry of connecting passages, or create a mini-dungeon of 2-3 encounters, perhaps 2 of Trival to Moderate Difficulty and a final one of Severe or Extreme Difficulty. Or you could set up your own map or use a custom map or scale poster and populate the existing geometry of rooms or passages with some adjustments to entries and exits. Finally, you might have your own dungeon, theme and encounter key and just want to pad it out with a few extra areas.
There are several types of possible entrance to the Area, including doors of different strengths that may be stuck, locked (with traps) or windowed.
Each Area may have one of several possible architectures, shapes, main features, side features, environmental features and exits, including secret doors, and treasure containers, giving over a billion combinations, though not all rooms will have each type of distinguishing feature.
Wilderness and Urban locales have several possible random descriptions for each type of creature encountered, (e.g. humanoid, animal, elemental, undead). These may increase as I develop the App, or you may suggest your own!
Aquatic and Extraplanar Locales are rather niche and vary widely according to the particular aquatic setting (e.g. riverbank, seashore, bridge, river boat, ocean vessel, sea bed) or planar environment and so are left to the user's discretion.
Creatures are generated according to the standard system of level range compared to party level according to the encounter difficulty, and then the number is made up to match the encounter budget for the encounter difficulty. Many creatures may have allied creatures that fight with them, or lower ranking creatures, mounts or minions. Again these are made up to the encounter difficulty. Almost all standard Pathfinder 2e creatures are represented. It an encounter doesn't "fit", it takes less than a second to click and generate another!
The XP award may be a little lower than the desired budget level for the encounter, because it is the actual calculated award from the type and number of creatures set without going over-budget. The award for any hazard is included here.
Each creature encounter describes their behaviour, whether they are likely to be surprised or to surprise, or what they are doing at the time. This behaviour is generated randomly according to each broad creature type.
Hazards are generated like creatures according to the standard rules of level range compared to party level. Different hazards may occur in different locales. The XP award for the Hazard is shown, and is in addition to that for the Creatures as if it was a separate Encounter. Choose where in the Area is best to set the Hazard before starting the combat.
Rewards may be loose, or in containers which may be locked or trapped. Rewards are generated to fit the standard rules. A certain amount of treasure is expected to be won per level. This is divided between encounters according to what proprotion of a full level (1000 XP) the encounter would advance the party.
Gear is randomly awarded for flavour and skewed to lower levels where it is more useful. There is the same chance for armour and weapons.
The probability of Permanent items being present is encounter XP/1000 * number of items per level (4), with a small balanced chance for no items or 2 items in one Encounter. The level of the item is 50% that of the party and 50% one level higher than the party. Generic magic Weapons and Armor are overepresented and are of random type (e.g longsword, gnone flickmace). I have not adjusted probabilities for some weapons being more popular than others as this will vary by campaign and, unlike other RPGs, weapons are now more fairly balanced. I have not even adjusted for uncommon weapons. My feeling is that someone who specialises in gnome flickmaces will complain more if the likelihood of finding a +1 Striking Flickmace is 1 in 1000 instead of 1 in 100 than a longsword wielder will if a +1 Striking Longsword is found 1 in 100 as opposed to 1 in 99.
The probability of Consumable items being present is encounter XP/1000 * number of items per level (6, but 5 at first level), with a small balanced chance for no items or 2 items in one Encounter. The level of the item is 33% that of the party, 33% one level higher than the party and 33% one level lower than the party. I have slightly adjusted probabilities for a very few items, eg potions of healing, being more common than others, but in general probabilities are equal. All consumables, including snares and poisons, are represented.
The probability of other items being present falls under the currency reward. The party level currency table is used, with the proportion encounter XP/1000. There is 50% chance for no currency, and 50% chance for 1-3 times the base value. There is a 50% chance for a gem, 25% chance for an artwork and 25% chance for precious materials, and any left over is awarded as gp or sp. There are minimum party levels to be awarded particular gems, artworks and materials; these are set quite high to prevent the total award value dramatically overshooting that which the encounter merits when you do not have too many encounters to average this out.
Not all randomly generated creatures are likely to be hostile when encountered. You may wish to consider the following when running the encounter:
To initiate a combat encounter in Pathfinder 2e you may wish to run the following steps:
This tool generates random plots, perhaps to frame a series of random encounters. The quest givers, journeys, missions and rewards are put together from a number of options.
Currently the combinations would give 250,000 different plots!
Completion of a quest might merit a 100 xp award in addition to that gained from the individual encounters. If the quest-giver is actually a villain and they are ultimately defeated, award the party their listed XP as well.
Clicking this button will reset the session's values for attacks and opponent stats and return to the home screen.
When the user is logged in, it will also permanently delete all the saved rounds of Damage per Round (DPR) tables for the current user.
This is version 0.2 of the RPG Online Tools application.
Version 0.2
Added ability to select creature types in Encounter Generator
Encounter Generator includes some creatuers from Bestiary 3 and other sources
Version 0.1
Attacks and Saves Damage Calculators completed for 1-10 dice damage, extra 1-10 dice damage, fixed bonus damage and various forms of critical damage.
Plot Generator completed (further random options may be added).
Encounter Generator completed for creatures and treasures approx levels 1-10.