Delve Scoring

Black Plauge

First Post
Dungeon Delve introduced the idea of using Delves as a competitive format with players competing against the DM to complete the Delve and against the records of previous groups. Likewise, DMs are competing against their players to achieve a TPK and against the records of other DMs. However, no system was given for scoring these competitive style Delves so that different Delves could be compared to each other. This document serves to rectify that situation.
It should be noted, that while characters of differing levels have vastly different resources and powers available to them, the same holds true of the monsters they face. in creating this document the assumption is made that a group of 5 characters facing an encounter of their level can complete the encounter in the same number of combat rounds and that players should take the same amount of time to determine their actions for the round regardless of the character’s level.

1 Dungeon Delve Scoring Rules for Players
Each completed Delve is given a Score Time (T), measured in hours, minutes, and seconds, based on several factors that go into its completion. In all cases, a faster score time is considered a better score time. While the scoring methods for the two formats of the Delve (4 encounter, through the WPN, or 3 encounter, using Dungeon Delve), each format should maintain its own distinct record of score times. The components that make up the score time are described below.

1.1 Official Time — O
Measured by a stop watch, the official time is the elapsed time from the time initiative is rolled for the first encounter in the Delve to the time that last enemy is defeated in the final encounter. O is the official time of the Delve.

1.2 Delve Difficulty — D-L
Not all Delves are created equal. Some contain encounters which are harder than others, while others contain easier encounters. Of course, easy encounters can compensate for harder ones, so what is important is the overall difficulty of the Delve. This is accounted for in the form of a multiplier in finding the Score Time. D is the average level of the encounters in the Delve, while L is the average level of the characters participating in the Delve. In most cases L will be the level of the characters that the Delve was designed for, but particularly ambitious groups may handicap themselves by playing lower level characters, while overly cautious ones may give themselves the edge by playing higher level
ones.
While the use of a power law (2^((D−L)/4) ) makes the calculation of the Delve score difficult, and therefore unreasonable, it’s based on the fact that for every 4 level increase in the level of the encounter, the XP reward doubles. The following table can be used to approximate the Delve score for values of D−L near 0:
Code:
D-L   Approximate Multiplier

-4    x0.50
-3    x0.60
-2    x0.70
-1    x0.80
 0    x1.00
+1    x1.25
+2    x1.50
+3    x1.75
+4    x2.00

1.3 Extended Rest — E
In either Delve format there is generally no need for the characters to take an extended rest. However, some groups, desiring to use their more powerful dailies more often or needed to pull back and regain healing surges after a particularly rough going in a particular encounter, may pull back and take an extended rest. As such, the number of extended rests that the party engages in should be tracked and will apply a penalty to their score time. E is the number of extended rests that the party takes.

1.4 Number of Characters — C
Delves are designed for 5 characters, but can be run with 4 or 6 as officially sanctioned events, or with any number unofficially. Rather than attempt to scale the Delve encounters to the number of characters, the number of characters is used as a multiplier in finding the Score Time. More characters lead to longer Score Times for completed Delves to compensate for their ability to plow through the encounters faster, while fewer characters lead to short Score Times. C is the number of characters engaging in the Delve. If the number of characters changes during the course of the Delve (for instance because a player has to leave part way through) then C is the average number of characters present in each encounter.

1.5 Short Rest — S
Each Delve format as a specific number and timing of short rests built into it. However, tactics, by either the monsters or the characters, may allow the characters to take additional short rests. Since this gives players the opportunity to use their more powerful encounter powers more often, any short rest taken outside those built into the format is used to penalize the final score time. S is the number of additional short rests that the party takes.


When combining each of the above factors, we arrive at the following formula for calculating the players’ Delve score:
Players%20Score_white.png


Example Calculation
In February I ran “What You Wish For”, the WPN Delve for that month. Timing the Delve, my players took just over six and a half hours to complete it (O = 6:34:44). This Delve consists of 4 encounters of levels 11, 12, 13 and 13 (D = 12.25) and was designed, and run with, 11th level characters (L = 11). I had six players for the Delve (C = 6) who were all present for the entire thing (no adjustment to L needed). The players didn’t need any Extended Rests or extra Short Rests to complete the Delve (E = 0 and S = 0). Putting the factors into the above equation, we see that their Score time is as follows:
Players%20Example_white.png

Clearly this group needs to improve their ability to work together.

2 Dungeon Delve Scoring Rules for Dungeon Masters
Dungeon Masters who manage to force their party to fail at the Delve are given a Score Time in a manner similar to the Score Times given to players for completing the Delve, but with the way some of the factors listed above are used changed to reflect the fact that what was bad for the players, was good for the DM and vis versa.
In addition, there is one extra factor.

2.1 Kills — K
In the competitive Delve, the DM’s goal is character kills, ideally ending in the TPK. However, sometimes you have one or more players that’re either smarter than the rest or just yellower and you end up missing a character or two. To account for this, every character killed enters into the DM’s Score Time. K is the number of characters killed during the course of the Delve, and can easily be greater than C if the players mount a rescue operation (see Appendix A.2).
It should be noted that special care must be used in calculating K when running an epic Delve. Characters returned to life through the use of an Epic Destiny feature that can only be used once per day(such as the Archmage’s Arcane Spirit) then said death doesn’t contribute to K. Said ability is considered to be a normal resource for the character. Deaths negated via the Raise Dead ritual, however, still count.

When combining Kills with the factors discussed earlier and accounting for what is actually beneficial to the DM, we arrive at the following formula for calculating the DM’s Delve score:
DMs%20Score_white.png


Example Calculation
In March I ran “Company of the Griffon”, the WPN Delve for that month. Timing the Delve, it took me to just under five and a half hours to force the players to fail (O = 5:26:30). This Delve consists of 4 encounters of levels 10, 11, 12, and 12 (D = 11.25) and was designed, and run with, 10th level characters (L = 10). I had only 2 players for this Delve, but each ran 2 characters for a total of four (C = 4). In the first encounter, the characters battled the skeletons by themselves near the entrance to the chamber, and then took a short rest to recuperate from the beating they took (one character was knocked into the negatives during the course of the fight and they didn’t have a healer). After that, they explored the room and encountered and defeated the Shadow Slime before taking another short rest and heading to the second encounter (S = 1). After battling through the second encounter, in which the boulder trap dealt a critical hit to one character, the party elected to take an Extended Rest before pushing forward (E = 1). Finally, they faced the third encounter, in which three of the four characters were killed while one escaped (K = 3). Putting these factors into the above equation, we see that my DM Score Time is as follows:
DMs%20Example_white.png

Letting that character hurt my Delve score, but the fact that I forced the players into an extra short rest and an extended rest made up for most of it. Seems I'm winning.

A Optional Factors
A.1 Appropriate Number of Characters — A
It should be noted that in the above examples the Delves were run as written even though the number of characters was different from the designed 5. This serves to make life easier on the DM because no on the fly adjustments to the encounters was required as all Delves are written for 5 characters. However, it also means that the completion of the February Delve and the failure of the March Delve were the “expected” outcomes (the February party was packing extra power in the form of the additional character, while the March party was underpowered because they were a character short). If you want to leave things a bit more up to chance and don’t mind making the adjustments, then scaling the Delves by adding/removing, upgrading/downgrading, and leveling up/down monsters to make the encounters appropriate to the party size is the way to go. While the DMG provides instructions for how to make these adjustments, it should be noted that the above scoring system doesn’t account for them. If you are scaling encounters (i.e. running a Delve that is appropriate for a number of characters other than 5), then A is the number of characters for which your adjusted Delve is designed (or the average there of, if it changes from encounter to encounter).

A.2 Rescue — R
Sometimes things just go horribly wrong for the players and they are forced to flee from the Delve, leaving behind dead and dying comrades in the process. So long as at least one character escapes, the party may, at their option, elect to mount a rescue operation with a new set of characters (clones of the party destroyed are acceptable if extra characters are not available). This rescue operation is tasked with facing and defeating the encounter that defeated the original party as well as any encounters not yet completed in the Delve. Doing so, however, is much the same as having faced the delve with the additional characters from the beginning. R is the number of such rescue operations that are mounted.
In the event of a TPK, it is left to the DM to decide whether a rescue operation can be mounted (as there is no PC left to organize it).

When these two optional factors are included in the formulas, they look like this:
Expanded%20Scores_white.png


* * *

Any comments or suggestions?
 
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Well, one thing I notice is that using (D/L) as the encounter difficulty probably isn't a good idea, because the difficulty is based more on the difference in levels than their ratio. For example, completing a 2nd level dungeon with 1st level characters probably isn't too much harder than with 2nd level characters, but I would be very impressed if anyone managed to even come close to completing a 30th level dungeon with 15th level characters.

Maybe something like 2^((D-L)/4)?
 

And one more thing: Wouldn't the best strategy for the DM under this system just be to take as long as possible to do their actions? There are also lots of other ways the DM could stall for time, like constantly asking players to look up rules. It seems like if you were using this system then the way to avoid this would be to have something like a chess clock where time is only counted against the players when it's actually their turn.
 

Well, one thing I notice is that using (D/L) as the encounter difficulty probably isn't a good idea, because the difficulty is based more on the difference in levels than their ratio. For example, completing a 2nd level dungeon with 1st level characters probably isn't too much harder than with 2nd level characters, but I would be very impressed if anyone managed to even come close to completing a 30th level dungeon with 15th level characters.

Maybe something like 2^((D-L)/4)?
That's a good point, and one I hadn't considered because I was mostly expecting the D/L to be close to one. Indeed, my first draft didn't include it at all. It wasn't until I got to writing up the examples that I realized there were some discrepancies in the relative difficulties of the Delves (in particular between January's delve, which I didn't use as a final example, and the ones that I did use).

Ideally the factor should get bigger when D < L, smaller when D > L and equal to 1 when D = L. It should also be easy to "invert" these rules to come up with the factor the the DM's score. The one you propose does meet all these criteria, but so would countless others (including my original one). Do you have any justification for the form you propose beyond the fact that it uses the difference between the D and L rather than the ratio (which I admit, makes it better than my original proposal). In particular, why base 2 and a factor of 1/4 in the exponent?

And one more thing: Wouldn't the best strategy for the DM under this system just be to take as long as possible to do their actions? There are also lots of other ways the DM could stall for time, like constantly asking players to look up rules. It seems like if you were using this system then the way to avoid this would be to have something like a chess clock where time is only counted against the players when it's actually their turn.

A DM stalling for time might hurt the player's time should they complete the Delve, but it also hurts the DM's time should he manage a TPKR (Total Party Kill or Rout). Both the DM and the players are striving to complete their goal (TPKR in the case of the DM, a completed Delve in the case of the players) as quickly as possible. So long as the eventual outcome of the Delve is in doubt it is within both the DM's and the Party's interest to act as efficiently as possible. It's only once the outcome becomes obvious that stalling by the eventual loser becomes an effective tactic to hurt the eventual winner. I assume that between self-interest early on and good sportsmanship later on, such tactics wouldn't take place.

However, I'm not adverse to correcting the formula to take sportsmanship out of the equation. I'm just not sure timing the players' and DM's actions seperately is an effective way of doing that. A chess clock like timer would certianly take care of that, but that isn't a piece of equipment I would expect everyone to have ready access to. I'd like to make this system as easy to use as possible without specialized equipment. Since most watches come with stopwatches these days, I expected that to be a readily available resource. Furthermore, it's very easy to start and stop a single stopwatch once. If timing the players' and DM's actions seperately, it becomes necessary to "tap the clock" several times each round. When one then considers Immediate actions and the possibility of chained readied actions, one can easily see that this kind of tracking system can become nightmarish.
 

Do you have any justification for the form you propose beyond the fact that it uses the difference between the D and L rather than the ratio (which I admit, makes it better than my original proposal). In particular, why base 2 and a factor of 1/4 in the exponent?

My reasoning behind this formula was that the XP progression of monsters is x2 per 4 levels (as is the progression of XP required per level.) Thus my interpretation of this is that the designers believe that every 4 levels of difference makes the monster twice as hard to defeat, hence the x2 multiplier per 4 levels.

Admittedly, though, this formula does lead to complicated fractions (off the top of your head, what's the fourth root of 2?) so to make it easier it might be a good idea to use a table with close to the same progression but more rounded numbers like this

Code:
D-L   Multiplier

-4    x0.50
-3    x0.60
-2    x0.70
-1    x0.80
 0    x1.00
+1    x1.25
+2    x1.50
+3    x1.75
+4    x2.00
For a D-L above 4, continue the progression above with x2 per 4 levels. For example, a D-L of 9 is worth x5 (x1.25 for +1, plus two doublings for the next 8 levels.)

For a D-L below -4, continue the progression above with x0.5 per 4 levels difference. For example, a D-L of -7 is worth x0.3 (x0.6 for -3, and halve it for the 4 more levels
 
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Okay, that's an argument that I can buy. The issue with the complications that a power law introduces are something to note, but not a deal breaker in my mind. Given the necessity of multiplying a time, I'm already prone to using a calculator as it makes the conversion from hours to minutes to seconds and back again easier. The table might be provided to approximate scores, but I wouldn't make that the official way of calculating the score because it's entierly possible that D - L isn't going to be a whole number (especially D). Just look at the two examples I provided, both have D - L of 1.25.

I'll work on a revision and update my first post.
 

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