Monday, March 19, 2018

Healing Through the Ages

Today we look at the legacy of natural healing rules, without the benefit of magical aid. This is an issue that has a clear and dramatic trend over different editions of D&D. Was it the right one?

Medical Research

Obviously, different bodies, and different types of injuries, heal at different rates. But consider the following as a sample of non-lethal, mid-level injuries:
So the pattern is clear: For these mid-level injuries (not even talking about third-degree burns or major head wounds, etc.), the time for healing is on the order of some weeks. If you dig into the details, this can be aggravated or lengthened if the injured member is used or stressed too early in the process.

Original D&D

HEALING WOUNDS: As noted previously, energy levels can only be regained by fresh experience, but common wounds can be healed with the passage of time (or the use of magics already explained). On the first day of complete rest no hit points will be regained, but every other day thereafter one hit point will be regained until the character is completely healed. This can take a long time. (Vol-3, p. 35)
I think previously I read this as 1 hp/day (after the first), but now that I look at it more closely, it seems that I missed the key phrase "every other day", which seems to indicate an effective ½ hp/day of complete rest? (Note that Chainmail had no rules for recovery; and in fact no campaign rules or context outside the combat encounter itself.)

Basic D&D

Each day of rest and recuperation back "home" will regenerate 1 to 3 of his hit points for the next adventure. (Holmes Basic D&D, p. 7)
We can see this same rule in the Moldvay (p. B25). However, I'm unable to find any rule for natural healing in the later Mentzer (1983) or Allston (1991) rules. Was this an editorial oversight? (The piecemeal choose-your-own-adventure organization of Mentzer's Basic Players Manual makes this seem likely.) Regarding Allston, while I can't find a rule for natural healing, other passages seem to imply that it should exist (e.g., constructs "do not heal normally; magic must be used", p. 155; and regarding nonlethal combat, "he heals them through the usual means, such as a cure light wounds spell or rest", p. 267). Can anyone find a rule for natural healing over time in these books?

Another interesting place to look in this line would be Mentzer's "War Machine" rules in the Companion set. Clashes between armies in these rules result in casualty percentages, half of which are deaths, and half of which are wounded. Regarding the wounded, Mentzer writes:
If a force retreats from the field, treat all wounded killed. If a force holds the field after the battle, those wounded troops can return to action in 1d4 months. (DM's Companion, p. 15)
Now, that 1d4 month (4-16 weeks) recovery is actually a pretty good model of our real-world medical data above (where we saw 3, 6, or 12 weeks for moderate injuries). However, it's totally out-of-sync with the current or any other edition of D&D; there is no mechanic in any published D&D which would produce recoveries for normal troops at the (realistically slow) rate shown here. So while noble in intent, this highlights just one of the many ways in which Mentzer's War Machine is essentially blind and/or in contradiction with results from the normal D&D system itself.

1st Edition AD&D

For game purposes it is absolutely necessary that the character rest in order to recuperate, i.e. any combat, spell using, or similar activity does not constitute rest, so no hit points can be regained. For each day of rest a character will regain 1 hit point, up to and including 7 days. However a character with a penalty for poor constitution must deduct weekly the penalty score from his or her days of healing, i.e., a -2 for a person means that 5 hit points healing per week is maximum, and the first two days of rest will restore no hit points. After the first week of continuous rest, characters with a bonus for high constitution add the bonus score to the number of hit points they recover due to resting, i.e., the second week of rest will restore 11 (7 + 4) hit points to a fighter character with an 18 constitution. Regardless of the number of hit points a character has, 4 weeks of continuous rest will restore any character to full strength. (DMG, p. 82)
This is something like a doubling from OD&D's "every other day... one hit point" rule. (Note that the basic D&D rule from Holmes is on the order of quadrupling.) One problem that may be obvious with these starting rules is that characters with more hit points, presumably the heartier and healthier types, take longer to heal from injuries -- for very high level characters, maybe ten times as long as a normal man. Hence, I think, the addition of the last line: no matter what one's level or hit points, healing is always complete within one month. (We may or may not consider that a fully successful adjustment.)

2nd Edition AD&D

Characters heal naturally at a rate of 1 hit point per day of rest. Rest is defined as low activity--nothing more strenuous than riding a horse or traveling from one place to another. Fighting, running in fear, lifting a heavy boulder, or any other physical activity, prevents resting, since it strains old wounds and may even reopen them.

If a character has complete bed-rest (doing nothing for an entire day), he can regain 3 hit points for the day. For each complete week of bed rest, the character can add any Constitution hit point bonus he might have to the base of 21 points (3 points per day) he regained during that week.

In both cases above, the character is assumed to be getting adequate food, water, and sleep. If these are lacking, the character does not regain any hit points that day.
Part of the transition we see here is that while OD&D demanded "complete rest" for any healing, 1st Ed. left out the word "complete", and here in 2nd Ed. the editor has taken advantage of that gap to distinguish between normal healing (1 hp/day, even on the march), and "complete bed-rest" (3 hp/day). This is now something like six times the initial healing rate we began with in OD&D. It still suffers from the healthier/longer-to-heal phenomenon (lacking the last line from 1st Ed.).

3rd Edition D&D

Natural Healing: You recover 1 hit point per character level per day of rest. For example, a 5th-level fighter recovers 5 hit points per day of rest. You may engage in light, nonstrenuous travel or activity, but any combat or spellcasting prevents you from healing that day.

If you undergo complete bed rest (doing nothing for an entire day), you recover one and one half times your character level in hit points. A 5th-level fighter recovers 7 hit points per day of bed rest.

Higher-level characters recover lost hit points faster than lower-level characters because they're tougher, and also because a given number of hit points represents a lighter wound for a higher-level character. A 5th-level fighter who has lost 10 hit points isn't seriously wounded, but a 1st-level fighter who has taken 10 points of damage is. (PHB, p. 129)
So this rule finally addresses the healthier/longer-to-heal problem, by scaling natural healing to character level. In so doing, it leaves healing at lower levels about the same (actually reduced in the case of "complete bed rest", the category being maintained from 2nd Ed), but radically increases healing at higher levels. For example, for a 6th-level character, healing is now 12 times over the OD&D baseline, or 18 times in the "complete bed rest" case.

The 3.5 rules accelerate this further:
Natural Healing: With a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.

If you undergo complete bed rest for an entire day and night, you recover twice your character level in hit points. (3.5 SRD)
In this revision, you don't even need a day of light work to regain hit points; it can happen in just 8 hours of time. And the "complete bed rest" is upped from ×1.5 to ×2 instead. So in this latter case it's about 24 times the healing rate seen in OD&D, for a 6th-level character.

4th Edition D&D

I don't normally go past the 3rd Edition of the game (and I've never played any such edition), but in this case the information is easily available online, and I think instructive -- it's actually a fundamental part of the 4th edition system design. Looking at a helpful blog post by MerricB on the subject:
Characters in 4E could heal themselves from a pool of healing surges – each equal to a quarter of their hit points. A typical character might have 8 of them available each day, and they were also expended by healing magic (which would provide a bonus to the healing). Whenever a character took a rest between combats, they could use healing surges to regain hit points. (Merric's Musings)
So -- in case you're not already aware of this -- in 4th Edition, characters could heal themselves effectively instantaneously, as soon as they had a minute or so breather outside of combat, for fully a quarter of their total hit points. At about 8 times a day, that's actually double their full hit points within one day, with no outside aid required; i.e., come back from a mortal injury twice every day. By my calculation for a sample 6th-level character, this represents approximately 100 times the healing rate from the OD&D basis.

5th Edition D&D

Again quoting MerricB regarding 5th edition:
Part of this idea [4th Ed. healing surges] remains in 5E, but with a couple of changes. First of all, they’re called Hit Dice, and they’re equal to the number of dice you roll to determine your hit points. Whenever you rest for an hour or more, you may expend as many Hit Dice as you like, rolling them and adding the total to your current hit points. Your constitution modifier applies to each hit die rolled.

A Short Rest is defined as being a period of 1 hour or more when you get a chance to bind wounds and generally recover. There are several abilities possessed by characters that also recharge when you take a short rest. It’s a lot longer than the time in 4E, so won’t be as frequently employed...

Long Rests and Full Healing: If you rest for eight or more hours, you get the benefit of a long rest: all your hit points are healed, and you regain half (rounded down) of your hit dice. For those who are used to AD&D, this is a major change in how the rules work. Without magic, it’d take weeks for a badly wounded fighter to get back on his feet! For those in 3E, it’s a change but they had wands of cure light wounds so it didn’t matter. For 4E players, this is less than they had, as they got all of their healing surges back! (Merric's Musings)
Note that none of this information seems to be in the free 5E basic rules release, or the SRD, so I'm taking for granted that Merric has it correct here. So, it seems like in 5th Edition, you can effectively get on the order of all your hit points back with a 1-hour rest, and then another all-your-hit-points unit back with the next 8 hours rest. That is: Similar to 4th Ed., two units of full hit points back in less than a day (although not all at once, instantly, as in 4th). So again that sounds like about 100 times the healing rate we started with in Original D&D (for a sample 6th-level character).


A summary of our findings are shown below (for the later editions, a 6th-level character is taken as the basis):

As we can see from the chart, the overall trend follows an exponential acceleration in healing with each new edition of the game, approximately following a rule of f(x) = e^(0.72x), where f(x) is the multiplier on the OD&D baseline, and x is the sequential edition ID of the game as given above. Since e^0.72 = 2.05, this shows that, roughly speaking, the natural healing rate has regularly doubled with the release of each new edition of D&D (over the half-dozen or so editions to date).

If we go back to OD&D and look at our 6th-level fighter example, say hit points of 6 × 4.5 = 27, and a healing rate of ½ hp/day, we see that this character can regain all of their hit points in 27 × 2 = 54 days ≈ 8 weeks. That's actually a fair simulation of how long it realistically takes to heal one or two deep cuts, a halfway bad burn, or a broken bone (see the top section above). The most recent editions (4th/5th), granting something like 100 times the healing rate, or recovery from 2 mortal wounds every day, can only be considered as cartoonish. (Note that the entire analysis above pretends that we keep character hit points constant over the years; if we also take into account that PC hit points were themselves getting inflated, then the multipliers would look even more ridiculous.)

Now, someone might argue that hit points don't represent real injuries, but this is a debauched interpretation seen in 4th+ edition, and doesn't square with earlier editions of the game. Yes, 4th/5th edition makes the assertion that lost hit points may not be any real injuries at all; possibly just temporary fatigue or windedness instead. But even if we look at the 3rd Edition text above, there is no such indication; lost hit points are always some kind of injury, even for high-level characters (possibly just a minor cut or bruise). Moreover, the fact that side-effects of attacks trigger on any successful hit -- e.g., poison triggers for saves, energy-draining attacks, etc. -- contradicts the idea that a hit or lost hit point may not be any injury.

So: What to do in our house rules for an OD&D game? We are sensitive to the problem that healthier (higher-level) characters take geometrically longer to heal with a fixed ½ hp/day rule (or any other fixed number of hit points per day). We could also say this: Another problem with this rule is that it's still unrealistically too fast for low-level creatures. For example: take a normal man of around 3 hit points; even the worst wound which takes him to near zero hit points will be healed fully in less than a week, only 6 days. If we want something resembling the 3-12 weeks healing time from our initial medical examples, then we would argue for slowing it down in these cases even more. (See also the Mentzer War Machine rules above for a similar intent.)

Let's say we want any character to recover from zero to full hit points in some number of weeks like this. There is little to do but subjectively pick the number of weeks that makes us happy: this number could be 3, or 6, or 12, or something like that. I'll suggest picking 4 weeks to be a bit generous, and also to sync up with the 1E AD&D rule for capping the healing time. Hence:

Characters heal one-quarter of their full hit points for each week of complete rest.

Let's say we round this up to the next whole number to be charitable in cases where a creature has less than 4 hit points (like half of normal men). It occurs to me that (Crom help me) this slightly echoes the increment regained from 4th Edition's "healing surges" -- although on a time increment of weeks instead of seconds. Also assume that this requires comfortable rest in bed with amenities -- as in, a hostel or inn at town.

If we compare to the OD&D rule, the major change is of course scaling our healing rate to the overall hit points of the character in question. For 1st-level characters, the healing rate has decreased (to about a quarter of the book rate). For a 3rd-level character with around 15 hit points, healing rate is about the same as the OD&D book rule (hey, 3rd-level again: links one, two). For a 6th-level character, the rate has approximately doubled (and so in line with the 1E text). You can extrapolate the rest, I'm sure. 

I think I can imagine someone complaining "that's too slow for our adventures!" but I actually don't think there's any legitimate justification for such a position. For example, MerricB writes above: "Without magic, it’d take weeks for a badly wounded fighter to get back on his feet!", but I don't see any fundamental reason why that's a bad thing -- merely non-cartoonish. We can, of course, simply hand-wave the weeks of recovery time in-game, just like we do for days or nights or whatever the camping pace is.

Moreover, this rate of time actually helps to solve a bunch of other problems we commonly encounter in the D&D game. Some examples: (1) The party retreats to rest overnight, and the DM is confronted with coming up with some reason why the depleted monsters don't immediately get overrun the next morning. (2) The party wants to camp in a room of the dungeon, as they can get most of their needed recovery back in just 8 hours if they can only hold the door shut. (3) Our campaigns and timelines routinely run on an overly-accelerated basis: whole adventure paths take only days in-game, and PCs advance from 1st to 20th level within the course of a single game year. Slowing down the recovery time (to a realistic basis) could serve to put the brakes on all of that, and generate campaign stories that better resemble what we read in fantasy literature. (Especially in conjunction with reduced clerical healing magic, and possibly seasonal effects like no-travel-in-winter, etc.)

Comments or modifications?

Saturday, March 17, 2018

The Master's Monastery, Ep. 1

A minimalist game log.

Real date: 3/16/18. Fantasy date: Mars 1st, 4729.
  • Briefly describe island kingdom of Ormea and village of Hospilmas. Create six new 2nd-level characters, equip, and provision them.
  • Depart for legendary monastery on edge of bogs, between long lake and dark woods. No lost or wandering results.
  • Explore outbuildings. First room: midden. The dwarf, Aslak the Unclean is lowered by rope into the filth and returns with a fine silver pendant.
  • Berserkers! One is charmed, but breaks the spell when he becomes enraged. A series of terrible rolls (e.g., three attacks in sequence all with natural 1) causes various fumbles, slips, lost weapons, etc. Two PCs are slain: One of the elven sisters, Tamara Birdfoot, with a crippling hit for 18 points of damage. 
  • A shadowing member of village runs into the fight and shatters one of the berserkers' heads with a morning star, turning the fight; the third elven sister shows up soon after. The berserkers are put to the sword and a sack with 100 gold nobles is found.
  • Searching a collapsed chimney: a wandering giant ant rushes upon the fighter. He plunges his polearm deep into the thing's maw: 10 points, and the thing keeps coming, crawling up the weapon to attack. A dagger in the flank puts it down.
  • Stables: The back room has giant mushrooms and more ants. The PCs withdraw, and reaction roll shows the ants let them.
  • An old destroyed brewery, and then a bakery are entered. The air is thick and yeasty; the back room old flour covered with yellow growth. The dwarf pokes it with a 10' pole, and a few spores slightly puff into the air.
  • Return to the ant's lair; a ruckus is made to lure them into an ambush. Two appear, and the wizard's sleep spell fells one (the other: natural 20 save). The party fall upon the other one and kill it.
  • Dwarf carefully avoid the mushrooms in the deeper room, and reappears with an old, gem-encusted horse halter. Another gold buckle is turned up by a searching elf. The party returns to the village.
  • Tia Birdfoot levels up: now a 1st-level Wizard/3rd-level Thief.

Thursday, March 15, 2018

GaryCon on Paul's Gameblog

Paul's Gameblog has really ramped up his output recently. This week he's been writing great retrospectives of his experiences at GaryCon... and since half of the time we were in the same games together, I figured I'd just get out of his way and let him tell the whole story. Here's what he has up so far:
Who knows, maybe by the time you see this he has even more postings (search for "GaryCon"). Highly recommended.

P.S. If you're not already aware, "Delta" and "Dan" are synonymous.

Monday, March 12, 2018

Gygax on Dungeon Design

I've always struggled with dungeon design. Nowadays I finally do have a process which gives me some amount of traction, which is like (1) map out a dungeon (likely with the GridMapper application), (2) outline the monsters & treasures in each area with a spreadsheet, and (3) write the descriptive text for each area with a word processor. Nothing earth-shattering; but it did take me a few decades to settle on this. (Also, the spreadsheet step gives me a convenient opportunity to crunch statistics on the overall dungeon.)

Coming back from GaryCon, it's on my mind that many of us at this point are aware that Gygax himself played with very minimalistic dungeon keys -- as evidenced by inspection of the famous photo above, which appears to show a listing on the left with just a single line per encounter area, likely only documenting the monster & treasure in each room. Also: When I had a few minutes to chat with Ernie Gygax on Saturday, he brought this same thing up. Coincidentally, I recently came back across a fairly lengthy answer on the old ENWorld Q&A thread in which Gygax Sr. explicates this, and expands on the fact that all other setting/dressing information was made up improvisationally during the play session.

I think this is worth highlighting (particularly for new DMs and players) for a few reasons. One: This is not suggested anywhere in the published rulebooks, and is in stark contrast to the published dungeons with the company imprint. For example, the 3-room sample key in the DMG is very wordy (and I've previously looked askance at module B1 for likewise presenting a model of very complicated room descriptions). Two: It explains the difficulty he had in converting his Castle Greyhawk to a published product, because the style of his play notes, and the style he expected for a published product, were worlds apart (as he describes below). Three: Perhaps this gives additional credence to the one-page dungeon format which I normally resist -- or at least a two-page dungeon format, perhaps.

In retrospect, I really, really wish that this process had been explicated in the original dungeon-design advice in the core OD&D/AD&D rulebooks -- not effectively kept masked/hidden. It's among the most important revelations that could have been included, I think. Here's the full answer from the ENWorld Gygax Q&A, dated 15th September, 2005, in response to a question from user Clangador:
As to your questions, I usually made one-line notes for my duneon encounters, from around 20 to 25 of same for a typical level done on four-lines-to-the inch graph paper-a few more on five-, six, or seldom used 8-line graph paper, the other spaces were empty save for perhaps a few traps or transporter areas and the like.

I did indeed create details for the PC party on the spot, adding whatever seemed appropriate, and as Rob played and learned from me, he did the same, and when we were actively co-DMing we could often create some really exciting material on the spot, if you will.

When the encounter was elimiated I simply drew a line through it, and the place was empty for the foreseeable future. I'd give Rob the details of any session he was not at and vice versa, so we winged all of it. Sometimes a map change and encouunter kkey note of something special in nature was made, but not often. We both remembered things well, Rob very well and when necessary something was made up out of whole cloth for the sake of continuity of adventuring.

When new maps were made it was often nearly impossible to have the stairs and other connections line up with other maps, so a note or two and "fudging" served perfectly well, this was particularly true of the means of entering and exiting lower levels from secret locations surrounding the castle ruins.

Now you understand why the Castle Zagyg project is such a major design undertaking. If we handed over the binders containing the maps and the notes don't think even thge ablest of DMs would feel empowered to direct adventures using the materials. ..unless that worthy was someone who had spent many hours playing with Rob and me as DM.

I have laid out a new schematic of castle and dungeo levels based on both my original design of 13 levels plus sideadjuncts, and the "New Greyhawk Castle" that resulted when Rob and I combihned our efforts and added a lot no new level too. From that Rob will draft the level plans for the newest version of the work. Meantime, I am collecting all the most salient feature, encounters, tricks, traps, etc. for inclusion on the various levels.

So the end result will be what is essentially the best of our old work in a coherent presentation usable by all DMs, the material having all the known and yet to be discussed features of the original work that are outstanding. .I hope :uhoh:


Monday, March 5, 2018

Going to GaryCon

GaryCon X is this coming weekend! I don't get out to a lot of conventions, but after hearty recommendations from those who have gone, I'll be attending for the first time this year. Flying out late-ish after my Thursday classes, and with a full schedule of games-playing Friday through Sunday morning (no DM'ing for me this cycle). Rooming with Paul, who was a big help with the run-up logistics (and with whom I was furiously SMS'ing as we navigated the unique event registration process that particular Saturday afternoon).

Hope to see some of you there, if schedules permit. Pinging me on Livre de Visage may be the best way to get in touch that weekend. Safe travels to everyone!

Thursday, March 1, 2018

Skeleton/Zombie Hit Dice are Confusing

Last weekend, I was copying some information from my OD&D Reference Sheet roster and realized that the line for Skeletons/Zombies was totally different from what I recalled from the Vol-2 text itself. Then I backtracked and realized that the entry in the 1st Printing PDF was totally different from the 6th Printing. I wrote a whole blog analysis about that, then realized that the folks at the OD&D Discussion forum hashed this out a few years ago. Here I ruthlessly swipe the findings by moderator "waysofthearth" and other researchers:

This hot mess completely changes how I've thought of Skeletons and Zombies in OD&D over the last ten years. To my surprise, their hit dice actually started off at (1, 2), and then through a series of typographical confusions and bum-fungled attempts at correcting the ambiguous use of two slashes, changed to (½, 1) in the main text... and some semi-random permutation of those in places like the Reference Sheets and Holmes Basic. By AD&D Gygax had them back at (1, 2) where they started (and likewise any other edition post-Holmes). In the linked thread, Mike Mornard also testifies that the classical play always had them at those latter values.

So at this point I'm going to chalk up the (½, 1) values as just a never-fully-corrected typo confusion that crept into OD&D, and should likely be ignored. The (1, 2) values are certainly what almost all players of classic D&D are familiar with.

As a result, in the last few days I've changed those values in the OED Monster Database to (1, 2), and thus relievedly have them more compatible with most editions of D&D. At some point I need to inject the edits into other places like assessments, monster level tables, Book of War armies, etc. Glad I looked into this, and big thanks to the OD&D Discussion guys for the invaluable work.

P.S.: It's slightly awkward that with Zombies at 2 HD, the Monster Metrics program assesses them at 1.4 EHD, which nominally rounds down to 1 (the same as Skeletons). Zombies with 2 HD and crappy armor, attacks, and move are either the toughest monster in the Level 1 table, or the weakest monster in the Level 2 table. I guess I'll manually set them to 2 EHD so that they're in the Level 2 table, partly for purposes of tradition and completion.

Monday, February 26, 2018

Target 20 System Accuracy

We've discussed the Target 20 mechanic a few times (such as in the "Best Combat Algorithm" discussion, a top-10 post for this blog, per sidebar), in which we replace all the standard D&D combat tables with a mechanic of roll d20 + level + modifiers, and check for a total of 20 or more. This simple, time- and space-saving rule has always been the core mechanic in the OED House Rules; I first jotted it down in my AD&D DMG some time in the 90's; and it frequently winds up bleeding into other people's games after they play with me a few times. I recently created a new explanatory page at the OEDGames website.

A question that the more discriminating gamers are right to ask is: How accurate is it, as compared to the classic D&D rules (of any edition)? There's definitely a smoothing-out effect, such that it's not 100% exactly the same as the combat tables used in those early editions (in some sense, that's the point; to get away from those slow and clunky table-lookups; however, see later comments by Gygax & Lakofka further below). Let's compute to answer that question precisely.

For this purpose, we'll use the statistic called Root-Mean-Square Deviation (RMSD). This is the standard way of measuring the difference between a model and real-world observations (or, in our case, two combat models) when you have a bunch of data points to consider. Basically, we find the difference in each pair of data points, square them so they're all positive (and also extra-punish severe misses in the model), take the average of those squares, and then square-root it to get it back in scale with the original data. The basic concept is almost exactly the same as for standard deviation, and you see this RMSD tactic get played out over and over again in various descriptive statistics. In our present case, you can effectively interpret the result as just "average pips off from the book table results". Let's look at a summary of Target 20 vs. results in several early editions of D&D:

The executive summary, for all of these editions, is this: For attacks and saves, Target 20 tends to be 1 or 2 pips off the book table results. If you want to see the full individual level-by-level data set, you can download an ODS spreadsheet here. Each analysis has been done for levels 1 to 14 (which is where most of the book tables tend to top out). Note that the OD&D and B/X rules used the exact same combat and save tables for the standard classes (so I put those editions next to each other); AD&D represented more of an evolution of the system. However, if you dig into the details, you'll see that the "1 or 2 pip" variation is level-dependent, as follows:

Attack rolls in Target 20 are, at 1st level, exactly equal to the OD&D-B/X combat tables; at middle levels they are very close; and they deviate more at the higher levels, with Target 20 being more generous by a few points. The Target 20 fighter attacks are even closer to AD&D, on average, because the AD&D table was explicitly set up to give a regular 5% boost for every added fighter level (see "Special Note" at bottom of DMG p. 74).

Saving throws vs. spells (for brevity, the only one shown here; others are similar) likewise tends to vary from the book results by about 2 points on average. In this case, looking at the details, you'll see that Target 20 is a bit more harsh at 1st level; closely matches the book at middle levels; and is again more generous at the highest levels.

Thief skills, looking at the grey-highlighted part of the chart, appear to be more at odds with the book rules; however, this is only the base rule, and in practice we apply the thief's Dexterity modifier to their rolls, presumably a 1- or 2-point shift closer to the book. Given that, the Target 20 results are again exactly the same as the OD&D-B/X rules at 1st level, and then track a little bit below the book rule at higher levels. (Note that in this particular case we used a Normalized root-mean-square deviation (NRMSD) statistic, because we changed the scale from percentile 1-100 to a die roll of 1-20.) My overall interpretation: At the most commonly played levels, Target 20 is maximally accurate to the book; at the more exotic higher levels, it deviates a bit.

It bears mentioning that, in later years, Gygax and Lakofka themselves signed off on a smoothed-out progression system (see Dragon #80, "New charts, using the '5% principle'"); although for some reason they were sufficiently locked into their wargame-tablature legacy that they presented this via even larger, mammoth-sized tables. If the system were essentially nonlinear, that could be a time-saving trick -- but since the D&D combat system is indeed fundamentally linear, there's really no need for those tables.

It further bears noting that in practice, when a PC attacks a monster, we (as DM) keep the AC secret -- so players just report the d20 + attack bonus modifiers (a single addition), and the DM mentally adds the monster AC in their head. (Of course, if the player-announced total is itself 20 or more, then they've almost surely scored a hit.) On the other hand, in the case of mass monster attacks or saving throws, the DM may perform a mental reverse-subtraction to come up with the raw die-roll needed, and then roll a fistful of d20's in the open, so that players can immediately confirm if they've been hit or not. But that reverse-subtraction (as is customary with the THACO technique) is never something we ever ask the players to do.

Final thought: If you like the Target 20 method (and we hope you do!), the image at the top here is actually the official Target 20 Compatibility Mark, and you should feel free to use in a new gaming product of your authorship (also, a link to the explanatory web page could be helpful; questions via the email there are welcome). Above all, we hope it's a simplification that helps make your game more fast-paced and furious. Fight on!