Why Descending AC?

Descending Armor Class is a trope of BX, but as new retro clones appear, you also see THAC0 and Ascending Armor classes. Those are all choices, but which is best depends on who and when you are. And to be honest, which one you pick makes no difference. 

Way...way... way... back... to the DMG for AD&D, AC had a different mechanic than simply beating a number. There was a chart or series of charts that had endpoints. Characters reached a certain level where it was simply listed as "level n+". For Fighters, at the first level, you needed a 25 to hit AC -10 and an 11 to hit AC 10. Going to the other end, it didn't matter how high your level was; there was just one line labeled "This level or over". There were bounds to the charts. 

But if you ignore boundaries, all three attack systems are basically the same. 

For descending AC, you could fill out the Attack Value Matrix on your character sheet like so: 

Except this tool was in the hands of the DM! You would tell your DM what you rolled, and what your bonuses were. 

It would be up to the DM to consult the chart and tell you if you hit. What number you really need to succeed is obscured. This makes B/X and AD&D e1 especially deadly because you don't know what you don't know. Also, the tables had steps or jumps in probability not so much to keep one guessing, but due to the boundaries set by the charts and the progression of classes.   

For THAC0, instead of using the chart, you'd figure out what you need to hit AC 0, then calculate what you need to hit. In this case, roll a d20, subtract your opponent's AC, and see if it was better than what you needed. The two issues with this method are: first, the probabilities are different, and second, the monster's AC isn't obscured at all. 

You could either calculate on the fly all the time or fill out the Attack Value Matrix. It didn't matter, except as before, the tables were often not listed on your character sheet, and it still felt like the DM was slightly obscuring the needed info to calculate a hit. 

For Accending AC, you roll a d20, add your bonuses, and compare that number to your opponent's AC. This is different because this is all on the players, not the DM. A chart isn't necessary at all. 

So, why was Descending Armor Class ever a thing? 

A lot of people would answer: "Wargames have charts, and that is simply the way it was done". That's true, not the whole story. 

It comes down to how you were taught math and WHEN. For people coming of age in the 1960, you'd have a very different way of learning math. Check out this video. 

Believe it or not, the audio of this video is from 1965 as an objection to what was called "New Math". New math was what was taught from 1965 on. Math teaching changes. If you played D&D in the 1970s, you have experienced 4 changes in how math was taught. 

So, when Gary Gygax learned math, he didn't learn like the youngsters today. But he knew what he was talking about. 

Ask yourself, what is 3+4? Virtually every adult has this fact memorized, and no real math occurs. Even if you use your fingers. 

We'll call this the 7 configuration. 

Or does it? 

Ask a young child the same thing. 

Literally, 3 and 4. 

They will probably hold up 4 fingers on one hand and 3 on the other. There will be a pause while they put down one figure from the 3 hand and put up another finger on the group of 4 hand. 

And we are back to the 7 configuration.

Ok. They did some math right there, but what exactly did they do? Can you show your work, like the video jokes about? 

Yes, but you need to think in terms of spaces, not numbers or fingers. Theoretically, everyone has 10 fingers. 

 

Most of the time, I have 10 fingers.

OR we have 10 places to record things... numbers usually. But it could be pips, or apples, or oranges. 

Ok. So what is the point? 

We are back to the young child. The young child did some sleight of hand. First, he or she held up 4 fingers, then 3 fingers, then showed you all of them together. Next, he moved one figure from one hand to the other, to land in the seven configuration. If you live in a different country, which fingers you show would probably be culturally different, but still showing 7 fingers between two hands.

Now, let's show the work: 

10+4=14
10-3=7
14-7=7

Did I just do addition with subtraction?

Yup. 

That Trad Math, if you will. To add and subtract, you have a boundary - 10 fingers to hold information. If your range is between -10 to 10, you never need more than 10 fingers. 

Let's take slightly large numbers to prove it works, with more than 10 slots. Consider 47+38. 

100+47=147
100-38=62
147-62=85

Notice that for bigger numbers, I need the place above it. In this case, for numbers between 1-99, I need the 100's place. 

That is very different from putting 47 on top of 38 on the page, adding 8+7 for 15, adding 4+3 for seven, shifting the 7 to the left to represent the 10s place, and adding 70+15 to get 85. Watch that video again. Tom Lehrer found New Math totally perplexing. And it IS to some people. 

We are missing a step. In 1989, there were the NCTM Standards, which were different standards than New Math and also very different from the Common Core. The order is Traditional Math, New Math, NCTM Standards, and Common Core. All of which you would have lived with if you played D&D in the 1970s. 

This is why there was a progression from Descending Armor Class, to THAC0 and finally Ascending Armor Class. AD&D and BX are in the transition period between Traditional Math and New Math. 1989 marks the transition between New Math and the NCTM Standards. And Third Edition D&D and above marks the transition between the NCTM Standard and Common Core. 

Funny how that all works, with the dates lining up so neatly. 

So at my table, Traditional Math is king, with Descending AC. At your table, I bet it's something else, and you will have to thank your math teachers for making you just as right as me.