Pathfinder Monster Database: AC vs Touch AC

Ok, one more visit to this pathfinder monster database before I’m on to a new dataset. This time, I wanted to take a look at the relationship between Armor Class (i.e., how hard a monster is to hit) and Challenge Rating (i.e., how tough the monster is, according to the game developers). There should be a pretty strong linear relationship between AC and CR.

However, the thing I’m really interested in is the relationship between Touch AC and CR. Because pathfinder is needlessly complicated, monsters have a separate AC for just touching them (or getting hit with certain kinds of attacks like rays or bullets). It’s been my experience that touch AC is always low, and doesn’t seem to change at all as the game progresses. Pragmatically speaking, this means that at a certain point touch attacks basically always hit. Let’s see if that’s the case. I think some run-of-the mill scatterplots will do here, but might as well make them fancy. Three packages needed: (a) ggplot2 for the basic plotting; (b) ggExtra to add density distributions to the plot; (c) cowplot, to stitch the two plots together at the end and (d) ggthemes, in case I want some custom color palettes.


Then, I can make the plots. Made the dots transparent with “alpha = 0.3” to deal with overplotting. Personally, I find it looks cleaner than geom_jitter(); it’s always low-key bothered me that the randomness added by geom_jitter() actually changes the positions of the raw data a little. Feels a little like lying with data to me, sometimes. With the ggmarginal command, I added in the density plots so we can see the overall distributions. Then at the end, I used cowplot to stitch them together side-by-side. Knowing this, I made sure both graphs had the same y-axis lengths to facilitate easier comparison, a key component of the small multiples approach.

p1 <- ggplot(mydata, aes(x = CR, y = AC)) +
  geom_point(size = 2, alpha = 0.3, color = "steelblue") +
  theme_classic() +
  geom_smooth(col = "royalblue", se = FALSE) +
  scale_y_continuous(breaks = seq(0, 70, 5)) +
  scale_x_continuous(breaks = seq(0, 40, 5)) 

p1m <- ggMarginal(p1, type = "density", fill = "steelblue")

p2 <- ggplot(mydata, aes(x = CR, y = AC_Touch)) +
  geom_point(size = 2, alpha = 0.3, color = "steelblue") +
  theme_classic() +
  geom_smooth(col = "royalblue", se = FALSE) +
  scale_y_continuous(limits = c(0, 70), breaks = seq(0, 70, 5)) +
  scale_x_continuous(breaks = seq(0, 40, 5)) +
  labs(y = "Touch AC")

p2m <- ggMarginal(p2, type = "density", fill = "steelblue")

totalplot2 <- cowplot::plot_grid(p1m, p2m, labels = "auto", ncol = 2)
base_aspect_ratio = 2)
Scatterplots of AC and CR

Ok, well there’s a clear (very strong) linear relationship between CR and AC (r = .91). That’s probably not surprising, given that the game designers probably wanted that to happen by design, to keep up with increases to attack bonuses that players get each level. However, touch AC is very weakly related to touch AC (r = .12). In fact, it’s really only mythic level monsters beyond CR 20 that see any increase in Touch AC at all! So for the vast majority of play, there’s no relationship between CR and Touch AC. I got to wondering then, what is the variance in touch AC actually attributed to? A good first guess would be a creature’s size:

ggplot(mydata, aes(x = CR, y = AC_Touch, col = Size)) +
  geom_point(size = 2, alpha = 0.3) +
  theme_classic() +
  geom_smooth(method = "lm", se = FALSE) +
  scale_y_continuous(limits = c(0, 70), breaks = seq(0, 70, 5)) +
  scale_x_continuous(breaks = seq(0, 40, 5)) +
  labs(y = "Touch AC") +

Yup, looks like the majority of variation is due to that. So in summary, touch AC doesn’t really change as monster CR increases, and most of the variation is due to size. It’s a weird mechanic to add to the game, and easily abusable by additions like the gunslinger that always hit touch AC. Far as I can tell though, hasn’t been removed from the second version under playtest. Oh well, add it to the list of weird broken mechanics, I suppose.

Scatterplots of touch AC and CR, split by size

Syntax and data available on the blog’s OSF page.

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