In the last edition of this series, I separated TagPro.eu public games into "matchups". As a refresher, a matchup is any continuous stretch of time with 4v4 teams in a public game. The first 15 seconds after a player joins are not counted as part of a matchup.

In this edition, it's time we start looking at some players. But before we get to individuals, we ought to look at the names used by all sorts of balls. Mostly, the name is "Some Ball". But there are others. As far as I can tell, there are four types of name that correspond to groups of players: - Some Ball (new accounts that haven't chosen a name) - Some Ball 1, 2, 3, etc. (unregistered) - elephant, hare, etc. (names given to muted players. these came into use mainly in 2019. I am grouping them all under the name "[muted player]".) - . (I don't know what the deal with this name is, but it pops up a lot in my data. possibly some quirk of the TagPro.eu userscript)

To get a grasp of how common each of these names are, let's plot them:

Chart

Not all Some Ball numbers are equally common—thanks to aaron for explaining why. Muted names are about as common as the 8th-most common Some Ball number, and . and Some Ball are more common than Some Ball 10. Since these names are not assigned uniformly, we might also wonder whether the players using them are the same quality:

Chart

It seems like there's some slight variation in quality among Some Ball numbers, with Some Ball 1 being the best and, for some reason, Some Ball 6 being the worst. There doesn't seem to be a consistent pattern with which Some Ball numbers are good and bad, but there is some variation beyond what you'd expect by chance. I don't know what to do with that. Muted players and .s are pretty good. New accounts without names are basically like unregistered players.

Inventing some stats

In the above charts, you might notice I've used two metrics called "adjusted duration" and "average cap differential". Here's how they work:

Duration is the amount of time someone played in all of their matchups combined. Adjusted duration is like that, but it reduces the weight of games played a long time ago. I've chosen to give it a half-life of one year, meaning that if you played a 4-minute matchup one year ago, it would be counted as 2 minutes now. And if you had a 2 cap differential in that matchup, it would be counted as 1 now. Players' skill changes over time, so this adjustment helps player metrics reflect their current skill instead of their skill from four years ago.

Average cap differential (or ACD) is a player's total cap differential divided by the number of minutes they played. If a player is 5 caps in 40 minutes, their ACD is 5/40 = 0.125. If they are -10 caps in 200 minutes, their ACD is -10/200 = 0.05.

Now that we've defined these two metrics that apply to players, we might wonder how they relate.

Chart (regular version) | (version with duration on a log scale)

Players with more playtime seem to perform slightly better, but that's not the most important takeaway from this image. Do you notice that there are lots of players with cap differential more than 0.3 or less than -0.3, but they all have a very small amount of playtime? This is because it's much easier to have an unusually high/low average over a small sample size than a large one. So if we tried to find the best pubbers based on ACD alone, we would end up with a bunch of players who played a very small amount of time.

That's why I'm defining one more metric in this post, which I call estimated ACD. This stat uses Bayesian inference to calculate an estimate of a player's true skill based on their known performances. It's kind of like "regression to the mean", based on some prior assumptions about the nature of the data. The estimates aren't super different from plain ACD, but players with small samples have their estimates taken with a grain of salt.

(Note: the prior I used was that the distribution of true skill was mu ~ N(0.01, 0.1). I assumed a player's observed ACD was X ~ N(mu, 2.7 / adj. duration). This model is a gross oversimplification, and it probably regresses players to the mean by too much, but I will address these shortcomings in the next post.)

If we had plotted a histogram of everyone's ACD, it would have been all over the board. But a histogram of everyone's estimated ACD shows a bell-curve-ish shape with most players close to neutral. That seems about right. But this isn't a series about all pubbers. This is a series about the greatest pubbers. So finally, let's look at them.

The greatest pubbers (based on an oversimplified but still pretty ok model)

In the first post, I asked whether Ballkenende (displayed as '!') was the best pub player. According to ACD, the answer is... maybe? There are at least 5 players with a reasonable claim to being the best, by this metric, and they are some very good TagPro players for sure. Kudos to them; in the next post, we'll see if their performances hold up to a more sophisticated analysis...

Appendix: more smurfs

There are quite a few more players who played very well on a small sample size. If you know which players use these names, please tell me so that they can be rewarded for their mad skillz. Or if they are someone's main account who usually smurfs, that would be nice to know too. (I think Frothy is in this category? or else doesn't pub much.) Those names are:

motorbot, kif, Sayu, ):, zoo, baroo, Ao, Qiang Bi, !?, wumbsky, vibin, Dudemeister, Ava, MOW EM $AYIN, Edward, anus pleaser, RamPrasad, Bow Meow, Siesta, salah, Frothy, Alydar, lil Ieopard, Calamitous, rupay, YS, Czars, chill breh, Wrath, (*), washed up, soulja ball, Badoinked