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[Accatitippi]

Some of the recent discussion on Stef and SCSN's great news thread left me wondering about what Dominion's player base looks like.
I ran some elementary analyses on the full unfiltered Isotropish leaderboard for Dominion 2.0 (as of 13th of April 2016), this means that I took into account:
- 2p games only (which may mask/underrate players who play mostly 3p+)
- Only botless games.
- Isotropish level (mu-3sigma) rather than mu, which will severely underrate players with a low volume of plays. I also compared functions of number of plays with Isotropish level (also a function of play number), so some analyses might be skewed. Also, Isotropish level is a the result of an algorythm I don't know much about, but I suspect some of the results are artifacts due to how TrueSkill works.
- Only games played since Goko 2.0 went online (around June 2015, I believe) were taken into account.
I'm no statistician, and this was the first time I used array formula in excel, so if anybody spots errrors or has suggestions, please speak up!
Anyway, to the numbers!

Since June 2015, 36296 players have played 1787686 2-player games of Dominion Online. Of these players, only 12,174 played at least 20 games, which drops to 5,892 if you set the inactivity treshold to 100 games.
Minimum level is -75, maximum is 65.
As you might expect, median and average level are very low in this population since it contains a lot of extremely-low volume players (in addition to being inexperienced ones). The mean is -22, median is -26. (incidentally, these are very similar to starting values of mu-3sigma=0-25, is that significant? Who knows.)

Trying to get more useful data out of the leaderboard, I tried to calculate the mean after filtering the values by minimum number of plays:
Treshold  Mean
20          2,57
50          8,21
100         11,98
500         18,48
The mean grows slowly even when applying quite strict filters.

Weighting the mean by number of plays, we get 13.
I believe that the most interesting parameter of this set is the median Iso level calculated on the "gameplays" population. It returns 15. This means that half of the games played on MF were played by players with a level lower than 15.
When I calculated the proportion of games played by players with level above a treshold of 30 (where I arbitrarily drew the line for "competitivish" players), I got 18%.
The player mode is an exhilarating -54, most likely due to how Trueskill makes players with very few (losing) plays converge.

I also made a couple simple distribution histograms for players, plays, and play density on Iso level:

I scaled plays number to get both histograms on the same picture.
The player distribution is frankly multimodal, with peaks at -54, -33 and 0. This is probably due to artifacts from the Trueskill algorythm (players with one or two losing games might converge here?). Anyway, the curve is quite far to the left.
The plays distribution looks nearly normal, I haven't had time to try and model it, but I might try to do that.
The big difference in the curve locations inspired me to do another histogram:

It seems that playing more dominion makes you better at it.  But also, it makes your rating better by lowering your sigma.
I suspect this "sigma effect" might be more pronounced around the level interval between 0 and 20, while skill matters more for higher levels. The far right region gets more erratic due to low player density.

So, conclusions.
It was fun to make this simple analysis. It seems like there's plenty of people who play a lot of 2p online dominion while not being very good at it, I guess.
I'd write more, but I really have to go.
Extra chart:

[Mic Qsenoch]

I've always wanted to be a whole bin.

[Infthitbox]

I don't know how you ran your stats, but particularly in the context of the Dominion Online 2017 thread, it would be very interesting to know what percentage of 2p games were base-only. This shouldn't be that difficult to figure out. What perhaps would be more interesting is what percentage of 2p games were played by a player who played most of their games base-only. That should give a reasonable indicator of how much of the playership is "free". Thats a little more difficult to calculate.

[JW]

What perhaps would be more interesting is what percentage of 2p games were played by a player who played most of their games base-only. That should give a reasonable indicator of how much of the playership is "free". Thats a little more difficult to calculate.

It should be easy to figure out if a player is "base only" and the threshold is much lower than "most games base-only." If a player has more than a very small percentage of their pro games in a given time period contain only base set cards, that player is base only, as this is very unlikely to happen once you buy even one set.

Re: the original analysis. Playing more isn't just causing higher level: people with higher level also play more. For example, you would see that higher level on Dominion 1.0 predicts playing more games. So you shouldn't interpret anything causal about the effect of playing more games on making you better at Dominion.

[ben_king]

I don't know how you ran your stats, but particularly in the context of the Dominion Online 2017 thread, it would be very interesting to know what percentage of 2p games were base-only. This shouldn't be that difficult to figure out. What perhaps would be more interesting is what percentage of 2p games were played by a player who played most of their games base-only. That should give a reasonable indicator of how much of the playership is "free". Thats a little more difficult to calculate.

If we're just interested in rough estimate, we can assume that base-only games happen only when two non-paying players are matched up.  If matches are uniformly random among all players (which they're not since lower-rated players are both more likely to be matched with each other and more likely not to be paying, plus paying players probably play more games on average than non-paying players), then you can estimate the proportion of base-only players as the square root of the proportion of base-only games.

Obviously though, that's an extremely rough estimate.

[Infthitbox]

What perhaps would be more interesting is what percentage of 2p games were played by a player who played most of their games base-only. That should give a reasonable indicator of how much of the playership is "free". Thats a little more difficult to calculate.

It should be easy to figure out if a player is "base only" and the threshold is much lower than "most games base-only." If a player has more than a very small percentage of their pro games in a given time period contain only base set cards, that player is base only, as this is very unlikely to happen once you buy even one set.

Well, or you ended up playing someone who has the 'Allow Cards I Don't Own' unchecked for whatever reason. I don't think that's a very popular option.

[Accatitippi]

What perhaps would be more interesting is what percentage of 2p games were played by a player who played most of their games base-only. That should give a reasonable indicator of how much of the playership is "free". Thats a little more difficult to calculate.

It should be easy to figure out if a player is "base only" and the threshold is much lower than "most games base-only." If a player has more than a very small percentage of their pro games in a given time period contain only base set cards, that player is base only, as this is very unlikely to happen once you buy even one set.

Re: the original analysis. Playing more isn't just causing higher level: people with higher level also play more. For example, you would see that higher level on Dominion 1.0 predicts playing more games. So you shouldn't interpret anything causal about the effect of playing more games on making you better at Dominion.

Good point, and in second thought, I'm not even sure about how strong the correlation between skill and plays is. Comparing mu's (maybe filtering by number of plays) would give a less muddled vision, I guess.

I definitely can't do the thing with the single-game analysis, since it requires some sort of program to collect the data, but I definitely would love to see that. If you do it, make sure not to make gokosalvager.com implode by DoS. 

[Dingan]

if anybody spots errrors or has suggestions, please speak up!

I found one!!!

Awesome stuff.  Super-random other things off the top of my head:

- Average number of things per turn (counted as the number of log entries created per turn) as a function of iso level.  I would think this could be plotted, as game logs are public.
- Average (accumulated) amount of money spent on Dominion online as a function of iso level.  Is public assuming you can determine what expansions a player has bought based on their game logs.
- I've always wondered how things look like as a function of iso level rate of change.  So for example, what would your 'average games per player' look like as a function of di/dt, where di/dt = rate of change of iso level with respect to time (or even with respect to games).  Not sure if past iso levels are public, but you might be able to calculate them if you know how TrueSkill works.