Thursday, April 17, 2014

[POE] Maps, Levels, and Quantity

I love maps in Path of Exile. But I've always been curious about the details of the map drop system. Does it get harder to get higher level maps? Exactly what does quantity do?  What about the desirable mods (pack size, more magic monsters, more rare monsters) - how much quantity are they worth?

As usual, the forums have an abundance of speculation about these answers. But I wanted math.

So I started to collect data on the maps that I've been running in PoE. Unfortunately, this kind of data gathering takes time, so I was only able to gather data on around 500 maps. Which just isn't enough data to study processes that are based on rare events.

To take this further, I combined my data with a few other projects that had collected data from maps into one, larger, spreadsheet of doom. (Note: all of these sources were gathered since 1.0, which substantially changed the mapping system.)
  • My data - link
  • /u/dansenMONSEN - link
  • /u/jddogg - link
  • /u/IcyRespawn - link
  • /u/Shadowclaimer- link
  • /u/pyrodan2 - link
  • /u/Skyl3lazer - link
This gave a total 4076 map runs, covering a wide range of map levels and map quantity.

From this data, I can take a look at the basics of map drops.

Map Level
One finding is painfully apparent for anyone that runs maps in PoE: it gets harder to progress your map pool on higher level maps.  For every increase in map level, the average level of maps dropped increases by 0.71. For 66 maps, the average drop is an increase in map levels (66.5).  By level 70, the average drop is only 69.1, and by 78 maps the average drop is down to 74.6. Maintaining a high level map pool gets harder with each level.

Map Quantity
Declining average drop level makes getting high quantity critically important for maps (since higher quantity means more maps, which increases the odds of getting equal-or-higher level maps).
On average, I estimate that every 100% quantity increases the number of maps dropped by 0.85 maps. (Results from a negative binomial regression - full table after the break.) This, in turn, improves the chance of getting a higher level map.  The same 100% quantity increases the chance of getting a higher level map by around 20%.

Pack Size / Magic Monsters / Rare Monsters
But what about the desirable mods (pack size, magic monsters, rare monsters) - what effect do they have on map drops?
  • Pack Size: aids in getting both more and higher level maps. However, the data suggests that pack size isn't as game-breaking as others suggest. From the models, every 2% pack size is worth about 1% quantity. So a 20% pack size roll is worth only about 10% quantity - less than the other available suffixes that could roll on a map.
  • Magic / Rare monsters: have no effect on the number of maps (or, whatever effect is there is lost to noise / too small to estimate). Rare monsters increases the likelihood of getting a higher level map (it is likely that magic monsters does too, just that the effect is fairly small).  Again, the mod is about half as valuable as quantity.  So a low rare monsters roll is equivalent to about 13% quantity.

These results are... surprising.

While I've always been told to roll for the desirable affixes, these results suggest that they may be overrated. Of course, there is one caveat: some maps - like tunnel - don't have much room for large packs to spawn, diminishing the effect of the mod. I'll try and gather more data to evaluate this claim.

I'm really surprised that the magic monsters mod didn't show any statistical significance, no matter how I looked at the data. I'm thinking this might have to do with selection effects. The problem is how highly the mod is rated: if players immediately run a map with +magic monsters regardless of the other mods, this would result in +magic monsters being associated with worse maps and fewer drops. I'll try some quasi-experimental methods out to get around this problem.

I'm also surprised that 1% quantity doesn't equate to another 1% chance to get a map... this makes me think something else may be going on with the models, so I'll take another pass at the topic soon.

So very excited to have data to play with!

For the stats nerds:  full table after the break.

Monday, April 7, 2014

[GW2] Server Transfers

I've been tracking players on the GW2 achievement leaderboards.

The boards enable me to track when a player transfers off of a server: players that disappear from the boards - but have enough points to appear on them - have likely jumped ship.  (Or, alternatively, been banned: I'm not sure what happens with the boards then.)

I was able to track players on 23 EU servers for one month [February 20th to March 23rd]. In that month, I observed 1456 players that likely transferred servers. That makes a 0.2% chance that a top 1000 player server transfers on any given day - or - a 6.6% chance that a top 1000 player changes servers over the course of a month.
Caveat: some of my data collection was corrupted - from both my ISP (TimeWarner <glare>) and the ArenaNet website (the website got angst-y partway through my data collection). So I'm missing some servers. Take the resulting numbers with salt.
Transfers are highly clustered: on most days on most servers, at most one player out of the top 1000 transfers (65% of all server-days look like this). However, on some servers, on some days, large clusters of players leave the server (record observed: 57 of the top 1000 players left Underworld on March 20th).

Transfers also differ by day: on March 7th, ArenaNet announced a reduction in the cost of server transfers starting on March 18th.  This resulted in a considerable rise in the number of transfers. Before March 18th, an average of 1.9 top 1000 players transferred per server each day. After March 19, that number jumped to 4.7.

Pre March 18 Post March 18
Gold 1.1 1.4
Silver 2.0 9.2
Bronze 2.4 4.8

But while these transfers were designed to encourage players to move to lower-tiered servers, they had something of a bandwagon effect.  After the update, very few top 1000 players left gold-tier servers. Most of the movement came from the Silver / Bronze tiers.

I'm actually surprised at just how common server transfers are. Post-March 18, nearly 10 of the top 1000 players in Silver tier on every server changed servers each day. That is a remarkable change in the population of each server.

I'm also not surprised that most transfers originate on Silver / Bronze servers.  WvW match-ups on these servers can be frustrating, and it makes sense that players would seek a stronger world environment.

Thursday, February 27, 2014

[GW2] Server Populations and Achievement Scores

After observing large differences in Marionette success rates across servers, I've become interested in understanding a bit more about server populations.

So the achievement point leaderboards were of particular interest to me.

Players earn achievements by completing milestones, participating in living story events, and completing dailies. They're a great measure of player activity, since you get achievement points for just about everything. Even better, ArenaNet publicly tracks achievement points for the top 1000 players on each server.
Here, I've plotted the achievement points of the top 1000 players on each server.  The servers are organized by the average achievement point score of these players (highest top left to lowest bottom right), and colored by their WvW season 1 tier (gold / silver / bronze).

There are vast differences between servers.

As a snapshot, the leaderboards are interesting.  But tracked over time, they contain much more information. For this, I collected data from the leaderboards during the Edge of the Mists update. This gives three measures of server activity:  (1) transfers, (2) inactive players, and (3) points gained among the active players.

Server Transfers: Jumping Ship
Server transfers show up on the leaderboards in two ways. A player could appear on one server, and later on another. So I can track accounts that move between servers.

Other players disappeared from the leaderboards. So, for example, if a player on Eredon Terrace had over 4217 points at the start of the Edge of the Mists update, they should appear on that server's top 1000 list unless they transferred off the server.
Overall, 1.6% of players listed on the leaderboards transferred servers. Given the small number of transfers from each server (and the reasonable expectation that some of the 'large' moves are due to guilds) it is hard to make a general pattern from the server transfer data, but I'll look at it again in future updates.

However, of the transfers I observed, 84% are to servers with higher average achievement point scores than the starting server.

Inactive Players
Overall, 17% of players on the server top 1000 didn't earn any achievement points during the Edge of the Mists update, and therefore likely didn't play GW2 during the update. Here are the percent of inactive players by server:
Inactive players are more common in lower-tiered servers, with the Bronze tier averaging over 23% of players inactive, compared to an average 12% for the gold servers.

Points Gained by Server
During the two-week update, active players on the leaderboards gained an average of 170 points, around 12 points per day. Pretty impressive, considering that the daily requires only 5 points. (The average top 1000 player earned about one-third of the total possible points to be earned from living story / daily content.)
Across all servers, players with more achievement points earned more points than those with fewer points (rich get richer faster).

Several Thoughts
By now, it is clear that there are large differences in server populations and activity. It is simply a myth that there are 'pve servers' that just happen to do poorly in WvW. Players tend to transfer to higher-tiered servers. Those servers have fewer inactive players. And the players on higher tiered servers tend to be more active.

Time to think about a server transfer myself...

Sidenote: the results presented here don't change under more complicated statistical models (which I ran, but excluded from the presentation because this is a long post already). Though, I did have to run a nonparametric model due to the interesting structure underlying the data.

Tuesday, February 25, 2014

[GW2] Professional Voting

Today, Guild Wars 2 extended their Collaborative Development Initiative (CDI) to ask players to post their feedback on the ranger profession.  (Note: 'professions' are what most MMOs would classes).

Ranger was chosen in this thread, where the developers asked players to list 3 professions (in order of priority) they would like to see discussed first.  But isn't choosing a profession based on posting in a thread open for 24 hours on the forum problematic? Particularly active forum users would be likely to overwhelm the thread. And its reasonable to expect that posters would be biased toward their own class, instead of looking out for game balance as a whole.

So how reasonable was the thread as a method of getting feedback?

The results:

Ranger was the most mentioned profession, followed by elementalist and then necromancer to round out the top three. Rangers are particularly weak in GW2's pve, and one playstyle (bearbow) is consistently viewed with scorn.

Breaking down the votes by order of priority indicates that not only was ranger the overall top choice, it was most frequently listed as priority #1 by voters. Most of the ordering between professions remains the same.

But are these votes contaminated by bias?

Prior Posting Activity
One objection to this poll might be that not only are forums generally unrepresentative of player opinions, but frequent forum posters might be likely to overwhelm any thread. Hardcore and casual players might be expected to disagree on which professions need the most attention.

While generally valid objections, they don't apply particularly well to this poll.
For nearly 20% of voters, voting in this thread was their first post on the forums. For others, posting is a pretty frequent activity. Voters had an average 205 posts before the thread (with a maximum of over 4600 posts!). 

Curiously, however, prior posting activity doesn't change the results. Both first-time and prior posters overwhelmingly agree on their preference order, favoring rangers, elementalists and necromancers. (Though mesmers do a little less well among first-time posters).

Profession(al) Bias
Another way to look at the votes is to examine what other forums voters are active on. Players might be expected to be biased toward voting for their own profession, which could be reflected by their posting in profession-specific subforums.

Here, I took a look at the past 50 forum posts of each voter (excluding first-time posters), and recorded whether they'd posted in one of the profession-specific subforums.  I compared this against their listed vote preferences.
In general, the votes are only slightly biased toward forums voters are active in.  For example, 30% of those who ranked elementalist as priority #2 had posted in the elementalist subforums, compared to only 15% of all voters. But this pattern doesn't hold generally. Those who picked engineer, mesmer, thief or warrior were no more likely to be active in those professions' subforums. So, in general, forum posting activity is at best weakly related to vote choice.

The exception - as ever - is rangers.  While only 5% of voters had posted in the ranger forums previously, 45% of those who listed ranger as their top pick had posted in those forums. Among top choices, ranger is the only profession that shows such a strong pattern. However, even excluding these voters, ranger would still be the top pick.

Clearly, a 24-hour poll isn't the best way to generate clear feedback on which profession requires the most attention.  In this case, however, the ranger profession is so overwhelmingly in need of attention that the effect of these (otherwise valid) concerns is overwhelmed.

Fingers crossed for some pretty excellent fixes.

Disclaimer: I have a ranger at 80, but I only use it to loot jumping puzzle chests since returning to GW2.

Tuesday, February 11, 2014

[GW2] Back! And Marionette Success Rates

Hello Tyria!

We're back with a blast. After over a year without MMOs, I decided to take a quick check at what was new in GW2.

... and quickly wandered into another data-driven gaming argument.

In the Origins of Madness update, ArenaNet introduced two world raid bosses: The Twisted Marionette and a three headed Great Jungle Wurm. While the encounters have difficult mechanics, they're part of the open world - you simply cannot choose the other players you'll fight alongside. Since each boss has mechanics that make it possible for a single player to cause the whole server to fail the encounter, players have taken to complaining about the mechanics of both fights on the forums (shocker!).

I'm particularly interested in the Marionette because of this comment, made by Josh Foreman (Environment Design for ANet), in responding to complaints about the fight's difficulty:
if after a week the Marionette is still only being beaten 1 out of 10 times, then I would say we may have tuned it a bit too difficult.
That was 14 days ago. A week after he made that comment, I started tracking the success of the Marionette event via the GW2 API. The Events section of the api tracks the status of each event on every server, noting its outcome (success/fail). This gives me six days of data on Marionette kill attempts. Since the Marionette fight occurs once every two hours, that is data on just over 70 Marionette attempts.

The overall Marionette success rate for the past week is 6.6%.
  • on North American servers the success rate is 6.1%.
  • on European servers the success rate is 7.0%.

Server Population
One issue with the Marionette is that the fight takes a large number of players to be successful. The fight is divided into five lanes, which are periodically divided further, into five platforms. Most guides for the fight mention 20-25 players per lane (100-125 players for a successful attempt), though a coordinated group could get by with less. So active, well-populated, coordinated servers should do better on this boss.
There are vast differences between servers.  The top EU server (Desolation) succeeds on 63% of its attempts, and the top NA server isn't far behind (Blackgate - 59%). On the other hand, I have never observed a successful Marionette attempt on half of all servers (25 of 51 servers).
As might be expected, servers with a higher WvW rank are much more successful at the Marionette. While top 5 WvW servers average a greater than 20% success rate, all other servers have a less than 5% sucess rate at the event.

Prime Time
In addition to vast differences between servers, it matters what time the event is being attempted. NA primetime (starting at 7 EST) has a much higher success rate than afternoons (students getting off school?).
With this in mind, I have two caveats:
  1. GuildWars 2 has an overflow system, where if too many players are in a zone, an overflow server is created for any additional players that arrive (or several overflows, if need be). I don't have any information about what happens on these servers (or how many there are).
  2. It could be that the GW2:Events API is not accurate. Completely unsuccessful servers are pretty shocking, so much so that I doubt the source. Then again, I do the Marionette at least once per day, and the outcome of each of those attempts is accurate, when I check against the data. 
Further Questions
So what does this mean for events like the Marionette?

Feedback based on a particular server (or time) isn't really representative of the experience of the event as a whole.  Someone trying the event at 7 or 9 pm EST on Blackgate is virtually guaranteed a successful run. But there are 25 servers that I've never seen succeed at the event.

On the other hand, vast differences between servers (and times) suggests that the fight isn't balanced across the wide range of situations GW2 players are likely to encounter. Hopefully, future events will be open to a wider range of the community, instead of being limited / exclusive content.

Time willing, I'll take another look at the Marionette sometime this week, and see if I can break this apart even more.

Tuesday, March 12, 2013

[POE] Hardcore

Time for some ARPG shenanigans.

I've been playing Path of Exile.

Its probably the best game I've picked up in a years. I could write pages and pages on why I love this game. The races. The skill trees. The complexity. But this blog is about being a video game data nerd, not persuading others to play awesome games. So instead: a video.

Great, now that everyone is playing, here comes the data.

Like most ARPGs, Path of Exile has a hardcore league. A single death kicks you out of the league, and into default. Since staying alive gets comically difficult, the hardcore league is super competitive. Players speculate on the best builds, watch the top characters, and get global announcements when a top 25 player dies. They debate whether duelists are viable, marauders overpowered, witches death-prone...

Of course, the best way to answer these arguments would be to track the progress of characters through hardcore, recording when they die, how quickly they gain experience, and whether class choice matters.

Fortunately, the PoE website lists the top 15000 characters in the hardcore league. By periodically recording this information, I can get a timeline of characters, as the league progresses.

Classy Breakdowns
Here is the breakdown of default and hardcore characters, by class:
While witches are the most second-most popular option on default, they're the second-least-popular class in the hardcore league. Hardcore is dominated by Templars, Marauders, and Rangers. Duelists, who have the weakest starting position, are the least popular class in both leagues. (They've recently been buffed, though.)

But why are there differences between the two leagues?  Is hardcore just harder for some classes? Are witches just too squishy? Or do players just prefer some classes over others?

Changing Classes
Minimally, if hardcore was harder for some classes, you'd expect to see dramatic changes in the proportions of each class over time.  So, if witches were really weak, at the start of the league there would be a ton of witches, they'd die, and the result would be fewer witches over time.

Here is the distribution of classes over the past month.
Over the past month, there have been small changes in the class distribution of players. Witches have increased their share, while duelists have steadily declined. Marauders have fallen in popularity, only to rise again. Rangers and templars have remained remarkably stable at the top.

Overall, though, class proportions have remained fairly stable. This suggests that whatever imbalances exist, they are small, and being amplified via player choices.

The Final Death
Another way to look at difficulty across classes is via deaths.  If POE is harder on some classes, then those classes should die more. In particular, if a class is harder in the mid or late-game, then there should be relatively more deaths for those classes at the higher levels.
Here, I'm looking at the average chance a character dies for every 15 minutes that they're online, by level and class.

Overall, gameplay becomes less lethal as characters level up. Characters in the 60s are less likely to die (per minutes played) than characters in the 40s.

While *slight* differences exist between the classes (witches die more frequently than rangers, for example), they're relatively small, and not large enough to explain overall class divisions on their own.

There are, of course, other ways to look at differences between classes: experience gains, survival analysis, etc... but for the moment, I need to keep leveling in merciless difficulty. =D

Tuesday, January 29, 2013

[GW2] Crafting Update - January

Time for another monthly update on the cost of legendary items in GW2. (First post here, update here).

Prices have steadily risen since my last look at the end of December.  From December 29 to Jan 29th the average cost of crafting a legendary has risen by 170 gold, or just over 5.5 gold per day.

Breaking down legendary weapons by type, I was surprised to find that the ranged weapons (Dreamer, Kudzu, and Predator) have risen in cost faster than the other legendaries, averaging a 240g increase over the past month.  Visually, here is the rise in cost of each legendary weapon, excluding vendor materials:

Breaking down legendary weapons by their components, its still clear that - for most legendaries - the precursor is the predominant cost.
This is particularly unfortunate, given news that the precursor scavenger hunt would not be in the Jan/Feb/March update.

Looking across all legendary items, the relatively steady prices across the end of December were driven by a decline in the cost of most components offsetting a rise in the cost of Globs of Ectoplasm. Since then, while the price of globs has fallen, the cost of all other components has steadily risen, leading to an overall surge in prices each week.
Happy hunting!

If you have any other questions, leave a note in the comments / send an email, I'll see what I can find.