A recurring discussion in Overwatch (as well as other online games) is whether or not women are treated differently from men. If you do a quick search, you can find hundreds of discussions about this, some of which have well over a thousand comments. These discussions tend to go the same way and involve the same debate every time, with the same points being made on both sides. Just for example, these three threads on reddit that spun out of a single post that have a total of 10.4k comments. On one side, you have people saying "sure, women get trash talked, but I'm a dude and I get trash talked, everyone gets trash talked there's no difference", "I've never seen this, it can't be real", etc., and on the other side you have people saying things like "when I play with my boyfriend, I get accused of being carried by him all the time but the reverse never happens", "people regularly tell me I should play mercy[, a character that's a female healer]", and so on and so forth. In less time than has been spent on a single large discussion, we could just run the experiment, so here it is.
This is the result of playing 339 games in the two main game modes, quick play (QP) and competitive (comp), where roughly half the games were played with a masculine name (where the username was a generic term for a man) and half were played with a feminine name (where the username was a woman's name). I recorded all of the comments made in each of the games and then classified the comments by type. Classes of comments were "sexual/gendered comments", "being told how to play", "insults", and "compliments".
In each game that's included, I decided to include the game (or not) in the experiment before the character selection screen loaded. In games that were included, I used the same character selection algorithm, I wouldn't mute anyone for spamming chat or being a jerk, I didn't speak on voice chat (although I had it enabled), I never sent friend requests, and I was playing outside of a group in order to get matched with 5 random players. When playing normally, I might choose a character I don't know how to use well and I'll mute people who pollute chat with bad comments. There are a lot of games that weren't included in the experiment because I wasn't in a mood to listen to someone rage at their team for fifteen minutes and the procedure I used involved pre-committing to not muting people who do that.
I thought I'd see more sexual comments when using the feminine name as opposed to the masculine name, but that turned out to not be the case. There was some mention of sex, genitals, etc., in both cases and the rate wasn't obviously different and was actually higher in the masculine condition.
Zero games featured comments were directed specifically at me in the masculine condition and two (out of 184) games in the feminine condition featured comments that were directed at me. Most comments were comments either directed at other players or just general comments to team or game chat.
Examples of typical undirected comments that would occur in either condition include ""my girlfriend keeps sexting me how do I get her to stop?", "going in balls deep", "what a surprise. *strokes dick* [during the post-game highlight]", and "support your local boobies".
The two games that featured sexual comments directed at me had the following comments:
During games not included in the experiment (I generally didn't pay attention to which username I was on when not in the experiment), I also got comments like "send nudes". Anecdotally, there appears to be a different in the rate of these kinds of comments directed at the player, but the rate observed in the experiment is so low that uncertainty intervals around any estimates of the true rate will be similar in both conditions unless we use a strong prior.
The fact that this difference couldn't be observed in 339 games was surprising to me, although it's not inconsistent with McDaniel's thesis, a survey of women who play video games. 339 games probably sounds like a small number to serious gamers, but the only other randomized experiment I know of on this topic (besides this experiment) is Kasumovic et al., which notes that "[w]e stopped at 163 [games] as this is a substantial time effort".
All of the analysis uses the number of games in which a type of comment occured and not tone to avoid having to code comments as having a certain tone in order to avoid possibly injecting bias into the process. Sentiment analysis models, even state-of-the-art ones often return nonsensical results, so this basically has to be done by hand, at least today. With much more data, some kind of sentiment analysis, done with liberal spot checking and re-training of the model, could work, but the total number of comments is so small in this case that it would amount to coding each comment by hand.
Coding comments manually in an unbiased fashion can also be done with a level of blinding, but doing that would probably require getting more people involved (since I see and hear comments while I'm playing) and relying on unpaid or poorly paid labor.
The most striking, easy to quantify, difference was the rate at which I played games in which people told me how I should play. Since it's unclear how much confidence we should have in the difference if we just look at the raw rates, we'll use a simple statistical model to get the uncertainty interval around the estimates. Since I'm not sure what my belief about this should be, this uses an uninformative prior, so the estimate is close to the actual rate. Anyway, here are the uncertainty intervals a simple model puts on the percent of games where at least one person told me I was playing wrong, that I should change how I'm playing, or that I switch characters:
The experimental conditions in this table are masculine vs. feminine name (M/F) and competitive mode vs quick play (comp/QP). The numbers are percents.
Est is the estimate,
P25 is the 25%-ile estimate, and
P75 is the 75%-ile estimate. Competitive mode and using a feminine name are both correlated with being told how to play. See this post by Andrew Gelman for why you might want to look at the 50% interval instead of the 95% interval.
For people not familiar with overwatch, in competitive mode, you're explicitly told what your ELO-like rating is and you get a badge that reflects your rating. In quick play, you have a rating that's tracked, but it's never directly surfaced to the user and you don't get a badge.
It's generally believed that people are more on edge during competitive play and are more likely to lash out (and, for example, tell you how you should play). The data is consistent with this common belief.
Per above, I didn't want to code tone of messages to avoid bias, so this table only indicates the rate at which people told me I was playing incorrectly or asked that I switch to a different character. The qualitative difference in experience is understated by this table. For example, the one time someone asked me to switch characters in the masculine condition, the request was a one sentence, polite, request ("hey, we're dying too quickly, could we switch [from the standard one primary healer / one off healer setup] to double primary healer or switch our tank to [a tank that can block more damage]?"). When using the feminine name, a typical case would involve 1-4 people calling me human garbage for most of the game and consoling themselves with the idea that the entire reason our team is losing is that I won't change characters.
The simple model we're using indicates that there's probably a difference between both competitive and QP and playing with a masculine vs. a feminine name. However, most published results are pretty bogus, so let's look at reasons this result might be bogus and then you can decide for yourself.
The biggest issue is that this wasn't a pre-registered trial. I'm obviously not going to go and officially register a trial like this, but I also didn't informally "register" this by having this comparison in mind when I started the experiment. A problem with non-pre-registered trials is that there are a lot of degrees of freedom, both in terms of what we could look at, and in terms of the methodology we used to look at things, so it's unclear if the result is "real" or an artifact of fishing for something that looks interesting. A standard example of this is that, if you look for 100 possible effects, you're likely to find 1 that appears to be statistically significant with p = 0.01.
There are standard techniques to correct for this problem (e.g., Bonferroni correction), but I don't find these convincing because they usually don't capture all of the degrees of freedom that go into a statistical model. An example is that it's common to take a variable and discretize it into a few buckets. There are many ways to do this and you generally won't see papers talk about the impact of this or correct for this in any way, although changing how these buckets are arranged can drastically change the results of a study. Another common knob people can use to manipulate results is curve fitting to an inappropriate curve (often a 2nd a 3rd degree polynomial when a scatterplot shows that's clearly incorrect). Another way to handle this would be to use a more complex model, but I wanted to keep this as simple as possible.
If I wanted to really be convinced on this, I'd want to, at a minimum, re-run this experiment with this exact comparison in mind. As a result, this experiment would need to be replicated to provide more than a preliminary result that is, at best, weak evidence.
One other large class of problem with randomized controlled trials (RCTs) is that, despite randomization, the two arms of the experiment might be different in some way that wasn't randomized. Since Overwatch doesn't allow you to keep changing your name, this experiment was done with two different accounts and these accounts had different ratings in competitive mode. On average, the masculine account had a higher rating due to starting with a higher rating, which meant that I was playing against stronger players and having worse games on the masculine account. In the long run, this will even out, but since most games in this experiment were in QP, this didn't have time to even out in comp. As a result, I had a higher win rate as well as just generally much better games with the feminine account in comp.
With no other information, we might expect that people who are playing worse get told how to play more frequently and people who are playing better should get told how to play less frequently, which would mean that the table above understates the actual difference.
However Kasumovic et al., in a gender-based randomized trial of Halo 3, found that players who were playing poorly were more negative towards women, especially women who were playing well (there's enough statistical manipulation of the data that a statement this concise can only be roughly correct, see study for details). If that result holds, it's possible that I would've gotten fewer people telling me that I'm human garbage and need to switch characters if I was average instead of dominating most of my games in the feminine condition.
If that result generalizes to OW, that would explain something which I thought was odd, which was that a lot of demands to switch and general vitriol came during my best performances with the feminine account. A typical example of this would be a game where we have a 2-2-2 team composition (2 players playing each of the three roles in the game) where my counterpart in the same role ran into the enemy team and died at the beginning of the fight in almost every engagement. I happened to be having a good day and dominated the other team (37-2 in a ten minute comp game, while focusing on protecting our team's healers) while only dying twice, once on purpose as a sacrifice and second time after a stupid blunder. Immediately after I died, someone asked me to switch roles so they could take over for me, but at no point did someone ask the other player in my role to switch despite their total uselesses all game (for OW players this was a Rein who immediately charged into the middle of the enemy team at every opportunity, from a range where our team could not possibly support them; this was Hanamura 2CP, where it's very easy for Rein to set up situations where their team cannot help them). This kind of performance was typical of games where my team jumped on me for playing incorrectly. This isn't to say I didn't have bad games; I had plenty of bad games, but a disproportionate number of the most toxic experiences came when I was having a great game.
I tracked how well I did in games, but this sample doesn't have enough ranty games to do a meaningful statistical analysis of my performance vs. probability of getting thrown under the bus.
Games at different ratings are probably also generally different environments and get different comments, but it's not clear if there are more negative comments at 2000 than 2500 or vice versa. There are a lot of online debates about this; for any rating level other than the very lowest or the very highest ratings, you can find a lot of people who say that the rating band they're in has the highest volume of toxic comments.
Here are some things that happened while playing with the feminine name that didn't happen with the masculine name during this experiment or in any game outside of this experiment:
The rate of all these was low enough that I'd have to play many more games to observe something without a huge uncertainty interval.
I didn't accept any friend requests from people I had no interaction with. Anecdotally, some people report people will send sexual comments or berate them after an unsolicited friend request. It's possible that the effect show in the table would be larger if I accepted these friend requests and it couldn't be smaller.
I didn't attempt to classify comments as flirty or not because, unlike the kinds of commments I did classify, this is often somewhat subtle and you could make a good case that any particular comment is or isn't flirting. Without responding (which I didn't do), many of these kinds of comments are ambiguous
Another difference was in the tone of the compliments. The rate of games where I was complimented wasn't too different, but compliments under the masculine condition tended to be short and factual (e.g., someone from the other team saying "no answer for [name of character I was playing]" after a dominant game) and compliments under the feminine condition tended to be more effusive and multiple people would sometimes chime in about how great I was.
The rate of complements and the rate of insults in games that didn't include explanations of how I'm playing wrong or how I need to switch characters were similar in both conditions.
Some other factors that would be interesting to look at would be time of day, server, playing solo or in a group, specific character choice, being more or less communicative, etc., but it would take a lot more data to be able to get good estimates when adding it more variables. Blizzard should have the data necessary to do analyses like this in aggregate, but they're notoriously private with their data, so someone at Blizzard would have to do the work and then publish it publicly, and they're not really in the habit of doing that kind of thing. If you work at Blizzard and are interested in letting a third party do some analysis on an anonymized data set, let me know and I'd be happy to dig in.
Under both conditions, I avoided ever using voice chat and would call things out in text chat when time permitted. Also under both conditions, I mostly filled in with whatever character class the team needed most, although I'd sometimes pick DPS (in general, DPS are heavily oversubscribed, so you'll rarely play DPS if you don't pick one even when unnecessary).
For quickplay, backfill games weren't counted (backfill games are games where you join after the game started to fill in for a player who left; comp doesn't allow backfills). 6% of QP games were backfills.
These games are from before the "endorsements" patch; most games were played around May 2018. All games were played in "solo q" (with 5 random teammates). In order to avoid correlations between games depending on how long playing sessions were, I quit between games and waited for enough time (since you're otherwise likely to end up in a game with some or many of the same players as before).
The model used probability of a comment happening in a game to avoid the problem that Kasumovic et al. ran into, where a person who's ranting can skew the total number of comments. Kasumovic et al. addressed this by removing outliers, but I really don't like manually reaching in and removing data to adjust results. This could also be addressed by using a more sophisticated model, but a more sophisticated model means more knobs which means more ways for bias to sneak in. Using the number of players who made comments instead would be one way to mitigate this problem, but I think this still isn't ideal because these aren't independent -- when one player starts being negative, this greatly increases the odds that another player in that game will be negative, but just using the number of players makes four games with one negative person the same as one game with four negative people. This can also be accounted for with a slightly more sophisticated model, but that also involves adding more knobs to the model.
If I step back from the gender experiment, the most baffling thing to me about Overwatch is the Herculean level of self-delusion adult Overwatch players have (based on the sounds of people's voice, I think that most people who are absolutely livid about the performance of a teammate are adults).
Just for example, if you look at games where someone leaves in the early phase of the game, causing it to get canceled, IME, this is almost always because one player was AFK and eventually timed out. I've seen this happen maybe 40 times, and the vast majority of the time, 1-3 players will rage about how they were crushing the other team and are being unfairly denied a (probable) victory. I have not seen a single case where someone notices that the game was 6v5 the entire time because someone was AFK out of nearly 40 games of people compaining about this.
If this were a field sport, I'd expect that players would notice that the other team is literally missing a player for the entire game by second grade. The median person at my rank (amazingly, above median for all players) who's raging at other players has roughly the same level of game sense as a first grader. And yet, they'll provide detailed (wrong, but detailed) commentary on other people's shortcomings, suggest that someone is "throwing [the game]" if they don't attempt to use a sophisticated strategy that pros have to practice to get right, etc.
Of course, by definition, people can't be aware that they're not aware that the other team is missing a player. However, someone with awareness that poor must get surprised by events in the game all the time (my awareness is substantially better than median for my rank because my technical skill is worse, and I still get blindsided multiple times per game; each time, it's a reminder that I'm not properly tracking what's happening in the game and can't even keep up with what my character should be doing).
It requires a staggering level of willful blindness to be that unaware, get surprised by events all the time, and still think that your understanding of the game is deep enough that you can, while playing your own character and tracking everything you're supposed to track, also track everything someone on your team is supposed to track and understand what's going on deeply enough to provide advice.
This stupefying level of confidence combined with willfull blindness was also found in this survey of people's perception of their own skill level vs. their actual rating found that 1% of people thought they were overrated, 32% of people thought they were rated accurately, and the other 77% of people thought they were underrated. If you're paying attention, you get feedback about how good you are all the time (for example, the game helpfully shows you exactly how you died every time you die), but the majority of players manage to ignore this feedback.
There's nothing wrong with not paying attention to how good you are and playing "just for fun", but these guys who rage at their teammates for bringing them down aren't playing for fun, they're serious. I don't understand how people who are so serious that they'd get angry at strangers for their perceived lack of skill in a video game would choose to ignore all of this information that they could use to get better and choose to yell at teammates (increasing the probability of a loss) instead of fixing the gross errors in their own gameplay (decreasing the probability of a loss).
A common complaint, perhaps the most common complaint by people below 2000 SR (roughly 30%-ile) or perhaps 1500 SR (roughly 10%-ile) is that they're in "ELO hell" and are kept down because their teammates are too bad. Based on my experience, I find this to be extremely unlikely.
People often split skill up into "mechanics" and "gamesense". My mechanics are pretty much as bad as it's possible to get. The last game I played seriously was a 90s video game that's basically online asteroids and the last game before that I put any time into was the original SNES super mario kart. As you'd expect from someone who hasn't put significant time into a post-90s video game or any kind of FPS game, my aim and dodging are both atrocious. On top of that, I'm an old dude with slow reflexes and I was able to get to 2500 SR (roughly 60%-ile among players who play "competitive", likely higher among all players) by avoiding a few basic fallacies and blunders despite have approximately zero mechanical skill. If you're also an old dude with basically no FPS experience, you can do the same thing; if you have good reflexes or enough FPS experience to actually aim or dodge, you basically can't be worse mechnically than I am and you can do much better by avoiding a few basic mistakes.
The most common fallacy I see repeated is that you have to play DPS to move out of bronze or gold. The evidence people give for this is that, when a GM streamer plays flex, tank, or healer, they sometimes lose in bronze. I guess the idea is that, because the only way to ensure a 99.9% win rate in bronze is to be a GM level DPS player and play DPS, the best way to maintain a 55% or a 60% win rate is to play DPS, but this doesn't follow.
Healers and tanks are both very powerful in low ranks. Because low ranks feature both poor coordination and relatively poor aim (players with good coordination or aim tend to move up quickly), time-to-kill is very slow compared to higher ranks. As a result, an off healer can tilt the result of a 1v1 (and sometimes even a 2v1) matchup and a primary healer can often determine the result of a 2v1 matchup. Because coordination is poor, most matchups end up being 2v1 or 1v1. The flip side of the lack of coordination is that you'll almost never get help from teammates. It's common to see an enemy player walk into the middle of my team, attack someone, and then walk out while literally no one else notices. If the person being attacked is you, the other healer typically won't notice and will continue healing someone at full health and none of the classic "peel" characters will help or even notice what's happening. That means it's on you to pay attention to your surroundings and watching flank routes to avoid getting murdered.
If you can avoid getting murdered constantly and actually try to heal (as opposed to many healers at low ranks, who will try to kill people or stick to a single character and continue healing them all the time even if they're at full health), you outheal a primary healer half the time when playing an off healer and, as a primary healer, you'll usually be able to get 10k-12k healing per 10 min compared to 6k to 8k for most people in Silver (sometimes less if they're playing DPS Moira). That's like having an extra half a healer on your team, which basically makes the game 6.5 v 6 instead of 6v6. You can still lose a 6.5v6 game, and you'll lose plenty of games, but if you're consistently healing 50% more than an normal healer at your rank, you'll tend to move up even if you get a lot of major things wrong (heal order, healing when that only feeds the other team, etc.).
A corollary to having to watch out for yourself 95% when playing a healer is that, as a character who can peel, you can actually watch out for your teammates and put your team at a significant advantage in 95% of games. As Zarya or Hog, if you just boringly play towards the front of your team, you can basically always save at least one teammate from death in a team fight, and you can often do this 2 or 3 times. Meanwhile, your counterpart on the other team is walking around looking for 1v1 matchups. If they find a good one, they'll probably kill someone, and if they don't (if they run into someone with a mobility skill or a counter like brig or reaper), they won't. Even in the case where they kill someone and you don't do a lot, you still provide as much value as them and, on average, you'll provide more value. A similar thing is true of many DPS characters, although it depends on the character (e.g., McCree is effective as a peeler, at least at the low ranks that I've played in). If you play a non-sniper DPS that isn't suited for peeling, you can find a DPS on your team who's looking for 1v1 fights and turn those fights into 2v1 fights (at low ranks, there's no shortage of these folks on both teams, so there are plenty of 1v1 fights you can control by making them 2v1).
All of these things I've mentioned amount to actually trying to help your team instead of going for flashy PotG setups or trying to dominate the entire team by yourself. If you say this in the abstract, it seems obvious, but most people think they're better than their rating. It doesn't help that OW is designed to make people think they're doing well when they're not and the best way to get "medals" or "play of the game" is to play in a way that severely reduces your odds of actually winning each game.
Outside of obvious gameplay mistakes, the other big thing that loses games is when someone tilts and either starts playing terribly or flips out and says something to enrage someone else on the team, who then starts playing terribly. I don't think you can actually do much about this directly, but you can never do this, so 5/6th of your team will do this at some base rate, whereas 6/6 of the other team will do this. Like all of the above, this won't cause you to win all of your games, but everything you do that increases your win rate makes a difference.
Poker players have the right attitude when they talk about leaks. The goal isn't to win every hand, it's to increase your EV by avoiding bad blunders (at high levels, it's about more than avoiding bad blunders, but we're talking about getting out of below median ranks, not becoming GM here). You're going to have terrible games where you get 5 people instalocking DPS. Your odds of winning a game are low, say 10%. If you get mad and pick DPS and reduce your odds even further (say this is to 2%), all that does is create a leak in your win rate during games when your teammates are being silly.
If you gain/lose 25 rating per game for a win or a loss, your average rating change from a game is
25 (W_rate - L_rate) = 25 (2W_rate - 1). Let's say 1/40 games are these silly games where your team decides to go all DPS. The per-game SR difference of trying to win these vs. soft throwing is maybe something like
1/40 * 25 (2 * 0.08) = 0.1. That doesn't sound like much and these numbers are just guesses, but everyone outside of very high-level games is full of leaks like these, and they add up. And if you look at a 60% win rate, which is pretty good considering that your influence is limited because you're only one person on a 6 person team, that only translates to an average of 5SR per game, so it doesn't actually take that many small leaks to really move your average SR gain or loss.
Since I'm unlikely to write another blog post on gaming any time soon, here are some other random thoughts that won't fit with any other post. My last serious experience with online games was with a game from the 90s. Even though I'd heard that things were a lot worse, I was still surprised by it. IRL, the only time I encounter the same level and rate of pointless nastiness in a recreational activity is down at the bridge club (casual bridge games tend to be very nice). When I say pointless nastiness, I mean things like getting angry and then making nasty comments to a teammate mid-game. Even if your "criticism" is correct (and, if you review OW games or bridge hands, you'll see that these kinds of angry comments are almost never correct), this has virtually no chance of getting your partner to change their behavior and it has a pretty good chance of tilting them and making them play worse. If you're trying to win, there's no reason to do this and good reason to avoid this.
If you look at the online commentary for this, it's common to see people blaming kids, but this doesn't match my experience at all. For one thing, when I was playing video games in the 90s, a huge fraction of the online gaming population was made up of kids, and online game communities were nicer than they are today. Saying that "kids nowadays" are worse than kids used to be is a pastime that goes back thousands of years, but it's generally not true and there doesn't seem to be any reason to think that it's true here.
Additionally, this simply doesn't match what I saw. If I just look at comments over audio chat, there were a couple of times when some kids were nasty, but almost all of the comments are from people who sound like adults. Moreover, if I look at when I played games that were bad, a disproportionately large number of those games were late (after 2am eastern time, on the central/east server), where the relative population of adults is larger.
Sure, maybe people tend to get more mature as they age, but in any particular activity, that effect seems to be dominated by other factors. I don't have enough data at hand to make a good guess as to what happened, but I'm entertained by the idea that this might have something to do with it:
I’ve said this before, but one of the single biggest culture shocks I’ve ever received was when I was talking to someone about five years younger than I was, and she said “Wait, you play video games? I’m surprised. You seem like way too much of a nerd to play video games. Isn’t that like a fratboy jock thing?”
Here are some responses to the most common online comments.
Plat? You suck at Overwatch
Yep. But I sucked roughly equally on both accounts (actually somewhat more on the masculine account because it was rated higher and I was playing a bit out of my depth). Also, that's not a question.
This is just a blog post, it's not an academic study, the results are crap.
There's nothing magic about academic papers. I have my name on a few publications, including one that won best paper award at the top conference in its field. My median blog post is more rigorous than my median paper or, for that matter, the median paper that I read.
When I write a paper, I have to deal with co-authors who push for putting in false or misleading material that makes the paper look good and my ability to push back against this has been fairly limited. On my blog, I don't have to deal with that and I can write up results that are accurate (to the best of my abillity) even if it makes the result look less interesting or less likely to win an award.
Gamers have always been toxic, that's just nostalgia talking.
If I pull game logs for subspace, this seems to be false. YMMV depending on what games you played, I suppose. FWIW, airmash seems to be the modern version of subspace, and (until the game died), it was much more toxic than subspace even if you just compare on a per-game basis despite having much smaller games (25 people for a good sized game in airmash, vs. 95 for subsace).
This is totally invalid because you didn't talk on voice chat.
At the ranks I played, not talking on voice was the norm. It would be nice to have talking or not talking on voice chat be an indepedent variable, but that would require playing even more games to get data for another set of conditions, and if I wasn't going to do that, choosing the condition that's most common doesn't make the entire experiment invalid, IMO.
Some people report that, post "endorsements" patch, talking on voice chat is much more common. I tested this out by playing 20 (non-comp) games just after the "Paris" patch. Three had comments on voice chat. One was someone playing random music clips, one had someone screaming at someone else for playing incorrectly, and one had useful callouts on voice chat. It's possible I'd see something different with more games or in comp, but I don't think it's obvious that voice chat is common for most people after the "endorsements" patch.
If you want to play with this data and model yourself, experiment with different priors, run a posterior predictive check, etc., here's a snippet of R code that embeds the data:
library(brms) library(modelr) library(tidybayes) library(tidyverse) d <- tribble( ~game_type, ~gender, ~xplain, ~games, "comp", "female", 7, 35, "comp", "male", 1, 23, "qp", "female", 6, 149, "qp", "male", 2, 132 ) d <- d %>% mutate(female = ifelse(gender == "female", 1, 0), comp = ifelse(game_type == "comp", 1, 0)) result <- brm(data = d, family = binomial, xplain | trials(games) ~ female + comp, prior = c(set_prior("normal(0,10)", class = "b")), iter = 25000, warmup = 500, cores = 4, chains = 4)
The model here is simple enough that I wouldn't expect the version of software used to significantly affect results, but in case you're curious, this was done with
rstan 2.18.2, on
Thanks to Leah Hanson, Sean Talts and Sean's math/stats reading group, Annie Cherkaev, Robert Schuessler, Wesley Aptekar-Cassels, Julia Evans, Paul Gowder, Jonathan Dahan, Bradley Boccuzzi, Akiva Leffert, and one or more anonymous commenters for comments/corrections/discussion.