The Best Way to Rank Everyone | Stats + Stories Episode 80 / by Stats Stories


Mark Glickman, a Fellow of the American Statistical Association, is Senior Lecturer on Statistics at Harvard University, and Senior Statistician at the Center for Healthcare Organization and Implementation Research, a VA Center of Innovation.  He is well-known for his work in games and sports, having created the Glicko and Glicko-2 rating systems that are widely used in online gaming. 

+ Full Transcript

(Background music plays)

John Bailer: I'd like to welcome you to today's Stats and Short Stories episode. Stats and Short Stories is a partnership between Miami University and the American Statistical Association. I'm John Bailer, Chair of the department of Statistics at Miami University and I'm joined today by Rosemary Pennington from the Department of Media Journalism and Film, also at Miami. We're delighted to be joined today by guest Mark Glickman. Mark is a senior lecturer of statistics at Harvard University and also a senior statistician for the Center for Health Care Organization and implementation research. He's also someone that's been a leader in terms of trying to rank competitors in many sports. He's been a leader in Sports Analytics and some of his work has really been well implemented and embraced by the world of chess and other competitions. Mark, I'd like to say welcome and glad you are here with us.

Mark Glickman: I appreciate you having me on your show.

Bailer: Oh great! And Mark I'd like to say, how did you get involved in chess ranking?

Glickman: Well I got involved in chess ranking because when I was a little kid I played a lot of chess and I started playing in chess tournaments. And I was pretty fascinated when I started playing in tournaments, that they had this numerical rating system in place and you know, the way the rating system worked is that when you played an opponent with a rating and you defeated that opponent, your rating would go up and if your opponent was, you know, very high rated, your own rating would increase a lot. And then similarly, if you lost a game, you would have your rating decrease and there were all these formulas that described how to compute your own rating. And even as an eleven-year old, I was fascinated with how this formula worked, and you know, to make a long story short, I ended up studying a little bit about ratings in college. I wrote my PhD dissertation essentially developing an approach to modeling competitors, to understand their playing strength from first principles. I eventually became the chair of the ratings committee for US chess.

Rosemary Pennington: Oh wow!

Glickman: …which I've basically been doing continuously since 1992 and you know, that basically led into kind of this whole world of, you know, rating competitors in games and sports, which is a major area of research.

Bailer: It seems like a lot of the ratings that we hear about, especially team sports, they're not going to be playing head to head very often and it often seems very subjective in terms of how much a team might move, based on a victory or on a loss. What's special about the way some of the ratings are being done in chess?

Glickman: Well the ratings in chess are all based on your head to head outcomes. So the idea is that you know the goal of all these rating systems, the ones that are you know related to you know the methods are implemented for chess including the ones that I've developed are, they are aiming for you to be able to compute the probability that once two new teams or two players are about to compete head to head, what's the likelihood one's going to defeat the other. So all these systems, that at least I've been involved with, are really trying to estimate the probability of one player defeating another, all based on previous game results.

Pennington: So Mark, I am a current Cleveland Cavaliers fan…

Glickman: I’m sorry

Pennington:…and grew up rooting for the Bulls and so there is that constant debate in basketball, of who's the goat of basketball - is it M.J. or is it LeBron. Are there models, this one or some other that could actually help us understand if Michael Jordan or LeBron James is the better basketball player?

Glickman: Yeah…the kind of work that I've been doing doesn't really directly address that question and that's a tricky question, because you know a lot of the decision has to do with what measure you're using, you know, to say somebody is the best of all time. There are couple issues that make it a tricky problem. I mean, not to say that people haven't tried, but you know one of the problems is just simply, what is the metric by which you say someone is a better player than another. I know that some of the better strategies are kind of aimed at like, if this player were somehow not involved in the team, how would they be doing.

Pennington: Yeah yeah.

Glickman: But the other problem of course, when you're comparing different eras of players, and even you know, the nineties isn't so far away from you know, the LeBron era, but when comparing Michael Jordan and LeBron James, but you know the game itself has changed a little bit and you know, preparation and practice for the game has changed. So it's not entirely clear except relative to the current context that each of those players has played, are you really going to be able to answer the question. So you know you could probably have a better chance at answering the question that says how much better was Michael Jordan than all of his contemporaries, and compare that to how LeBron James is you know arguably better than all of his contemporaries and measure that magnitude of that relative difference. What would happen if he were playing at the same time period is an open question and be pretty tricky to get at.

Pennington: Yeah. I just I had to ask.

(Collective laughter)

Bailer: Well you know it seems like with some of the stuff that you're doing with chess with pairwise comparisons, I mean you've might have some connection across eras. You know, because you’ll have some of the players, you know, if you wanted to compare a chess master from the nineties to a chess master 20 years later, even if they didn't directly compete, they may have competed against people, you know, they may have had common competitors perhaps, or they may have competed in…there may be a chain that would connect them, in terms of this type of comparison.

Glickman: Right. So there is a similar issue in chess, as what I was describing in basketball, which is that the state of knowledge of chess actually advanced quite a bit. I mean certainly over time, you know, most people don't really, you know, we never really think about this. But much like there being like, you know, different schools of thought in art or music or you know various humanities there actually is very different schools of thought in chess. So like even in the early nineteen hundreds, there was this revolutionary movement called hyper modernism which had a completely different attitude towards what sort of strategy is going to be the most successful and it was a big revolution, relative to a much more classical style that was in place before then. And so by the time the 1930s and 40’s rolled around you had, pretty much the top players in the world were adopting this new approach to playing chess. And if you were to try to compare the abilities of the people in the forties versus those in say, you know, the 1910s, it's very hard to do that comparison because the way games were played is just completely different. So that is a confounding factor in being able to you know, draw some conclusion about strength even though you have these connections across players like you're saying John.

Bailer: Yeah, there's a drift there. Well, very interesting Mark! I'm afraid that's all the time we have for this episode of Stats and Short Stories, Mark, thank you so much for joining us.

Glickman: Well thank you very much for having me.

Bailer: Stats and Short Stories is a partnership between Miami University's departments of Statistics and Media Journalism and Film and the American Statistical Association. You can follow us on Twitter, on Apple podcast or other places where you can find your favorite source of podcasts. If you'd like to share your thoughts on our program, send your e-mail at and be sure to listen for future episodes of Stats and Stories, where we discuss the statistics behind the stories and the stories behind the statistics.