Abstract: Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of similar strength in online gaming, and for players to track their own strength over time. Most implemented rating systems assume only win/loss outcomes, and treat occurrences of ties as the equivalent to half a win and half a loss. However, in games such as chess, the probability of a tie (draw) is demonstrably higher for stronger players than for weaker players, so that rating systems ignoring this aspect of game results may produce strength estimates that are unreliable. We develop a new rating system for head-to-head games that explicitly acknowledges a tie as a third outcome, and that the probability of a tie may depend on the strengths of the competitors. Our approach relies on time-varying game outcomes following a Bayesian dynamic modeling framework, and that posterior updates within a time period are approximated by one iteration of Newton-Raphson evaluated at the prior mean. The approach is demonstrated on a large dataset of chess games played in International Correspondence Chess Federation tournaments.
Mark Glickman is a Senior
Lecturer on Statistics at Harvard University and a recognized
leader in sports analytics and statistical ranking methodology.
He is best known for developing the Glicko and Glicko-2 rating
systems, which extend the Elo framework by explicitly modeling
uncertainty in player strength and have been adopted in chess,
esports, and other competitive domains. His research spans
Bayesian inference, hierarchical modeling, paired-comparison
models, and decision-making under uncertainty, with applications
in sports, games, public policy, and the social sciences. Dr.
Glickman has played a visible leadership role in the statistics
and data science community through professional society service,
conference organization, and scholarly leadership. Particularly
relevant to CSAS, he has been one of the organizers of the New
England Symposium on Statistics in Sports (NESSIS), a
long-running and highly influential forum that brings together
students, researchers, and practitioners working at the
interface of statistics, data science, and sports analytics. His
work is widely cited for its clarity, practical relevance, and
principled statistical foundations, and it has shaped how modern
performance evaluation problems are formulated and solved.
Abstract: At ESPN, we have a wide receiver rating, a pass blocker rating, a quarterback rating, a net points rating for various basketball leagues. A player rating is useful because everyone talks about how good (or bad) players are --- fans, analysts, coaches, medical staff --- and just about everyone does it based on their eyes. Or, frankly, based on what the media feeds them. But I worked for NBA teams and you know what? Subjective opinions aren't very useful there. You gotta have something that does something that good scouts can't match --- you have to have something that sees all the plays. You gotta have something that not only says who is good, but why, when, and how. To do that needs metrics that work at a very granular level. And you know what you need to do that? A way to divide credit at a very fine level. I'll introduce some of the math and some of the intuition behind doing this the right way.
Dean
Oliver is a pioneer of modern basketball analytics and a
senior leader in sports analytics at ESPN. He is widely known
for his 2004 book Basketball on Paper, which helped establish
data-driven analysis as a central component of basketball
decision-making. Following its publication, he worked in
multiple NBA front offices and served as an assistant coach,
integrating statistical analysis directly into team strategy,
player evaluation, and organizational decisions. In 2011, he
helped create ESPN’s sports analytics group, contributing to the
development of quantitative analysis and data-informed
storytelling in sports media, and he rejoined the group in May.
His recent book, Basketball Beyond Paper (November 2024),
documents his professional experiences and presents studies on
player fit, psychology, and performance, reflecting the
continued evolution of analytics in basketball. His career
bridges analytics, coaching, and media, aligning closely with
CSAS’s emphasis on connecting statistical methodology with
real-world sports applications.