相关论文: Application of the Pythagorean Expected Wins Perce…
We ask if there are alternative contest models that minimize error or information loss from misspecification and outperform the Pythagorean model. This article aims to use simulated data to select the optimal expected win percentage model…
Bill James' Pythagorean formula has for decades done an excellent job estimating a baseball team's winning percentage from very little data: if the average runs scored and allowed are denoted respectively by ${\rm RS}$ and ${\rm RA}$, there…
Bill James invented the Pythagorean expectation in the late 70's to predict a baseball team's winning percentage knowing just their runs scored and allowed. His original formula estimates a winning percentage of ${\rm RS}^2/({\rm RS}^2+{\rm…
We mathematically prove that an existing linear predictor of baseball teams' winning percentages (Jones and Tappin 2005) is simply just a first-order approximation to Bill James' Pythagorean Won-Loss formula and can thus be written in terms…
Originally devised for baseball, the Pythagorean Won-Loss formula estimates the percentage of games a team should have won at a particular point in a season. For decades, this formula had no mathematical justification. In 2006, Steven…
The Pythagorean formula is one of the most popular ways to measure the true ability of a team. It is very easy to use, estimating a team's winning percentage from the runs they score and allow. This data is readily available on standings…
It has been noted that in many professional sports leagues a good predictor of a team's won-loss percentage is Bill James' Pythagorean Formula RSobs^c / (RSobs^c + RAobs^c), where RSobs (resp. RAobs) is the observed average number of runs…
As a dedicated follower of sports statistics and with the MLB season beginning in late March, I set out to predict how many wins each team would accumulate by the end of the 162 game season. The goal was to build a simulation framework…
In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…
Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game…
Probability estimation models play an important role in various fields, such as weather forecasting, recommendation systems, and sports analysis. Among several models estimating probabilities, it is difficult to evaluate which model gives…
We investigate the properties of the James function, associated with Bill James's so-called "log5 method," which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also…
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called…
Long-term time series forecasting (LTSF) is widely recognized as a central challenge in data mining and machine learning. LTSF has increasingly evolved into a benchmark-driven ''GAME,'' where models are ranked, compared, and declared…
In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this…
This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and the…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
Two new Bayesian methods for estimating and predicting in-game home team win probabilities are proposed. The first method has a prior that adjusts as a function of lead differential and time elapsed. The second is an adjusted version of the…
Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model…
This paper proposes a new way of evaluating the accuracy and validity of probabilistic forecasts that change over time (such as an in-game win probability model, or an election forecast). Under this approach, each model to be evaluated is…