A complete listing of our projects in chronological order. Click here to sort projects by topic.


Building a new NFL EP model: In his Senior Thesis, Daniel Tokarz ‘20 develops a new metric for evaluating NFL situations on the fly

A New Way To Evaluate Kickers: Daniel Tokarz ‘20 deploys a new metric of evaluating kickers in the NFL

East vs West Strength: Alex Kane ‘22

In this project, I examined whether the NBA’s Western Conference truly has been stronger than the East in recent years, as many people have hypothesized.  To do so, I used a linear model to determine each NBA team’s average expected point differential against teams in its own conference compared to against teams in the other conference.  According to this evaluation of strength, the West has been a “stronger” conference than the East for every season except 2008-2009.

Predicting PointsAlex Kane ‘22

This project investigates whether any team stats are good predictors of points scored.  The initial analysis showed that a combination Field Goals Made, Free Throws Made, and Three Pointers Made was very good at predicting points scored, except this result is somewhat obvious and unhelpful.  When removing all scoring variables, it appears there is some correlation between Assists and Defensive Rebounds and points scored, although there was significant error in the predictions.


BY THE NUMBERS: Yale Just Falls to LSU: Luke Benz ‘19 breaks down how Yale had a perfect game plan but fell short in March Madness against LSU.

BY THE NUMBERS: Most Exciting Ivy Games: Luke Benz ‘19 uses his Game Excitement Index metric to break down the most exciting basketball games of the Ivy conference slate. 

BY THE NUMBERS: Ivy Hoops Midseason Rankings: Luke Benz ‘19 uses his NCAA Basketball Model to give some Ivy League power rankings at the midpoint of the Ivy season.

BY THE NUMBERS: Ivy Hoops Power Rankings: Luke Benz ‘19 uses his NCAA Basketball Model to give some Ivy League power rankings in advance of conference play hitting full swing.

Game Excitement Index: An In-Depth Exploration: Luke Benz ‘19 takes a deep dive into his Game Excitement Index metric to deterimine which NCAA Men’s Basketball games, teams, and conferences have been the most exciting this season.

Weighting Schema for Regression Based Ratings and Prediction in Australian Rules Football: Luke Benz ‘19 examines how various weighting functions for weighted least squares regression impact prediction of Aussie Rules Football games.

A Bayesian Examination of Win Probability and Timeout Usage in NCAA Men’s Basketball: Luke Benz ‘19 presents a Bayesian win probability model for college basketball as part of a final project for BIS 567: Bayesian Statistics.

BY THE NUMBERS: Yale vs. Duke Preview: Krish Maypole ‘21 and Luke Benz ‘19 preview the upcoming Yale vs. Duke men’s basketball clash and analyze strengths and weaknesses of the two squads. 

BY THE NUMBERS: A Statistical History of The Game: Luke Benz ‘19 examines a the history of the Harvard-Yale football game since 1875.

BY THE NUMBERS: Princeton’s Success: Krish Maypole ‘21 and Luke Benz ‘19 place Princeton’s historically dominant football season in context and offer some keys to the Yale-Princeton football game.

Next Gen Stats xComp Thoughts: Evan Green ‘17 provides some thoughts on the newest NFL Next Gen Stats metrics, breaking down some key flaws and proposing future changes. 

NCAA Hoops Methodology Update: Luke Benz ‘19 debuts a new methodology for NCAA Hoops rankings, included player adjusted preseason priors.

BY THE NUMBERS: Rise of Ivy League Football Recruiting: Using data from 247Sports, Luke Benz ‘19 examines the recent rise in recruiting success in Ivy League football.

BY THE NUMBERS: Ivy League Football Preview: Luke Benz ‘19 gives a 2018 Ivy League Football preview based simulations using the YUSAG FCS model.

Summer 2018

ncaahoopR: Luke Benz ‘19 introduces ncaahoopR, an R package for working with NCAA Men’s Basketball Play-by-Play data.

You Play to … Lose the Game: Luke Benz ‘19 takes a stab at answering the question of whether England or Belgium shoud try and lose their final match in hopes of receiving a better draw in the Knockout Rounds of the World Cup.

World Cup Probability Quirks: Luke Benz ‘19 notes somes neat probability paradoxes in World Cup odds prior to matchday 3.

NBA Draft Curves: Daniel Tokarz ‘20 debuts a new R Shiny app for making team-specific draft curves.

World Cup Group Stage Preview: Daniel Tokarz ‘20 uses the new YUSAG World Cup model to break down each group in advance of the tournament’s kickoff.

NBA Draft SAM Score: Sam Vancini (Tulane ‘19) makes his debut as a guest columnist with a new model for predicting the NBA draft.

World Cup Model Methodology: Luke Benz ‘19 and Dan Tokarz ‘20 dive into the math underlying their World Cup poisson model in advance of the 2018 FIFA World Cup.


Per-Game NBA Team Stats: Dan Tokarz ‘20 takes a team dive into NBA per-game team stats for his S&DS 230 final project.

BY THE NUMBERS: Ivy Lax Approaches Final Week: Matt Robinson ‘18 breaks down the numbers in advance of the Ivy League Lacrosse tournaments in NYC.

BY THE NUMBERS: Baseball MVPs: Luke Benz ‘19 turns to Ivy League Baseball Wins Above Replacement to identify the most valuable players in the Ancient Eight.

BY THE NUMBERS: Softball MVPs: Luke Benz ‘19 turns to Ivy League Softball Wins Above Replacement to identify the most valuable players in the Ancient Eight.

NBA Playoff Simulator: Dan Tokarz ‘20 introduces an new R Shiny app for simulating an NBA playoff series between any two NBA teams.

538 Riddler: Transitive National Champions: Luke Benz ‘19 uses graph theory to show that all 351 Division 1 teams are transitive national champions in the solution to this week’s FiveThirtyEight riddler.

BY THE NUMBERS: How Mad was March?: Luke Benz ‘19 creates a new metric comparing each year’s NCAA basketball tournament to the average tournament in order to contextualize just how crazy the 2018 tournament was.

BY THE NUMBERS: Ivy League Lacrosse Predictions: Matt Robinson ‘18 uses the YUSAG college lacrosse rankings to break down each Ivy League’s teams chances at postseason success.

Ivy League Baseball Softball WAR 2018: Luke Benz ‘19 updates the Ivy League WAR database for 2018.

Do Deep NIT Runs Predict Future NCAA Success: Luke Benz ‘19 takes a dive into KenPom adjEM to see if deep NIT runs predict future NCAA success.

NBA Model Math: Daniel Tokarz ’20 explains some of the math behind the NBA Model, as well as the prediction models we use for other sports.

NBA R Scripts: Daniel Tokarz ‘20 goes through the R Scripts he uses to maintain the YUSAG NBA Model

Game Excitement Index Part II: Luke Benz ‘19 uses in game win probability charts to derive a new in-game game excitement index metric.

NBA Playoff Predictions: Daniel Tokarz ‘20 debuts his NBA playoff simulations, with playoff odds, expected wins, and lottery odds for each team.

Does Winning a Conference Championship Imply Tournament Success?: Judah Ellison ‘21 breaks down how regular season championships and conference tournament championships have translated to success in the NCAA Tournament.

BY THE NUMBERS: Yale Heads to Ivy Madness: Luke Benz ‘19 previews the 2nd iteration of the Ivy League Men’s and Women’s Basketball Tournament with title odds and breakdowns of potential championship matchups.

NBA Rankings: Daniel Tokarz ‘20 applies the YUSAG method to create NBA Power Rankings.

BY THE NUMBERS: Ivy Hoops Enters Home Stretch: With four games left in Ancient Eight Confernce Play, Luke Benz ‘19 details each’s teams math to the Palestra.

BY THE NUMBERS: Math to Ivy Madness: Luke Benz ‘19 hits reset on the Ivy League as conference play enters the seconf half of the season.

BY THE NUMBERS: Ivy Basketball Analytics: Luke Benz ‘19 assess each Ivy League’s team’s chances of reaching Ivy Madness and explains why this weekend’s games against Harvard and Dartmouth are especially important.

Mid-Season Assist Network Report: Luke Benz ‘19 creates “All-American Assist Teams” using various centrality metrics from his assist network charts.

Fantasy Football Year End Round Up: Daniel Tokarz ‘19, Guna Mandava ‘21, and Michael Blicher ‘21 introduce Fantasy “Points Above Replacement” as a better metric for evaluating fantasy football players.

Improving College Basketball Win Probability Model: Luke Benz ‘19 turns to Bart Torvik and Ken Pomeroy to improve his in-game college basketball win probability model minimum win probability estimates for late game scenarios.

NCAA Basketball Assist Network App: Luke Benz ‘19 rolls out an R Shiny App of his college basketball assist networks.

College Basketball Conference Title Favorites: On the dawn of conference play, Luke Benz ‘19 compiles a list of favorites to win each NCAA conference’s regular season tournament.

Union Street Hoops Podcast: Luke Benz ‘19 joins Paul Oren of the Northwest Indiana Times to discuss his recent article, “The Value of Switching Conferences”, previews the beginning of Missouri Valley Conference play, and explores Valparaiso’s long-term outlook in the MVC.

The Value of Switching Conferences: Luke Benz ‘19 quantifies how changing conferences has effected the men’s basketball teams from Wichita St., IUPUI, and Valparaiso.

NCAA Hockey Rankings: YUSAG college hockey rankings from Max Yuhas ’20 and Matt Robinson ‘18.

BY THE NUMBERS: Replacing Makai Mason: Luke Benz ‘19 debuts college basketball assist networks to examine how Yale’s offense has done without its star point guard.

NCAA Basketball Win Probability Model: Luke Benz ‘19 breaks down the methodology for his newly developed in-game win-probability model for college basketball.

BY THE NUMBERS: The Game 2017: Matt Robinson ‘18 gives a statistical preview of the 134th playing of the Harvard-Yale football game.

BY THE NUMBERS: Ivy Title Race Heats Up: Luke Benz ‘19 and Matt Robinson ‘18 break down the numbers you need to know for the final 3 weeks of the Ivy League Football season.

BY THE NUMBERS: Ivy League Football Quick Hits: Luke Benz ‘19 examines title odds and Yale’s outlook at the midway point of the football season.

BY THE NUMBERS: Ivy League Football Preview: Matt Robinson ‘18 uses the YUSAG college football model to simulate the Ivy League Football season in order to give predicted records and title odds for each team.

Rating Methods Part 3:YUSAG Linear Regression: Matt Robinson ‘18 breaks down the methodology used in the YUSAG football rankings and compares it to similar sports rating systems.

Rating Methods Part 2: Elo Ratings: Matt Robinson ‘18 breaks down the methodology behind the Elo sports rating system.

Ratings Methods Part 1: Massey Ratings: Matt Robinson ‘18 breaks down the methodology behind Ken Massey’s sports rating system.

BY THE NUMBERS: How to Win an Ivy League Football Championship: Luke Benz ‘19 breaks down why controlling the running game is much more important than controlling the passing game for winning titles in the Ivy League.

NCAA FBS Power Rankings: Matt Robinson ‘18 introduces YUSAG’s NCAA FBS Power Rankings. (Methodology)

NCAA FCS Power Rankings: Matt Robinson’ 18 introduces YUSAG’s NCAA FCS Power Rankings. (Methodology)

Summer 2017

Ivy League TiebreakR: Luke Benz ‘19 debuts an R Shiny App for breaking Ivy League basketball ties for any desired season permuation.

Bracket Math: The YUSAG Database for all metrics used in YUSAG Bracketology. (By: Luke Benz ‘19) 

YUSAG Bracketology: Luke Benz ‘19 debuts YUSAG Bracketology predictions for the NCAA Men’s Basketball Tournament.

NCAA Basketball Game Excitement Index: Luke Benz ‘19 introduces an new metric for predicting game excitement in order to help choose the best game(s) to watch on a limited time schedule. 

NCAA Basketball Model Methodology: Luke Benz ‘19 breaks down the inner workings of his NCAA hoops prediction model, and shares many new features for the 2017 season.

Effect of Base Runners on MLB Pitch Selection: Michael Bogaty ‘19, Tyler Duncan ‘18, and Luke Benz ‘19 examine how having runners on base–particularly base stealing threats–influences pitch selection in MLB.

2017 NBA Draft Preview: Daniel Tokarz uses analytics to break down the 2017 NBA draft, including who won the Celtics-Sixer pick swap.

NCAA Baseball Model Methodology: A little post about the workings of our NCAA Baseball Model.

Yale Baseball Postseason Predictions: Luke Benz ‘19 simulates the NCAA Baseball tournament to determine Yale’s chances for postseason success.

All-Ivy Baseball/Softball Snubs and Surprises: Luke Benz ‘19 uses his WAR project to evaluate the Ivy League’s all-conference honors and doles out some hot takes.

What Makes a Cy Young?: Luke Benz ‘19 examines whether dominance or consistency is more important in order to be named a Cy Young Award winner.

NBA Draft Pick Value: Daniel Tokarz ’20 does an deep dive into seed vs. pick value in the NBA draft, examines the talent drop off after the first three picks, and creates and new metric for determining when to trade picks.


BY THE NUMEBRS: Baseball/Softball MVPs: Luke Benz ‘19 analyzes the most valuable Ivy League Baseball/Softball players using Wins Above Replacement (WAR) and other advanced MLB stats.

NFL Timeout Tendencies: Evan Green ‘17 and Daniel Tokarz ’20 examine timeout strategy in the NFL.

NFL Timeout Analysis: Harrison Tracy ‘18 and Evan Green ‘17 examine timeout usage as a way to measure home field advantage in the NFL.

Ivy League Baseball/Softball WAR: Luke Benz ‘19 brings Wins Above Replacement (WAR) and other advanced MLB stats to Ivy League Baseball and Softball.

BY THE NUMBERS: Ivy League Track MVPs: Michael Menz ‘17 runs a 10,000 iterations of a simulated track meet to account for race-to-race variability and find the most valuable performers in the Ivy League.

BY THE NUMBERS: Ivy League Baseball Park Factors: Michael Bogaty ‘19 explores which Ivy League baseball stadiums can be classified as hitter-friendly and pitcher-friendly parks.

BY THE NUMBERS: Ivy League Lacrosse Predictions: Daniel Tokarz ‘20 and Luke Benz ‘19 break down the odds for the Yale Men’s and Women’s Lacrosse teams to reach the postseason.

BY THE NUMBERS: Ivy League Baseball Pythagorean Win Percentages: Michael Bogaty ‘19 calculates Pythagorean Win Percentages for each of the Ancient Eight teams and analyzes which teams under/over-performed last season in hopes of better predicting this season’s results.

NCAA Basketball Championship Difficulties: Luke Benz ‘19 creates a new metric as a way to measure which NCAA Basketball champions had the most difficult run to the title, and says to stop hating on Gonzaga.

MIT Sloan Hackathon: Defining Player Vision: Evan Green ‘17 creates two new metrics, entropy and clustering, to measure NBA players passing ability using SportVU data. This is a summary of the presentation Evan presented during the conference as a finalist for the Hackathon. 

BY THE NUMBERS: Ivy Math-ness: Luke Benz ‘19 previews the Ivy League basketball tournament, assigning odds to each team’s chances of reaching March Madness. Benz also breaks down what must go right for the Bulldogs if they wish to beat rival Harvard.

English Premier League Value Ratings (Part 1): Daniel Tokarz ‘20 examines Goaltender value in the EPL. This is the first part in a larger series examining player value in the top flight of English soccer.

BY THE NUMBERS: Math To The Palestra: Luke Benz ‘19 and Michael Bogaty ‘19 break down odds and scenarios for the Yale Men’s and Women’s Basketball teams for make the Ivy League tournament.

BY THE NUMBERS: Counting Yale’s Losses: Evan Green ‘17 breaks down shot charts from the Yale Men’s Basketball team’s graduating seniors and explores how team tendencies have changed this season.

On The Vine: Luke Benz ‘19 joins the Ivy Hoops Online weekly podcast, On the Vine, to discuss Ivy League Basketball and #MathToThePalestra

BY THE NUMBERS: Swimming MVPs: Michael Menz ‘17 offers an in-depth look at which Ivy League swimmers are most valuable to their respective teams.

BY THE NUMBERS: The Biggest Home-Field Advantage: Will Min ‘19 explores home-field advantage in the Ivy League, and examines whether away trips to Cornell (Ithaca, NY) are more difficult than the rest of the Ancient Eight.

BY THE NUMBERS: Hoops Analysis: Luke Benz ‘19 and Michael Bogaty ‘19 examine updated playoff odd for the inaugural Ivy League Tournament after the first full weekend of Ancient Eight play.

BY THE NUMBERS: ECAC Hockey Predictions: Michael Bogaty ’19 crunches playoff odds for the men’s and women’s ECAC hockey teams and analyzes the Yale men’s teams chances vs. rival Quinnipiac University in the “Battle for New Haven”.

BY THE NUMBERS: Ivy Hoops Games to Watch: Luke Benz ‘19 introduces the “Playoff Swing Factor” to Ivy League Basketball and analyzes which games will have the biggest impact on the playoff race.

BY THE NUMBERS: Women’s Hockey Predictions: Michael Bogaty ‘19 updates his ELO model and uses it to predict results for the Yale Women’s Hockey Team.

BY THE NUMBERS: Men’s Hockey Prediction’s: Michael Bogaty ‘19 begins a new series in our collaboration with the Yale Daily News, in which we make predictions for several Yale Sports Teams. In this first installment, Bogaty covers Yale Men’s Hockey.

Live Basketball Win Probabilities: Michael Menz ‘17, James Pastan ‘20, and Gabe Zanuttini-Frank’s ‘19 live NBA win probability charts tracks each times chances of winning based on the current game situation. Watch along as probabilities are updated in real time.

BY THE NUMBERS: Ivy Hoops Weekend Recap: We help the Yale Daily News kick off their new sports blog, “Down the Field”, with an analytical recap of last weekend’s Ivy League Men’s Basketball games.

BY THE NUMBERS: Basketball Begins: Continuing our collaboration with the Yale Daily News, Luke Benz ‘19 previews the Ivy League Men’s Basketball season and explores team’s chances of reaching the Ivy League Tournament in March.

CS50: What I Learned: Luke Benz ‘19 discusses his NBA related final project for CS50 and shares the analytical observations he made along the way.

BY THE NUMBERS: Harvard vs. Yale: Matt Robinson ‘18 breaks down Yale’s chances of winning “The Game” 2016.

Recruiting vs. Field Success in Ivy League Football: Matt Robinson ‘18 and Will Min ‘19 examine Yale Football’s success in recruiting as compared to the strength of the team. They also show how Yale’s talent performs relative to other teams: the answer is not very well.

ANALYSIS: Volleyball starts slow, ends strong: In another collaboration with the Yale Daily News, Michael Menz ‘17 explores the signal given by the first set in Ivy League Volleyball. Teams that win the first set by more are more likely to go onto the win the match. Additionally, the Yale Volleyball team was the team most likely to come back from losing the first set.

Ivy League Projections - Updated Through 3 Weeks: Matt Robinson ‘18 using updated ELO and Sagarin ratings analyzes the current state of Ivy League Football and chronicles the decline in Yale’s projected wins.

BY THE NUMBERS: Home-field advantage in the Ivy League: In another collaboration with the Yale Daily News, Evan Green ‘17 investigated the size of and factors behind home field advantage in different Ivy League sports. Despite the differences in fan attendance, travel accommodations, and skill level of athletes, home field advantage was not significantly different in the Ivy League than that seen in professional sports leagues. 

Total Defensive Pressure (TDP): Analysis of Off Ball Defense in the NBA: In the inaugural NBA Hackathon, we took the opportunity to analyze SportsVU tracking data and create a new metric for off ball defense which had mostly been neglected by the current  research. The metric was based on the sum of squared distances from each offensive player to the defender closer to him. We found that closer off ball defense was related to more missed shots and fewer three points attempts. We also noted individual differences in effort based on differences in on ball and off ball defense.

BY THE NUMBERS: Previewing the Ivy League football season: This article by Matthew Robinson ‘18 is the first piece in our collaboration with the Yale Daily News. Throughout this year we will be analyzing Ivy League sports and publishing them in the Yale Daily News and on our website here. In this article, he introduces ELO ratings for the Ivy League and projects the Ivy League standings using the ELO ratings and Sagarin Ratings.


The Success of Short Yardage Play Types on Fourth DownThe quarterback sneak is a play in football in which the quarterback pushes forward behind the offensive line immediately after the center hikes the ball. It is often employed in short yardage situations, especially when the defense has not had time to set their position. We sought to determine whether this play in under or overused by NFL coaches in such situations.

Player Clustering in the NBA: As a result of position, physical attributes, or basketball ability players in the NBA naturally gravitate toward certain roles within a team. We attempt to formalize this notion by clustering NBA players based on a combination of traditional and advanced statistics. These clusters can then be applied to examine how teams construct lineups.

NBA Daily Fantasy Lineup Generator: We sought to program a system to automatically created daily fantasy basketball lineups. We used penalized regression to predict players’ expected points and variances for a game based on their stats and opponents. We then used a probabilistic solution to the weighted knapsack problem to generate lineups.  Since we targeted “double up” games we created high expected points lineups with low variance.