Amateur Statistics For Professional Athletes Part 1
Let's do some math!
Announcements:
Still looking for work! If you or a loved one needs someone to write/report/edit/do anything for you, let me know! Thank you Alex Rubin for the shoutout in the D1 Natioals Twitter Roundup.
Welcome one and all to a new series on The Breakside I’m calling: Amateur Statistics for Professional Athletes. As you may know, I am a huge fan of Jon Bois, Foolish Baseball, and others creating fantastic work narratively and visually with statistics in sports. Unfortunately, both Ultimate and I are behind in the field of data visualization in sports. Ultimate lacks the raw data and historical stat keeping prevalent in other mainstream American sports, and I lack the math and video editing chops to make content on the same level as those two examples do. However, a stated goal of The Breakside is to chart new waters, so chart new waters we shall.
Existing Stats
I am not the first to want Ultimate to enter a modern analytic era. Stat keeping, in general, has been around for a long time. Fun fact: I kept stats for a Women’s Division consolation game at College D1 Nationals in 2016 in Raleigh. But only recently have the amount and depth of statistics available. Some good Ultimate stats are available online from Ultiworld, the AUDL, and my favorite, the WUL.
I loved scrolling through the WUL stat page but wanted a more interactive way to compare player performances other than looking at percentile graphs on individual player pages. It’s hard to create a page like a Basketball or Baseball-Reference. Still, the easy comparisons are fun, so I wanted to create something to standardize and compare player performance for an individual game.
What is Game Score?
In Basketball, Game Score is a metric calculated based on box score statistics used to roughly gauge the quality of a player’s performance in a specific game. It is calculated by adding important box score metrics weighted according to their impact on the game. You can read more here, but the formula is as follows.
Game Score = PTS + (0.4 * FG) - (0.7 * FGA) - 0.4*(FTA - FT) + (0.7 * ORB) + (0.3 * DRB) + STL + (0.7 * AST) + (0.7 * BLK) - (0.4 * PF) - TOV
This Michael Jordan masterpiece is the best game of all time, using Game Score as a metric. Game Score is certainly not the definitive metric for measuring player performance as it cannot view any context for the game that was played, treating every stat as the same whether it happened at 0-0 or in a one-point game with 30 seconds left. It also is blind to off-ball events like setting a good screen or ball denial defense. However, it can be a helpful tool to assess performance, and in my quest to develop some stats for Ultimate, I decided not to let perfect be the enemy of good.
Bringing Game Score to Ultimate
I found some similarities between individual stats in Ultimate and Basketball in the Game Score formula. Assists, points, turnovers, and blocks all have direct equivalencies. I thought that completion percentage had a neat correlation with shooting percentage. There even felt like some similar relationship between yards gained in Ultimate and Rebounds in Basketball. After some tinkering and algebra that would have made 12-year-old me proud, I had an epiphany on how Game Score in Ultimate should be structured.
For starters, it’s kind of annoying that all three pro leagues, USAU, and WFDF, play slightly different brands of Ultimate, so I settled on using the WUL as my statistical playground because I like the brand of Ultimate they play; all of their games are available for free on YouTube (with pretty darn good production to boot), and because some incredible people have poured their hearts and souls into this glorious trove of player and team stats.
I put all 1,323 instances of their “Player Data” page from the 2023 regular season into a spreadsheet. Each line represents one player’s complete box score. I went through several iterations of developing a formula that I felt both appropriately and fairly weighted statistical impact and my personal view of quality Ultimate. Here’s what the current formula looks like.
Goals + Assists + (Completions)/7.5 + (Throwing Yards +Recieving Yards)/80 + 2*Blocks- 2*Turns
Math Time
If you don’t want to do any math, feel free to skip to the next subheading! For those of you interested in how I arrived at this formula, though, this part is for you.
I started with the idea that a goal and assist should be valued equally, and as such, there would be two points available for scoring on any given point. That idea was then built out into what an ideal point of Ultimate (on a WUL field in 2023 WUL playing conditions) looks like. I calculated there were about 15 completions per point scored this season which led me to use the basic assumption that the ideal offensive point under standard WUL conditions (80-yard-long fields) is the following:
1 Goal + 1 Assist + 15 Completions + 80 Throwing Yards + 80 Recieving Yards + 0 Turns + 0 Blocks
Adding that all together seriously overvalues yards gained because there are so many more of them than points scored, so I needed a weighting mechanic to still place value on people who do things other than throw and catch scores but not come up with a useless number. So, I returned to the idea that scoring a goal is worth “two points” and decided to use that evaluation for the other parts of scoring a goal than throwing and catching it. Those being the completions and yards gained. That two-point assumption creates the following equation with the “ideal standard offensive point.”
1 Goal + 1 Assist + 15 Completions/7.5 + 160 Yards (Throwing + Recieving)/80 + 0 Turns + 0 Blocks
Extrapolating it to an empty formula while weighting blocks and turns as two points each (assuming that they are essentially each worth an ideal standard offensive point) gives the final equation from above:
Goals + Assists + (Completions)/7.5 + (Throwing Yards +Recieving Yards)/80 + 2*Blocks- 2*Turns
What Does This Stat Actually Say?
Disclaimers:
First, some acknowledgments: This is not the perfect stat! (Is anything, though?) In the future, I’d like to utilize some of the advanced metrics work others are doing to adjust Game Score or create something new that accounts for weather variance and “off-ball” defensive impact, which are not taken into account in this formula.
Additionally, some other observations I’ve had are that the blocks and turns values may be a bit high, considering, on average, there are about two turnovers per point. However, I like treating them with the assumption that a possession is ideally worth a goal. Additionally, I chose to use standard yards rather than WUL’s “Effective Yards,” which include yards “gained” via turnover, because I don’t want to reward players for yards gained like that. Additionally, there are a lot of other cool usage and rate stats that I don’t fully grasp yet but I am working on understanding more to include in future projects.
And finally, I still need to fully perfect this formula for edge cases like callahans, so the scores are not as precise and accurate in a couple of cases. I’m trying hard to stick to a consistent writing schedule, so a future version of The Breakside may include an improved formula.
Now the Data:
Across all 1,323 “games played” this season by WUL players, their individual Game Scores can be seen in the follwoing grpahs:
About half of all scores fall between 0 and 5, the approximate first and third quartiles of the Game Score data set. Thirty-nine positive outliers produced Game Scores over 12, and two even scored above 20. We can also see a couple of rough games for our negative outliers coming in with scores under -7.
Some highlights from the data set:
San Diego Super Bloom’s Avery Jones and Dena Elimelech were the two players who posted Game Scores above 20, with 21.875 and 21.675, respectively.
In fact, the top five individual Game Scores all belong to Super Bloom players, and three of the top seven Game Scores of the 2023 regular season belong to MVP Kaela Helton
Los Angeles Astra’s Maggie O’Connor had the best non-Super Bloom Game Score with a 17.213 for a 7 Assist, 4 Goal performance in a 15-13 win against San Fransico on 4/6
Utah Wild’s Paige Kercher (the Offensive Player of the Year) had an equivalent number of games that were statistical outliers in this data set (scores >12) and those that fit the set (four of each). This doesn’t include a fifth game she posted with a still incredible Game Score of 11.679
If you want to check out all the data, here is a link to my full spreadsheet.
Where to Next?
This week’s edition mainly served as a proof of concept, and I’m looking to take this project further in the coming weeks. If you liked this, please let me know because this has been a lot of fun to create, and there is a lot I want to do with it. Moving forward, I want to run through some of the season’s top games more in-depth, look at Game Score more deeply across individual games played and teams, and maybe even create some WAR/OPS+-like stat that considers the average player’s impact vs. the top-end impact. I’d also love to standardize the formula for USAU games, either in the college or club divisions and make some math and graphs about those games. At the very least, I plan to continue to play around with stats and data visualization in Ultimate, and I hope you all are even half as excited as I am.
Check out part two out now!
About The Breakside
The goal of this newsletter is to tackle what I see as a gap in the present coverage of Ultimate as a sport. I hope that this newsletter will provide an outlet for important, yet overlooked people and stories to receive the coverage and perspectives they deserve.
About the Author
My name is Noam Gumerman (he/him), and I am a senior at Brandeis University in Waltham, MA. I am from Chapel Hill, NC, and am currently studying Journalism and American Studies at Brandeis University. I am one of the current captains of Brandeis TRON, our open division team. My claim to fame within the Ultimate community is running the @being_ulti account during the week of the 2022 WUCC tournament. Contact me for discussions, feedback, story suggestions and more on Twitter at @noamgum, or via email at ngumerman@brandeis.edu.