The Flip’s In-Game Win Probability Model (v1.0) for Ultimate
Applying the win probability model from other sports to ultimate.
In the 2017 USAU Club Nationals final, Brute Squad scored to take half 8–5 over Fury. A comfortable but not insurmountable lead. Brute Squad coach, Ariel Jackson, gave his halftime interview saying “8–5 is the most dangerous score in ultimate.” So what were the chances Fury would make the comeback to win the game? And how would their chances change if Fury were not receiving out of halftime? And as they get closer to the cap, how does this reduce Fury’s chances of a comeback? Sounds like a great reason to make a win probability model for ultimate! Spoiler: Brute Squad lost 14–13 to Fury.
Win probability models have become quite popular for other sports and politics recently. These models come with their fair share of criticism but I still find them really enjoyable and insightful. So why not make one for ultimate?
Below is a high-level description of an in-game win probability model for ultimate that calculates both the receiving team and pulling team’s win probability for a certain score and time remaining in the game.
First, let’s talk through the results. A longer discussion of how the model works is at the bottom of the article.
Win Probability Table (Men’s — 70% O-Line Hold Rate)
If we assume equal teams that score offensive points with a 70% probability, what is the win probability for every score scenario? The table below shows the win probability for the receiving team for each score scenario.
- Note that the simulations are for games to 15 under the USAU cap rules used at Nationals for semis and finals games.
- The values below are for score scenarios where the soft cap is 85 minutes away. Essentially this is the same as the start of the game.
- I am calling this the “Men’s” table based on historical data for the club and college division (further discussion at the bottom of the article).
How to read the table below:
- Each square indicates the receiving team’s win probability for a given game score. All 1st half win probabilities assume the receiving team also received to start the game.
- The pulling team’s win probability is (1 -value shown below).
- You can chart the path of a game by looking at corresponding squares based on the result of a point. For example, a team receiving down 5–8 has a 15.5% chance of winning the game (assuming 85 min before soft cap). If they get broken, they are now receiving down 5–9 and have a 7.5% chance of winning. If they hold and are pulling down 6–8, they now have an 18.2% chance of winning (1–81.2%). Note that a true simulation would change the time remaining after each point so this is just an estimation of how to chart a game path with the win probability model.

Note that there is a +/-0.2% confidence interval around each value so there may be situations where the win probability skews slightly away from what we’d expect (for example, receiving at 5–5 has a 50.6% win probability while receiving at 4–4 has a 50.8% probability).
Win Probability Table (Women’s — 63% O-Line Hold Rate)
If we assume equal teams that score offensive points with a 63% probability (closer for the Women’s division), what is the win probability for every score scenario? The table below shows the win probability for the receiving team for each score scenario.
- Note that the simulations are for games to 15 under the USAU cap rules used at Nationals for semis and finals games.
- The values below are for score scenarios where the soft cap is 85 minutes away. Essentially this is the same as the start of the game.
- I am calling this the “Women’s” table based on historical data for the club and college division (further discussion at the bottom of the article).

Effect of who received to start the game (70% O-Line Hold Rate)
So how do the win probabilities change in the 1st half depending on who receives to start the 2nd half? Below are tables for the 1st half win probabilities showing both scenarios for 70% o-line hold rates. The table on the left shows the receiving team’s win probability when they are pulling after halftime. The table on the right shows the receiving team’s win probability when they are receiving after halftime.
For example, suppose it is a tied 7–7 game. The receiving team’s win probability is 51.9% if they have to pull out of half. This win probability rises to 60.4% if they get to receive out of half.

Effect of time and cap on win probability
If you have made it this far in the article, I’m sure you are someone who is aware that ultimate games don’t always make it to 15. The cap has a significant impact on the win probability for a given game scenario. Let’s look at the 8–5 game score mentioned in the intro for different times remaining before the cap.

As you can see from the table, the chance for the receiving team to make a comeback starts to decrease as time gets closer to the cap (as we would expect). With an 8–5 score, the team losing should start to feel anxious with about 40 min to go until the soft cap. At this point, with every minute, your chances of coming back start to decrease.
Just to reiterate the note from earlier, each simulation has a +/-0.2% confidence interval. This is why the win probability oscillates as the time remaining decreases from 85 min to ~40 min.
So what was Fury’s win probability out of half? And how does the win probability model compare to actual game results?
Looking at the table above Fury had a 17.4% chance of winning the 2017 Final coming out of half. This assumes the teams score 63% of o-line points and that there was approximately 35 minutes until the soft cap. But Fury did win the game. So is the model wrong? Let’s look at other game results from the club division.
Based on the point-by-point tables from USAU Club Nationals (2014–2017), we can look at very similar game situations. Unfortunately, we cannot tell who is receiving the point out of half from the USAU website and time remaining to the cap, so I looked at all game situations where the receiving team was down 6–9.
- For the Men’s club division, there were 55 Nationals games from 2014–2017 where the receiving team was down 6–9. The receiving team won 7 of these games or 12.7% of the games.
- For the Women’s club division, there were 44 Nationals games from 2014–2017 where the receiving team was down 6–9. The receiving team won 7 of these games or 15.9% of the games (including the Fury comeback in the 2017 Final).
- These results are comparable to what the win probability tables show earlier in this article. It would be great to compare the model to a larger data set in the future. One other note from the actual game data is that the teams may not be equal opponents. Likely the team leading 9–6 is a better team and therefore their probability to win will be better than a model which assume both teams have an equal chance of scoring offensive points.
- So is 8–5 the most dangerous lead in ultimate? ¯\_(ツ)_/¯ But it’s probably a good talking point to keep your team motivated for the 2nd half if you’re in the lead.
How did the model change the win probability for Brute Squad and Fury over the course of that game?
I am showing the win probability over the game in a table form as I think it gives a better representation of how the cap affects the win probability in the second half. Again, the model assumes both teams have a 63% probability of scoring o-line points.

What’s next for the model?
I’m hoping to use the model to write articles about in-game strategy as well as share insights about how specific plays in games swung a team’s win probability. Hopefully some more tech savvy individuals will enjoy the idea enough to incorporate it into some live broadcasts or websites that give live updates for big games. Charles Kerr already played around with the model with his JinxCam coverage of D-1 College Nationals this year. Please reach out to me if you have any interest or questions about the model.
How the model works
The model works by simulating game results based on a certain game scenario. These are the game scenario inputs.
- Score of the game
- Team that is receiving
- Team that received to start the game
- Cap on or time remaining before the cap
- Winning score required (e.g. game to 15)
The model then simulates the remainder of the game based on the following assumptions.
- Offensive hold rate: This is the probability that each team scores offensive points. Note that this does not indicate the scoring rate of each possession. The model can input different hold rates for each team (unequal opponents) but the default model shows results for teams with equal hold rates. The model assumes that a team’s probability to score an offensive point is the same regardless of what the score is in the game, the outcome of the previous point, or how early or late in the game it is. The model simulates every point of the game with this probability. For example, if 66% is the hold rate probability, every point of the game would be simulated like rolling a die. If 1–4 are rolled, the offensive team scores the point. If 5–6 are rolled, the defensive team breaks. This repeats until a team wins the simulated game.
- Offensive hold rate (by division): The default model uses an offensive hold rate of 70% for the Men’s division (college & club) and 63% for the Women’s division (college & club). The rates are based on average hold rates between winning and losing teams from USAU Club Nationals and USAU D-1 College Nationals. See the following articles (college, club) with more information.
- Wind: The default model does not factor in wind. The offensive team’s probability to score a point is the same regardless of which direction they are attacking.
- Time per point: The duration of each point is randomized based on a log normal distribution. The log normal distribution was selected based on data from the AUDL and WUGC 2016. See this article for a detailed breakdown. I used a log normal distribution with mean=4.75 and std.dev=0.75 in the natural logarithm. In English, this means that the average point duration is ~2.5 minutes and the median point duration is ~2 minutes. In addition, I added 1 minute between points. The fitted data below to the WUGC 2016 Men’s data shows a log normal distribution of mean=4.73 and std.dev=0.75 with an added 1 minute for time between points to give you a feel for the distribution of time per point in the simulations. Note that timeouts and injuries are reflected in the time per point distribution and therefore are not inputs to the model.

- Halftime length: This can be changed based on the tournament format. The default win probability model is based on USAU Nationals where halftime is 10 minutes.
- Cap rules: In my opinion this is the most annoying part about applying a win probability model to ultimate. Almost every tournament has different cap rules and USAU Nationals has different cap rules within the same tournament! Because of this, a new win probability model has to be built for each cap rule format. The default win probability model uses the cap rules for USAU Nationals semifinal and final games. Games are played to 15 with the soft cap going on after 85 minutes. Add 2 points to the high score and play to that number.
- Number of simulations: This is number of simulations run for each game scenario including time remaining. Since the win probabilities are simulated data, the more simulations the lower the standard error in the results. For the default win probability model, 250,000 simulations were run for each game scenario at 5 minute increments (it was a lot of computer simulations!). This results in a 95% confidence interval of +/- 0.2% for 50% win probability scenarios. The confidence interval becomes smaller as the win probability moves closer to 0%/100%.
Notes
- Huge shout out to Charles Kerr who helped run these simulations that took weeks. And to his enthusiasm in adding win probabilities to the his JinxCam coverage. He ran a beta of the calculation in the ticker of his USAU D-1 College Nationals 2018 coverage.
- There are a few others (that I’m aware of) that have built in-game win probability models for ultimate. Tom Murray had an article in Ultiworld that touches on this topic when predicting Club Nationals outcomes. In addition, Scott Grindy wrote an article using Markov Chains to estimate win probability. I used a different approach then they did but I still want to give some credit to others who have done this before.

