# How long do ultimate points take?

A look into the distribution of time per point at WUGC 2016 and in the AUDL 2014–2016. Also do points take longer as a game goes on?

I took a look at some point-by-point data from WUGC 2016 and from the AUDL to see what the distribution of time per point is in ultimate. So the first question that probably has popped in your head, why in the world do we care about this?

Well maybe you don’t, but I’ll share a few reasons why I think this is interesting to explore.

(1) In-Game Decision Making — If you’re a coach or captain making lineup decisions for your team, I think it’s very valuable to understand at any time how many more points will occur in a given game. For instance, if the score of a game is 8–8 and the soft cap comes on in 12 min, how many more points should we expect there to be? I’m sure most of us have intuition that we use in this context and adapt based on the weather conditions and other factors. For this article, I want to explore some data to complement each person’s intuition.

(2) Simulations — I’m interested in understanding how long points are expected to take so we can simulate the rest of a game from any given score and time remaining. More to come in future articles.

What follows are some plots fitting data to empirical data and a look into the question of if points take longer as game gets further along.

### What’s the best distribution to model the time per point in ultimate?

I found that a log normal distribution is the best fitting distribution to the game data studied. This applied consistently across data sets. I also explored gamma, geometric, negative binomial, and weibull distributions, but the log normal gave the best fit. For a quick background, a log normal distribution is just a normally distributed variable (X) with a given mean and standard deviation. The outcome or time per point (Y) is the exponential of this normally distributed variable (X).

Y = exp(X)

One downside of using a log normal distribution is that it probably gives too high of a probability for outlier points that are really long. Although maybe I am underestimating the frequency of really long points. Remember the 20+ minute point between Ironside and Ring of Fire in 2014. Regardless, I think it’s still a good estimate for the distribution of ultimate points.

Here is a look at the data and the distribution fitted to each data set. Note that 60 seconds was added to the log normal fit for the WUGC data to account for time between points.

### So, do points get longer as the game goes on?

I say yes under WFDF rules and not significantly under AUDL rules. I ran some very simple regressions to determine this and the outputs are provided at the end of the article.

WUGC 2016 — Men’s & Women’s

• Points DO get longer as it gets further into the game.
• Points DO get longer as the score is closer. Points get shorter as the point differential between teams increases.
• The output below shows regressions with the dependent variable being the “time per point (sec)” and the independent variables are “elapsed time in the game to that point (min)” and “point differential (points)”. As you can see, points get longer as it gets further into the game. Points also get shorter as the point differential gets higher.
• The output is pretty similar between the women’s and men’s divisions.
• I think this matches our intuition. As players get tired, they are more likely to get chippy and make calls. Also, they are probably going to take longer to get back to their positions after a stoppage of play and take longer between points.
• Also, shorter points in a blowout could correlate with (a) teams not worrying about making calls or (b) uneven opponents resulting in shorter points due to a talent discrepancy. My hunch is that it’s likely a combo of the two with (b) being a bigger factor.

AUDL 2014–2016

• Points DO get SLIGHTLY longer as it gets further into the game. Much less so than the WUGC data.
• The output below shows regressions with the dependent variable being the “time per point (sec)” and the independent variables are “elapsed time in the game to that point (min)” and “point differential (points)”. As you can see, points get slightly longer as it gets further into the game. Point length is not impacted by the differential in score.
• I think a logical theory for this is that refs prevent players from calling their own fouls, put discs back in to play quickly, and therefore prevent play from slowing down as the game goes along compared to WFDF rules.

Further Discussion

It would be great to get more data on club games to see how the data from WUGC 2016 relates to teams playing in the USAU club series. Also, I am hoping to do some analysis on how the magnitude of wind affects the length of points. Open to any other thoughts or suggestions.

Regression Outputs