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The Season of Ultimate Stats – Part 2

The interview with Thomas Kuhn that Ultimate Rob recently posted to his site reminded me that, last summer, I had the good fortune of watching Thomas play in a showcase game between Furious George and Sockeye at the Flowerbowl tournament in Vancouver. One part of that game that sticks out in my head is a play in which Thomas threw a short pass into the ground right near his own goal line. When that happened, the first thought that ran through my mind was: “Holy crap, I could have done that! Maybe I should be playing for Furious, too?!” But the difference between Thomas Kuhn and me is not that he is incapable of making simple mistakes. The difference is that he did not spend the next ten minutes of the game thinking about how much he sucked as a player because of one little mistake he had made.

That type of thinking does not come naturally to most human beings. It is hard for us to accept that not every detail of every game actually means something. But the science of statistics tells us that we are not in complete control of our destiny. Mistakes are going to happen, and sometimes they are going to come in bunches. And that sixty yard huck you
just threw for a score? Yeah, maybe that happened because you are truly awesome. But chances are good that you might have just gotten lucky on that one, too.

One of the reasons I wanted to create the database of statistics that I described in my previous post was to help players identify which aspects of their game they were truly good at, and which aspects of their game were just the result of the random chance that is an inherent part of every game of ultimate frisbee.

Through four weeks of play, I have been able to collect data on nearly 7,000 passes in the Calgary Ultimate Spring League. A logistic regression analysis has shown that there are two primary factors that affect whether or not a pass will be completed: (1) the length of the pass and (2) the distance the thrower is from the end zone that he is attacking. The two
influences are pretty simple: (1) the longer the throw, the less likely it is to be completed, and (2) the closer a thrower is to the end zone he is attacking, the less likely he is to complete the pass. These two factors do not interact, which means that they counterbalance each other nicely in a way that prevents the game of ultimate from ever becoming too easy. You can play it safe by chipping your way down the field with short, easy to complete passes, but it’s only going to become harder and harder to do so, the closer you get to the end zone. At some point, you’re going to have to

To help the players in the league visualize how much these two factors influence their own play, I have broken down everyone’s throwing statistics into two different tables. One of these shows the number of “passes on target” (POT) out of passes attempted–along with the yardage gained–on passes of various lengths. The other table shows the same
information for passes made at different spots on the field. Next to each table are posted the league averages for the same tabular breakdowns. This enables players to identify prominent deviations in their passing game from the league norms–the objective being to help each player identify the consistent trouble spots in their throwing game, rather than the
individual plays which may or may not have gone in their favor. A good example is Thomas’ page, which you can find here:

Or you can just poke through the directory of every player in the league:

For myself, I have learned that my completion percentage beyond the halfway point of the field is pretty miserable–63.2%, compared to the league average of 81.5%. That’s a pretty hard pill to swallow, but I also know that identifying what parts of my game need the most work is the first step I need to take to becoming a better player. And then, maybe
someday, I’ll be able to throw one into the ground for Furious George, too. 🙂

5 thoughts on “The Season of Ultimate Stats – Part 2”

  1. Interesting and awesome, can’t believe I missed this before.  Two comments:
    1. We took stats 20 years ago and found that forehands were a lower percentage than backhands, but I had always worried that it was due to almost all dump passes being backhands. Your stats show a higher completion percentage at all distances for backhands.  Also, the ratio is only about 2:1 backhand:forehand for short (<0 and 0-5) (I would have thought it even higher) but is closer to 1 for downfield throws.
    2. You say the “two factors do not interact”, but I don’t believe you (or maybe I’m mistaking your intent). There are two factors that explain completion rates going down near the endzone.  First, there is less space to throw to. The other is that both offense and defense behave differently near the goal line (and it’s rational, since teams don’t score 100% of the time they have the disc on the goal line).  Throwers will accept a lower completion rate in order to get a score, and defenders will allow a higher completion rate to prevent a score.  So, I’d be interested in seeing the stats on non-scoring throws as a function of distance from the goal line. (Also, wondering whether a 20 yard pass from the 10 gets scored as a 20 or a 10 yard completion and how this affects the stats.)

  2. Hi Jim–I’m glad you liked this post, and it’s cool to hear your thoughts on it, too. 🙂
    1. To answer your easiest question first, a 20 yard pass from the 10 was scored as a 20 yard pass. Passes were scored in terms of the yardlines where they began and ended (in your example, it would go from the 60 to the 80); the only time we lost yardage information was when passes went through the back of the end zone, which we scored as ending at “91” (end zones were twenty yards deep in our league). Since there were no more yard lines back there, we didn’t have much of a choice.
    2. Regarding the interaction…I’ll admit that I did the statistical analysis at an early stage of the project, but never went back to verify that the general trends still held, once all the data had been compiled. Your comment inspired me to do that, though, and I’m happy (?) to report that…there *was* a significant interaction between throw distance and distance to the goal line. It’s pretty strong, actually, so perhaps I just didn’t have enough data before. 
    Anyways, to try to help understand the interaction, I broke down the passing data by both factors and plotted both a table and graph of the numbers here, at the bottom of the page:
    The overall trends still hold for shorter passes (less than 20 yards), but with longer throws, there are some weird peculiarities. There was a 58% completion percentage for 31-40 yard throws from 20-34 yards out, for example. I’m not really sure why.
    3. The top half of that web page is an effort to try to work out your hypothesized reasons for why completion percentage might go down, the closer a team gets to the end zone. There’s a breakdown for “non-end zone” throws at the top, which shows a mildly u-shaped pattern for completion percentage (i.e., higher nearer each goal line than in the middle of the field). So there appears to be some (weak) evidence for your “defenses will allow a higher completion rate to prevent a score” hypothesis.
    I also charted completion percentage for end zone passes, which gets higher, the closer a team gets to the goal line. For a minute or two, I couldn’t figure out how both end zone and non-end zone throw percentages could go up, the closer a team got to the goal line–while the general completion percentage was going down–but then it occurred to me that shifting the proportion of throws to (riskier) end zone passes was driving the overall trend down. So I’ve got a table of how that proportion shifts, the closer teams get to the end zone, too. 
    Long story short: there seems to be stronger evidence for your hypothesis that “throwers will accept a lower completion rate in order to get a score.” So the distance-to-goal trend might be more about decision-making than it is about execution.
    Since there was a big difference in end zone pass completion percentage between the first league and elite games I scored last year (, I’d like to get some more data from top-level games, to see if distance-to-goal remains as big of a factor on completion percentage, overall, in the elite ranks.
    4. If you’d like to play around with the passing data, I’ve posted it here:
    Thanks for getting me thinking about all this once again. 🙂

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