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Using Statistics to Improve Your Game

A couple of months ago, I developed a paradigm for ultimate frisbee statistics. The goal of the paradigm was to capture all of the qualitatively distinct events in a game of ultimate. I’ve scored a few games with this system and thought I would share the results with the visitors to this site, just in case anybody out there might be interested in them.
For starters, you’re welcome to check out a box score for the Furious George vs. NexGen game that took place last week (and which can be seen in its entirety on here:

The philosophy of the scoring system used to develop this box score is as follows:
There are two kinds of events that advance the progression of play in ultimate frisbee: (1) a pull and (2) a pass. (There are a variety of other, miscellaneous events which may also occur, including fouls, substitutions, time outs, violations, etc., but I won’t address those here.)

There are three different kinds of passes. (1) Passes which an offensive team throws into its target end zone form a distinct subset, since they terminate possession for the offensive team, regardless of whether or not they are caught. (2) Passes in the regular field of play which are caught, of course, just maintain possession for the offensive team, and can lead to further passes. Finally, (3) passes which an offensive team throws into its own end zone are also distinct because they can result in Callahans if they are caught by the defensive team.

One of the things that makes ultimate unique is that an offensive player cannot accomplish anything by him/herself in the game; every offensive player has to pass the disc to a teammate in order to advance the disc or score. What this means is that, offensively, there are two roles that must be filled on any given pass: there must be (1) a thrower and (2) a target. Analogously, a member of the defensive side also always plays one of two roles on a pass: (3) they can defend the thrower or (4) they can defend the target. In this system, I have labeled a defensive player in role (3) as the “marker”, and a defensive player in role (4) as the “defender”.

Of course, defense is not necessarily an every-man-for-himself endeavor, and more than one defender may work together to defend either the thrower or the target. So long as the defensive team is playing man-to-man, however, the actors involved in the vast majority of passes boil down to just these four players. The minority of other cases can also generally be viewed in terms of this four-player paradigm without doing too much damage to the truth.

Along with a set of four actors, each pass has a result. The results that I have categorized here include: (1) a completion, (2) an incomplete pass, (3) a drop (by the target), (4) an interception (by the defender), (5) a pass “d’d” (by the defender), and a (6) block (by the marker).

Drops require a bit of a judgment call on the part of the scorer, which is unfortunately less than ideal. The basic rule of thumb (ha!) I went with was to count a drop whenever the disc hit the target’s hands but was not caught.

To record all of this information, for each event, I set up a (tab-delimited) score sheet which lists, for each pass, (1-4) who the four actors were, (5) what the result of the pass was, and (6) whether or not the pass was thrown into either end zone (= 1 for target end zone, -1 for own end zone). I then wrote a Perl script to automatically generate the box score from the scoresheet; the script is linked on the box score, for any other ultimate geeks out there who’d like to play around with it.

With pulls, there are only two basic actors: the puller, and the player who catches/picks up/drops the pull. I have included this information in the box score and score sheet, primarily for completeness’ sake.

For those who are interested, other fields of information could be straightforwardly added to each pass for analytical purposes (distance and direction of throw, type of throw, direction of force, etc.), but I have found that it is fairly time-consuming to do so.

Be that as it may, I will add one analytical note here. It is interesting to compare the box score up above with the box score for the first game that I scored with this method (a Calgary men’s league game that I played in a couple of months ago):

One of the things that jumped out at me about the stats for this game was how drastically completion percentage dropped for throws into the end zone; passes in the regular field of play were completed 87% of the time, but potential scoring passes were completed only 51% of the time. The difference between those numbers in the Furious-NexGen contest was hardly so drastic; passes between the lines were completed 94% of the time in that game, and end zone passes were still completed at an 88% clip.

The lesson, as always: if you want to be an elite player, you’d better be ready to take care of the disc. Especially when your desire for glory is the most likely to get the best of your better judgment.

3 thoughts on “Using Statistics to Improve Your Game”

  1. I don’t know if comparing completion percentages is the right thing; What you want to compare is probability of eventually scoring, not probability of completing the pass. A 51% completion percentage into the endzone is a throw that scores 51% of the time; An 87% complete pass in the field will lead to <87% chance of scoring, since further throws are required. An interesting stat would be “average regular field throws required to score” This could be zero, if a team always hucks to the endzone on its first throw, but is probably not. So, say it is 5; .87^5 = 0.498, less than a 51% throw to the endzone.

  2. Hey–sorry about the slow response, but you raise some good points. In effect, I was analyzing the breakdown of “field” passes to end zone passes because I happened to have made it convenient to do so. I am sure that completion percentage varies gradiently as teams move up and down the field, but I need more data on that aspect of the game to get a better sense of what, exactly, those numbers would look like.

    The idea of analyzing the “probability of eventually scoring” is interesting, and is something I (or somebody) should really look into. This is another case where the distinction between end zone and field passes is helpful, though, because an end zone pass *has* to result in either a score or a turnover. A field pass, on the other hand, isn’t quite so dramatic, because it just leads to further passes if it’s completed.

    At the top of both box scores, I list some very general stats for both teams, including their total number of points, possessions and passes. From this you can do the math to find that the elite teams scored on 28 of 47 possessions, for a success rate of 59.6%, while the league teams scored on only 22 of 85 possessions, for a much more modest success rate of 25.9%. If you think of a pass into the end zone in risk/reward terms of either (a) my team is scoring or (b) I’m giving the disc to the other team, then I’d suggest that the end zone completion percentages were actually quite acceptable in both games. In the elite game, the teams were trading off an 88% scoring rate against a 60% likelihood that the other team would score, while in the league game, the teams were scoring at a 51% rate against a 26% likelihood that the other team would score.

    I’m going to have to crunch the aforementioned numbers before I can do the same sort of risk/reward analysis for field throws, but it’s probably pretty safe to assume that a turnover closer to your end zone is a lot worse than a turnover further away. So as a player you should adjust the acceptable riskiness of your throws accordingly, I suppose…

    One last point: you mentioned the stat of “average regular field throws required to score”. It’s actually pretty easy to calculate those numbers with the way I’ve set up the data sheet; in the elite game, there were 7.54 passes (including the final throw), on average, on each scoring possession. On the other hand, there were only 4.16 passes on each non-scoring possession. The corresponding numbers for the league game were fairly similar; there was an average of 6.41 passes on scoring possessions, and only 3.59 passes on non-scoring possessions.

    I’m not entirely sure what those numbers mean, but I will say that one thing keeping the numbers down was the fact that not much zone was played in either game…

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