A thoughtful consideration of statistics and probabilities can aid a player or team and help to improve play. Too often, players go through life without ever taking a quantitative look at how things are going. They fixate on one particular incident as if it’s totally indicative of a greater trend. My team once cut a player largely because he looked extremely clumsy on one catch, and that was the impression he left with us (he was able to overcome this and make the team the next year, though, and became a solid contributor). Another player would huck recklessly until he was finally shown that he had only completed one of ten long passes (even then, unfortunately, he still didn’t get it, so we had to shoot him). It makes for a comfortable off-season to remember only the successes, but to improve, you need to have as many tools as possible to make a realistic assessment.

Stats

I’ve been a big fan of statistics ever since I was five years old and I grilled my mother about the numbers on the back of baseball cards. Stats can be overdone, as any baseball follower can attest, but they can often reveal hidden gems. I believe that a key factor in the rise of my team Earth Atomizer back in 1990 was its devotion to tracking throwing percentages on all types of throws. Players could no longer be the conscienceless turnover machines mentioned above, remembering only the occasional completion instead of the numerous incompletions. Some players took these shortcomings as challenges to overcome, and they benefited from this analysis, while others sadly became resentful of this intrusion in to their idyllic self-appraisal.

Individual statistics can be fun and help individuals develop, but team level statistics such as RUFUS are more useful and revealing if interpreted correctly. For example, if you’re trying to determine whether your man or your zone defense is better, it wouldn’t be proper to compare your zone numbers on a windy day against a bad team to the man numbers on a calm day against a good team. Also don’t forget to consider field position when evaluating scoring percentages. An offensive platoon receiving the pull almost always has to move the length of the field to score, while a defensive platoon might get a first pass turnover and only have to go five yards for the goal. Therefore, the defense ought to be able to score a higher percentage of the time when they have the disc. (Additionally, the defense plays against the other team’s offensive squad, which is usually weaker defensively.) In brief, don’t compare apples to oranges.

Strategic decisions and numbers

Someone recently emailed me to ask about her team’s zone, which was designed to shut down the dump and force a long throw, where the tall deeps would knock it down. This might work at forcing turnovers, I told her, but would mean that they’d have to travel 70 yards for a goal. A better strategy would be to craft a zone that forced turnovers near the thrower, even if it means that a higher percentage of possessions resulted in goals. Her team might have fewer chances, but each chance would be a better bet, and hence the defense would score more goals. Most teams are already aware of this phenomenon from the offensive perspective (called "punting"), but don’t think about it defensively.

Pulling strategy is changing due to the 20 yard brick and "play it where it stops" rule. A pull that hits the back line now costs the pulling team 45 yards (25 yards of the end zone plus the brick), while the old rules specified only a 10 yard penalty (goal-line versus 10 yard brick). Paul Greff’s huge upwind huck at 14-14 in last year’s finals of Nationals came after a pull sailed out the back of the end zone. Without those extra yards, the game might have ended differently.

Do-overs on close calls benefit the offense more than the defense. The below matrix reveals this for a foul. If an Observer is allowed to make the call, then the results are symmetrical. However, if do-over is the only option, then the offense has the advantage, as they retain the disc no matter what, even if they do lose the yardage of the pass.

Of course, if the offense is right, then no call will give them anything they didn’t already earn. However, this case suggests that in order for a do-over to be the call that doesn’t give either team an advantage, the offense has to be more than 50% likely to be correct.

Anyway, suppose the Observer does blow the call, and the defense gets the disc and scores. "Man, that call was a two-point swing." Well, not exactly, unless it’s a next-point-wins scenario, since the wronged team will start the next point with the disc instead of being on defense. Therefore, it is much closer to a one goal swing instead.

The following matrix depicts winning percentages in a game to 15 for teams with the given scoring percentages. These were derived using a Monte Carlo simulation, 10000 runs each.

I’ve also included how a scoring percentage translates into number of turnovers in a game to 15. As you can see, a 10% difference in scoring rate translates into a much higher percentage difference in turnovers.

Don’t give these numbers that much weight, since I’ve assumed that a team’s scoring percentage stays the same in all conditions. It’s just meant to give a rough idea of how often upsets can occur. A team that has a 40%-35% advantage over its opponent can expect to win about 2/3 of the games. Actually, I would have expected this number to be higher. But it shows that a worse team can win about 1/3 of the time just through sheer luck. So, be careful next time you claim "we were destined to win" or "we can never lose to those guys."

Games to 21 v 15

I did another simulation to show how many times the team that is winning at 15 loses at 21. This is especially dangerous to draw conclusions from, since teams change their strategies or intensities in the end game. I ran 1000 games for each of the following, and counted how many times a team that was losing at 15 came back to win at 21 (hard cap). Below are the percentages.

I’ll just point out that in games between evenly matched teams, you would expect about 15-20% of them to feature a late game comeback. A closer look also shows that a longer game favors the better team. If we look at the .60 vs .40 game above, it shows that in 3.2% of the games, the better team is losing at 15 but goes on to win. However, this represents about half the games in which the worse team gets to 15 first (see the 94% number in a previous table). Shorter games mean that upsets are more likely.

Finally, I’d like to throw in a few words about error bounds. Any statistical sampling such as a Monte Carlo simulation or an ultimate game is going to have some measurement error compared to the true values. Don’t place too much faith on small numbers or small differences, especially when there are uncontrolled variables. For example, suppose your zone defense got scored on 2/15 times, and your man defense got scored on 3/15. First off, it’s highly possible that such a variation came from pure luck. Second, as I mentioned earlier, maybe the zone was only played when the other team’s top handler weren’t on the field. So, have fun with the numbers, but don’t get carried away. Numbers can reveal A truth, but necessarily THE truth, and certainly not the whole truth.