So big thanks to everyone who helped with the nerdy challenge. You all saved me a ton of time. In thanks, I'd like to explain the frisbee reasons I was curious.

Mini is an awesome tool for development of individual skills. Unlike 7s, where a young player might touch the disc only 4 or 5 times a practice, Mini affords them a countless touches in a very short period of time. Touches, marking, defending, reading...every essential skill is practiced at game speed in a game like setting at a rate you can't match in a full-sided scrimmage.

I was interested in using it as a tool at the team level. In particular, I wondered if it would be possible to set a possession goal and use mini scores as a way to evaluate this goal. What I mean is, could you record the scores to a whole bunch of mini games and then go back and figure out what the possession rate was? Actually, I knew you could do this work, but I needed the algorithm to figure out the rates. That was the reason for the nerdy challenge.

Using Alpha Chen's probability generator, I cranked out possibilities established expected values and was able to come up with an expected value number for each possession probability. (The spreadsheet is here.) There is a bit of inaccuracy because Alpha Chen's simulator is a Monte Carlo generator and comes up with different values on each run, but from a frisbee standpoint, it doesn't need to be exact.

Here's how it would work: You play mini. Everyone keeps a running total of their score for all their games and how many games they played. (Golden Goal scenarios still 'score' as -1, -2.) When you are done, you add them all up and divide by how many games where played. Compare this number to the chart and voila! You know how you did on possession percentage.

10% = -1.4

20% = -1.2

30% = -1.0

40% = -0.5

50% = 0.1

60% = 0.7

70% = 1.2

80% = 1.4

Last thought. Some of the direction for this thinking came from Anson Dorrance's Vision of a Champion. In particular, Ch 12 and 13.

I think my reasoning is solid, but please, if I messed up, let me know. Thanks!

I think that's generally an accurate chart, except there's some nuance depending on the ability of the teams you're playing against. Your chart assumes that teams playing each other are always exactly equal in their completion rates (e.g. 10% vs 10% or 80% vs 80%). That may not matter much depending on the circumstances of your team-making, but I made this chart just in case you're interested in the details.

ReplyDeletehttps://docs.google.com/spreadsheet/pub?hl=en_US&hl=en_US&key=0ArWx-JRof0abdDdJSU9rZVYzaG1vNXZZUkg3RGtoM0E&single=true&gid=0&output=html

To use it, choose your team's % completion rate in the 1st column, then go over to the opponent's % completion rate, and you can see what you would expect your score to be against them on average (of course it highly depends on who starts with the disc, but if you average these 2 numbers then you get the expected score given equal times pulling or receiving).

So you can see that your 1.4 average score corresponding to an 80% completion rate is true only if all of your opponents also have an 80% completion rate.

I thought it was interesting to note that a bad team looks much better when playing against a good team, because this is the opposite of typical ultimate. For instance a team with a 10% completion rate that played against all teams with an 80% completion rate would end up looking like they had a 30% completion rate according to your chart above!

A good team, however, as usual, looks better when playing against a bad team.

@ Sherri: I wrote a really long, insightful comment and it disappeared. The chart you made reveals some interesting things. 50% is a nick point and the odds are almost even there. I'd be interested if it would be possible to prove that the EV = 0 and not the funny little small %ages the Monte Carlo provides.

ReplyDeleteThanks for the work.