Wednesday, November 14, 2007

Likely as not.

You know that probabilities multiply, right? Of course you do, but I'm going to tell you anyway.

For our first child there was a 50% chance of having a daughter, for our second child there was a 50% chance of having a daughter, so our chance of having both children be daughters was only 50% * 50% = 25% (Arthur and Corwin, Arthur and Iris, Hazel and Corwin, Hazel and Iris ftw!!!)

If you have to roll 7 or less on a d10 for your character to succeed at, say, climbing a wall, and you have to roll two times because the wall is high you only have about half a chance of success because 70% * 70% = 49%

So, as it happens, two 70% chances having to both succeed in order to get complete success (not falling off the wall) is about 50% and so are three 80% chances and six 90% chances.

70% * 70% = 49%
80% * 80% * 80% = 51.2%
90% * 90% * 90% * 90% * 90% * 90% = 53.1441%

In Ultimate we are often faced with a choice between a shorter pass to someone no closer to the zone than the thrower or a longer pass further up the field which may well have a smaller chance of success. If a pass fails then there's a turnover and we have to get the disc back off the other team or they score.

In order to avoid the other team getting the disc from us we are often advised to use short safe passes and listening to team-mates' commentary we often seem to feel that throwing a good pass that was only just missed is somehow morally better than throwing a less sure thing that was caught. Yet six 90% passes are mathematically only as good as one 53% pass, so if your not-sure-thing hugely reduces the number of passes needed to get a point it may be mathematically as good as using shorter passes and more dump options as they take more passes to get to the other end of the field. Shorter passes that make less ground also makes it more likely the disc will become the other team's nearer their end zone.

What chance of success a given pass has is not just about how much of the field it flies over. Long passes are not necessarily more risky than short: a 10° error looks bigger further away from the thrower but a catcher who is further away has more time to read the disc and get to the place the disc is coming to. Chance of success depends on the weather, the thrower's current condition, skills and abilities, and those of the catcher, the markers of both, and what all the other people on the field might do. There are too many variables changing too fast to tell what percentages to assign to two passes as we choose between them, nor would numerical values be useful. We have to just do it; kinesthetic tasks are best performed using the evolved and embodied distributed intelligence of the human animal rather than trying to organise responses from some sort of analytical central point-of-view that calls itself "I".

In conclusion: perhaps short safe passes aren't the only good option and it might be me to whom you throw it long and I love the running and the disc flying and floating and reaching out to snap it out of the air.

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