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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Anonymous Anonymous said...

You may find you're looking at the probability tree in the wrong place.

Let's say that your team have just picked up the disc, had a couple of short passes and your handler is now faced with a long option with 60% chance (that will score), and a short option with 95%. All the previous 95% passes are not at this time relevant, because their outcome can't change. The 60% throw has probably always been there, so if you looked at the start of the point, the short-pass options would have looked bad, but now that you're half way down them, your chance of getting the remaining passes needed is improving. (Because you must re-evaluate the remaining probabilities after each throw, not just at the begining of the sequence.)

The second thing is that each short pass also increases the odds of completing a moderate to long pass. So if you have a choice of a 95% pass moving up only a few metres and a60% pass leading to the zone, you might still throw the 95% pass realizing that the next guy in the chain will now have a 65% long-option. Often just rapidly moving the disc will disorient your opposition, creating good long options. Especially if they're playing a zone defence.

But the most important factor here is, I think, that a lot of people dramatically overestimate their ability to throw long. For example, Ronnie. She's a great player, don't get me wrong. But on Tuesday she tried for a 15m forehand break-force pass in moderate wind. Clearly she thought she had a realistic chance of making it, but in all honesty, she had a nearly zero chance, and the almost inevitable turnover happenned. When she stuck to throws she actually could make, she was pretty much unstoppable.

The question is: what do you do about all this? I think the first thing must be to ensure people know their own limitations. That's been a hard lesson for me. I often used to throw longer than I was really capable. I've gotten much better at that.

The second thing, which is pretty important, is to then teach people to throw longer. What if their disc skills are better? That 60% throw is now a 75% throw (for example), and starts to look a lot better than a huge number of short passes even at a very individual high pass percentage. Especially when you have good receivers who are used to receiving long and reading the disc in the air. I have been holding off on the long-throw drill that I've been planning because I want to focus a bit more on defence for the moment. But maybe I should rethink that timetable. :)

And of course, there are times when you have 2 very low percentage options. If you have a 35% short option and a 20% long option, you should go for the long option because you will gain territory.


8:28 AM  
Blogger Alasdair said...

Though, all that aside, your basic probability tree is probably right. It's the inputs feeding into the probability determination that are problematic.

9:29 AM  
Blogger Adrexia said...

I think the first thing must be to ensure people know their own limitations.

Actually I find the problem of self-doubt is a larger problem than people not knowing their limitations. If you are too scared to throw long, your long throws are always going to be bad. It depends on the individual of course. If people constantly over estimate how far they can throw - that is a problem. But if people constantly underestimate - that is a problem too. You have to choose your target audience. Ronnie knows her throwing isn't great outdoors, but she needs to try these things in order to get better at it. I have no problem with that. Ronnie is well aware of her limitations and is quite capable of learning from her mistakes. She doesn't tend to throw long often, and most of the time the throws she choses to make are good ones - she just didn't put enough spin on it, or she released the disc wrong. It's a bit different from the situation we had a while ago with some people constantly throwing long- to no one. All the options she picks are good ones. She just sometimes fails to make the right throw. Failing to make the right throw is better than succeeding to make the wrong throw... A beautiful throw is a beautiful throw - but it is much much nicer when it is caught. :D

Maybe it's just me, but I think putting confidence barriers in the way is a really bad thing. I guess if you have come from the other side, over confidence, you have a different perspective.

11:21 AM  
Blogger Alasdair said...

I guess I could tighten up my terminology here. We could call them "safe", "low risk" and "high risk."

You'll have, for example, a range where every throw will complete successfully. That's a "safe" throw. Then a bit further away you'll make most throws, that's a "low risk" and then there's the long-long throws which are "high risk." And these ranges will vary with the wind, the force, and a bunch of other things.

I am pretty comfortable with people operating in the "low risk" area during games. But I'd prefer they didn't play a high-risk style generally during games. Mostly because I don't think that a throw-away in that area really teaches them much, it just costs possession.

In general, I think confidence is built more quickly by success than failure, all else being equal. So you throw the throws you know you can make, deviating into the "low risk" as necessary, and as you get better at the "low risk" throws, they will become "safe" throws... the outermost range of your throw is always pushing out.

Also, the game is not the only place to learn skills! We have regular practices, and there's nothing to stop anyone getting throwing practice outside of those.

So, in terms of "knowing your limits" I don't necessarily mean you limit yourself so much as you realize when you're taking a risk. Be realistic about what the risk is. For example, there's no real reason for Sam B to restrict his throwing to the same extent as Fraser M: Sam's disc skills mean a "safe" throw is a long way typically.

You're right that confidence can cut both ways though. Realistic means just that: not optimistic, not pessimistic. You need to be realistic about your capabilities.

12:28 PM  
Anonymous Anonymous said...

Based on my experience of learning to be a soccer striker, I would definitely play with you if I ever took up Ultimate. Give me the quick long pass chance over the safe short pass anytime. In soccer, I love running for 50/50 balls, and I love to take unexpected snap shots. I'd drive Mash crazy, I'm sure :D

That said, the other advantage of the short game is that it allows you to control the tempo of the game better.


5:29 PM  
Blogger Mary said...

Compare this to netball. When you start playing as a youngster, you make little passes to each other. It takes many passes to get up the court.

Top teams make it up the court with as little as the compulsory touch in each third.

What changes? Skill in throwing and passing, skill in reading the game - plus the realisation that the longer throws gain heaps of territory. Even if the throw fails and the ball is turned over, the turn over occurs at the point where the long throw fails, rather than where the thrower was located.

But hey, I don't even play Ultimate! Just passing though....:-)

6:34 PM  
Anonymous Timoti da barbarian said...

In underwater hockey 2 people and a short pass will defeat one defender, easy like a stroll in the park. but then the long pass isn't an option for most players

6:06 AM  

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