Life In 19x19

emeraldemon wrote:One other thing to consider: when we lose several games in a row, it can feel like a slump, something that needs correcting. But often it's just that humans tend to perceive streaks trends where there aren't any. Let's say someone plays 20 games over a month and the record is like this:

LLWWLWLWLLLLLWWLLWLL

The player might despair after 5 losses in a row, and even after 20 games the win rate is only 35%. But flipping a coin 20 times will often give you results like this. (In this particular case I used a computer to generate this sequece because I'm too lazy to flip a coin 20 times...) The most likely scenario is that nothing in particular has changed with this player's abilities, they just lost a few more than they won this month.

That trend has a probability of .057 of being, purely random. Binary data can have a lot of power in small sample sizes, if you don't do something stupid like approximate it with a normal.

http://graphpad.com/quickcalcs/binomial2/

What do I do about a slump?

That is the easiest question I have been asked in ages. The answer is NOTHING. Time takes care of it.

Have you never heard that you never learn if you don't make mistakes. Well when you make mistakes you tend to slump. It is a simple consequence of the normal distribution. Some people slump more than others. But slumps end.

Now, if it is not a slump and you have genuinely reached a plataue then that is a completely different question. But that is not what you asked.

Bantari wrote:Speaking of trends....
If your 'normal' is to have, say, 60% or even 70% win rate over any given month, and then one month comes with 35% - is that a slump, or even significant? I mean, I know about coins, but you can't really flip humans like coins - most are too heavy and it might be against the law.

No, of course not, humans are different from coins because they have minds capable of seeking patterns (even if none exist). In evolutionary terms useful, because sometime patterns do exist and can be learned. And likewise useful in evolutionary terms if a useful pattern does exist, to be able to learn it quickly.

But there is a downside to that (which is what we are talking about now). As Emeraldemon is pointing out, an actual random sequence is likely to appear to us to have a pattern when it does not. In other words, we are making the judgement far too quickly in terms of what mathematics would justify. That does not have a very high cost in evolutionary terms because the "false learning" is likely balanced in both directions. We have learned a (useless) behavior but if the situation is actually random that won't matter much besides cluttering our brains, which have enough room to accept a great deal of clutter while still leaving space for useful learning to be added.

If you want to research this question of "streaks" in human play activities you might note that there have been academic studies investigating things like whether hitting streaks (or slumps) in baseball are more frequent/longer than would be expected if purely random. Unfortunately the conclusions that these are just what might be expected if purely random does not help the feelings of exaltation or despair felt by the players experiencing the streaks.

SmoothOper wrote:

emeraldemon wrote:One other thing to consider: when we lose several games in a row, it can feel like a slump, something that needs correcting. But often it's just that humans tend to perceive streaks trends where there aren't any. Let's say someone plays 20 games over a month and the record is like this:

LLWWLWLWLLLLLWWLLWLL

The player might despair after 5 losses in a row, and even after 20 games the win rate is only 35%. But flipping a coin 20 times will often give you results like this. (In this particular case I used a computer to generate this sequece because I'm too lazy to flip a coin 20 times...) The most likely scenario is that nothing in particular has changed with this player's abilities, they just lost a few more than they won this month.

That trend has a probability of .057 of being, purely random. Binary data can have a lot of power in small sample sizes, if you don't do something stupid like approximate it with a normal.

http://graphpad.com/quickcalcs/binomial2/

Where did you get this number? If I type the example above into the calculator you linked, it gives 0.1316 for the 1-sided p value and 0.2632 for the two-sided. Neither of those is exactly "the probability of being random", but they're high enough to say you probably shouldn't reject the possibility of a binomial distribution with 50% win rate.

Sign and binomial test
Number of "successes": 14
Number of trials (or subjects) per experiment: 20
Sign test. If the probability of "success" in each trial or subject is 0.500, then:
The one-tail P value is 0.0577
This is the chance of observing 14 or more successes in 20 trials.
The two-tail P value is 0.1153
This is the chance of observing either 14 or more successes, or 6 or fewer successes, in 20 trials.

if you're on KGS use this:

http://kgs.gosquares.net/

basically you'll find over a large enough period of time, you're just winning or losing about 50% of the time

SmoothOper wrote:The two-tail P value is 0.1153
This is the chance of observing either 14 or more successes, or 6 or fewer successes, in 20 trials.

And here is where naive thinking about streaks (good or bad) goes wrong. The outcome only about 1 in 20, not very likely you say (if there were no cause). But how about if you played 200 games? Now how likely that you would not experience that streak somewhere in there? Or if 20 people each played 20 games, how likely that none of them would have experienced that streak. Understand? The person in the throes of a losing streak that by chance would be 1 in a 100 feels that there must be something wrong with their play. But out of 1000 people playing that many games it would be very unlikely if some of them didn't have that experience by chance. The "why me" is misplaced.

If you have 100 honest coins and you flip each 5 times it is very likely that at least one coin would come up heads each time. Not meaningful to ask "why that coin?".

Mike Novack wrote:And here is where naive thinking about streaks (good or bad) goes wrong. The outcome only about 1 in 20, not very likely you say (if there were no cause). But how about if you played 200 games? Now how likely that you would not experience that streak somewhere in there? Or if 20 people each played 20 games, how likely that none of them would have experienced that streak. Understand? The person in the throes of a losing streak that by chance would be 1 in a 100 feels that there must be something wrong with their play. But out of 1000 people playing that many games it would be very unlikely if some of them didn't have that experience by chance. The "why me" is misplaced.

If you have 100 honest coins and you flip each 5 times it is very likely that at least one coin would come up heads each time. Not meaningful to ask "why that coin?".

This would all be very reasonable if we were discussing coin flip competitions instead of playing go, but we aren't so it isn't.

speedchase wrote:
This would all be very reasonable if we were discussing coin flip competitions instead of playing go, but we aren't so it isn't.

That is a mistake in thinking. Let me give an example (realistic to go).

Suppose we decide to hold a "dan promotion tournament". The rule for this tournament will be that each player entered will play four games. The winners of their games will play each other, the losers of one game each other, the losers of two games each other, and same with the losers of three games. Only a player that wins four games will receive promotion.

OK, lets say that there are 64 players contesting for this promotion. I can tell you with absolute certainty that there will be exactly four promotions. The go playing ability of the contestants is completely irrelevant to that outcome. It doesn't matter if 32 of the 64 are of proper strength to be promoted to dan because only four can win all four of their games. It doesn't matter if none are above 4 kyu. If they are allowed to enter this tournament four of them must win all four of their games.

See, just like coins.

You are assuming that just because these are humans playing go there must be a reason why the ones that won four games won them, that they must be the better players. Wrong. They could all be so drunk they can't see straight or they could all be 25 kyu players where 75% of their moves are mistakes and the outcome would be exactly they same.

Whenever we try to draw conclusions from events (find correlations) we are always needing to consider whether our observations are departing from purely random by a great enough likelihood.

I did explain in the beginning the probable evolutionary reasons why our brains are likely to overestimate the existence of patterns (to see patterns where there really aren't any). The cost of not spotting a real pattern is high while the cost of imagining patterns where there aren't any is low (because the behaviors learned likely cancelling out, as likely to be correct as wrong since there wasn't a real pattern). In other words, we are (correctly) "programmed" to perceive "streaks" because a real pattern looks the same.

Mike Novack wrote:
Whenever we try to draw conclusions from events (find correlations) we are always needing to consider whether our observations are departing from purely random by a great enough likelihood.

Just because there is a likelihood that the slump is merely a random and to be expected event does not mean that there is no cause for it. Do we know that he is playing just as good as ever? Is it not possible that his slump is because he has been playing worse? In another thread, he asked for advice about the transition from the opening to the middle game, and mentioned that he is just starting to learn about the fuseki. Is it not probable that his attempt to integrate new knowledge is what's been getting him into trouble? If this is the case (or some other real reason for his current sub-par play), then Speedchase is right, and the statistical probability of a slump is just irrelevant.

Mike Novack wrote:

SmoothOper wrote:The two-tail P value is 0.1153
This is the chance of observing either 14 or more successes, or 6 or fewer successes, in 20 trials.

And here is where naive thinking about streaks (good or bad) goes wrong. The outcome only about 1 in 20, not very likely you say (if there were no cause). But how about if you played 200 games? Now how likely that you would not experience that streak somewhere in there? Or if 20 people each played 20 games, how likely that none of them would have experienced that streak. Understand? The person in the throes of a losing streak that by chance would be 1 in a 100 feels that there must be something wrong with their play. But out of 1000 people playing that many games it would be very unlikely if some of them didn't have that experience by chance. The "why me" is misplaced.

If you have 100 honest coins and you flip each 5 times it is very likely that at least one coin would come up heads each time. Not meaningful to ask "why that coin?".

When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

DrStraw wrote:
When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

True, but go is not entirely a game of chance, right?

DrStraw wrote:When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

You'd have more issues convincing others that this person was using a fair coin. This is by far the real problem.

Boidhre wrote:

DrStraw wrote:When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

You'd have more issues convincing others that this person was using a fair coin. This is by far the real problem.

Well, that is actually how I put it to them, but in the current context the concept of a biased go board does not make sense.

daal wrote:

DrStraw wrote:
When teaching statistics I explain that if everyone in the world tossed a hundred coins then there is a very good chance that someone would get 100 heads. If you were that person then I doubt very much that anyone could convince you it was simply by chance.

True, but go is not entirely a game of chance, right?

Perhaps not, but if the handicap and komi are set right then it should still be a 50-50 proposition.