Statistical Approach and Efficiency of Play

[SmoothOper]

While it is obvious that if you have one too few liberties in certain situations that your stones will die and you will lose, I wonder if there is any notion of whole board liberties. For example how many liberties do all the stones have as play goes on, also what are the expected number of stones functioning in a one chain, number of stones in a two chain, number of stones in a three chain etc... Is there some optimum in the size of chains vs. number of liberties.

[Toge]

It's quite difficult trying to understand moves by just counting liberties. How would you analyze the example below? Left figure black has 6 liberties. Center and right figure black has 7. If white plays cutting point, he takes away 2 liberties, but protecting will only grant one. Playing empty spot with no adjacent or diagonal stones automatically grants the maximum 4 global liberties.

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[hyperpape]

I think one should be careful to distinguish a) optimal play will result in some statistically visible pattern in the number of liberties/chains, and b) there is some pattern of liberties/chains that if you play to maintain that pattern, you will get good results.

Not that I'm sure that either one is true. But while (b) is just obviously false, (a) is possible.

[SmoothOper]

I think one should be careful to distinguish a) optimal play will result in some statistically visible pattern in the number of liberties/chains, and b) there is some pattern of liberties/chains that if you play to maintain that pattern, you will get good results.

Not that I'm sure that either one is true. But while (b) is just obviously false, (a) is possible.

That seems like a fair judgement, I am thinking that a saber-metrics style analysis might apply to go though, and my first inclination would be liberties and thickness, I am not sure what else could be quantified. http://en.wikipedia.org/wiki/Sabermetrics

[Mef]

I think one should be careful to distinguish a) optimal play will result in some statistically visible pattern in the number of liberties/chains, and b) there is some pattern of liberties/chains that if you play to maintain that pattern, you will get good results.

Not that I'm sure that either one is true. But while (b) is just obviously false, (a) is possible.

That seems like a fair judgement, I am thinking that a saber-metrics style analysis might apply to go though, and my first inclination would be liberties and thickness, I am not sure what else could be quantified. http://en.wikipedia.org/wiki/Sabermetrics

Two things to note here: The reasons Sabermetrics works is because you have a large team of knowledgeable people quantifying every action in a game. In order to know that a cutter low and away leads to a sacrifice fly (so that it does not count as an at bat for the hitter) you have to have a person sitting there identifying the type of pitch, pitch location, and that the criteria are met playing for a sacrifice.

You could try to do this for go, and do something like "Lee SeDol gains an average of 3 additional points over his opponent in games with running fights that start from high pincers to high approaches to a 4-3 stone" however, much like in baseball, it will require having a person tallying statistics who is able to properly identify a running fight, and properly assess the amount of profit each player earns from the fight. Of course to make this useful, you will need to have a group of people identifying the occurrence and outcomes of many situations in many, many professional games, and then once you have all this data, hopefully you can tease something useful from it.

Right now the closest thing we really have is winning percentage based on opening variations, because this is easily done by database. Of course winning % by database is potentially a dubious exercise if not done properly, because it may be that a successful line has a killer-counter developed for it and never sees professional play again (in spite of the database suggesting it is a solid line). Frequency of use in professional play is also a metric that gets used, but of course using that is simply attempting to identify expert knowledge others are using, not come up with "new" expert knowledge.

Let's also not forget how connections with baseball can decrease go strength, which naturally makes go players avoid the work of SABR.

[SmoothOper]

Two things to note here: The reasons Sabermetrics works is because you have a large team of knowledgeable people quantifying every action in a game. In order to know that a cutter low and away leads to a sacrifice fly (so that it does not count as an at bat for the hitter) you have to have a person sitting there identifying the type of pitch, pitch location, and that the criteria are met playing for a sacrifice.

You could try to do this for go, and do something like "Lee SeDol gains an average of 3 additional points over his opponent in games with running fights that start from high pincers to high approaches to a 4-3 stone" however, much like in baseball, it will require having a person tallying statistics who is able to properly identify a running fight, and properly assess the amount of profit each player earns from the fight. Of course to make this useful, you will need to have a group of people identifying the occurrence and outcomes of many situations in many, many professional games, and then once you have all this data, hopefully you can tease something useful from it.

Right now the closest thing we really have is winning percentage based on opening variations, because this is easily done by database. Of course winning % by database is potentially a dubious exercise if not done properly, because it may be that a successful line has a killer-counter developed for it and never sees professional play again (in spite of the database suggesting it is a solid line). Frequency of use in professional play is also a metric that gets used, but of course using that is simply attempting to identify expert knowledge others are using, not come up with "new" expert knowledge.

Let's also not forget how connections with baseball can decrease go strength, which naturally makes go players avoid the work of SABR.

I was definitely thinking that the games would be analyzed via computer databases for this to work at all and that there should be other interesting things that could be done with technique statistics beyond the openings. The trouble is of course defining the techniques such that A) a computer could do the analysis and B) a person would recognize what they mean.

However you do bring up an interesting point about the value that is added by human observers recognizing situations as they occur. I could imagine a dojo master having all the 1 dans go through a series of games and find the number of double hanes on the second line and how often they contributed to a win, I am sure they do that already though.

[Darrell]

Sabermetrics generally does not concern itself with whether a particular act correlated with winning the game. They deal with smaller units - whether a run was scored in the inning or even whether the runner reached base. The game is considered the sum of the smaller units - the team that scores more runs wins and thus each act that scores a run is a positive event and allowing a run is negative event. They try to determine the factors that go into scoring runs or allowing runs, not directly winning. Go, of course, does not have such neat, divisible units. Even capturing a 30-pt group has to be evaluated against the value of the ko threat that was ignored to make the capture.

[SmoothOper]

Go, of course, does not have such neat, divisible units. Even capturing a 30-pt group has to be evaluated against the value of the ko threat that was ignored to make the capture.

In theory each play should be scoring points.

[hyperpape]

Or it may reduce the opponent's points. In any case, it's not measurable in any automatic way.

[ez4u]

What is the difference between this idea and the calculations that current Go-playing programs make in move selection?

[SmoothOper]

What is the difference between this idea and the calculations that current Go-playing programs make in move selection?

Most engines are based on Monte-Carlo go. Where they sort of randomly generate a bunch of games, then calculate the number of wins associated with a particular move, the move that leads to the most wins is selected.

The idea here is to look at games and try to determine which tesuji are the best.

[Mef]

Since this thread happens to be a collision of two topics I'm interested in, a few more thoughts --


One other reason why SABR style research might not be as directly helpful for go is that baseball statistics are generally looked at from the manager's perspective. The idea is they figure out what players are contributing value, and figuring out how to maximize that value for the team (not maximize an individual player's results). While there might be the occasional specific insight that can help a player (like teaching Dominicans to take more walks, or convincing Eric Hosmer to play farther off the bag at first) the vast majority is related to identifying players who are performing vs. those who aren't, and figuring out who will continue to perform as opposed to who had a fluke year. In go this is a non-issue, player performance is directly measured by wins so there is no need for indirect statistics. In the same vein, you don't see much advanced statistics used in tennis because it's easy to tell who the top performers are, they take home the trophies.

Now if you did want to try and do some "traditional" sabermetric style analysis, you could try to answer things like "Who contributed more to South Korea winning the 8th Nongshim Cup: Pak Yeonghun who eliminated 4 competitors in the middle stages, or Lee Changho who eliminated the final two?". You could try to approach this a variety of ways, maybe use historical winning percentages in international events and perhaps try to derive a tournament winning probability accumulated through each victory. Ultimately you might be able to make a case for one of the other...but will this type of knowledge help us play go better? I'm not so sure.

[ez4u]

What is the difference between this idea and the calculations that current Go-playing programs make in move selection?

Most engines are based on Monte-Carlo go. Where they sort of randomly generate a bunch of games, then calculate the number of wins associated with a particular move, the move that leads to the most wins is selected.

The idea here is to look at games and try to determine which tesuji are the best.

Yes, but if it could be done that way, the programs' authors would do it. The available pool of real games played is too small to reliably extract the 'right' next move. Hence the use of Monte Carlo techniques.

[Bill Spight]

On this general topic, I wondered about the question of whole board liberties and efficiency. To try to make a start, I looked at a few games at the end. OC, the proper index of efficiency is the score. However, I identified two distinct types of liberties: shared liberties and territory liberties. Assume that the shared liberties (outside of seki) are filled and any necessary repair moves are made. That leaves two types of territory, liberties and non-liberties.

I suspect that there is a correlation between non-liberty territory and score. I. e., efficiency means making territory at a distance.

[Mef]

On this general topic, I wondered about the question of whole board liberties and efficiency. To try to make a start, I looked at a few games at the end. OC, the proper index of efficiency is the score. However, I identified two distinct types of liberties: shared liberties and territory liberties. Assume that the shared liberties (outside of seki) are filled and any necessary repair moves are made. That leaves two types of territory, liberties and non-liberties.

I suspect that there is a correlation between non-liberty territory and score. I. e., efficiency means making territory at a distance.

To see if I follow what you're saying...

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Click Here To Show Diagram Code

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A is non-liberty territory, B is territory liberty, C is shared liberties? If I'm following right it seems like you're trying to (more or less) figure out average "points per territory-making stone" (let's go ahead and call a territory-making stone a stone with at least one territory liberty). I guess along those lines you would also have a dame stone (a living stone that does not have a territory liberty?). Assuming an equal number of plays for each player and an equal number of dame stones, then the player with the highest "points per territory-making stone" will win. It would get more interesting going into unequal number of dame stones, but I'm sure it would be pretty you could derive a relation to when playing a dame stone is worthwhile (if you reduce the amount of non-liberty territory, cause your opponent to require additional territory making stones, or ideally, both...as all of these things reduce your opponent's effective "point per territory-making stone").

I guess the real question is, will this be significantly different or more useful than simply looking at "points per stone" on its own. I'm inclined to believe it might be, since it would perhaps allow for comparison of play between a game with two large moyos (lots of points and few dame) vs. a fighting game with many groups (lots of dame few points).