Statistical Approach and Efficiency of Play

SmoothOper · #1

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 · #2

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.

Click Here To Show Diagram Code: [go]$$ $$ . . . . . . . . . . . . . . . . . . . $$ . . . . . . . . . . . . . . . . . . . $$ . . . . . . . . . . . . . . . . . . . $$ . . X 1 . . . . X . . . . . . X . . . $$ . . O X . . . . O X 1 . . . 1 O X . . $$ . . . . . . . . . . . . . . . . . . . $$ . . . . . . . . . . . . . . . . . . .[/go]

hyperpape · #3

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 · #4

hyperpape wrote:

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 · #5

SmoothOper wrote:

hyperpape wrote:

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 · #6

Mef wrote:

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 · #7

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 · #8

Darrell wrote:

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 · #9

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

ez4u · **#10**

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

SmoothOper · **#11**

ez4u wrote:

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 · **#12**

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 · **#13**

SmoothOper wrote:

ez4u wrote:

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 · **#14**

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 · **#15**

Bill Spight wrote:

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...

Click Here To Show Diagram Code: [go]$$ $$ ----------- $$ . . a . . . $$ . . b . . . $$ X X X X X X $$ . . c . . . $$ O O O O O O[/go]

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).

SmoothOper · **#16**

Mef wrote:

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).

That is an interesting point that the overall score of the game may bias the results of any evaluation of tesuji if the points per stone metric is used without any adjustment.

Bill Spight · **#17**

Mef wrote:

Bill Spight wrote:

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...

Click Here To Show Diagram Code: [go]$$ $$ ----------- $$ . . a . . . $$ . . b . . . $$ X X X X X X $$ . . c . . . $$ O O O O O O[/go]

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).

You got the empty point classification right.

But what I was musing about was not so specific. SmoothOper pointed out the importance of liberties in tactical situations and then asked about whole board liberties and efficiency. What I am suggesting is that, at the level of the whole board, efficiency is perhaps more related to non-liberty territory.

Mef · **#18**

SmoothOper wrote:

That is an interesting point that the overall score of the game may bias the results of any evaluation of tesuji if the points per stone metric is used without any adjustment.

Well, with any statistical comparison it is always important to properly normalize your results -- A recent example from baseball: (a digression about the triple crown, stats, and baseball history for those who care to read it).

Miguel Cabrera just won the Triple Crown with a .330 batting average, 44 home runs, and 139 RBIs. This has not been done since Carl Yastrzemski did it in 1967 scoring a .326 average, 44 home runs, and 126 RBIs. You might be tempted to make a direct comparison of these numbers and conclude that, while their seasons were similar, Cabrera's season was a bit better.

If you look beyond those numbers there's a much different story. One "normalized" way of measuring an offensive player's production is oWAR (Wins Above a Replacement Player - isolated for offensive stats only). In 1967, Yaz is said to have produced 9.5 oWAR, while in 2012 Cabrera generated "only" 7.4. This gives us a hint that Yaz's achievement might be better, but even this doesn't capture the whole story. You see WAR looks at the expected production of a "replacement level player", and a replacement leftfielder that Yastrzemski is being compared to is expected to be a significantly better hitter than a third baseman who would replace Cabrera (this because more teams will accept a poor hitting third baseman who has a strong fielding ability).

If you want to properly quantify the difference just for hitting, you can look at a normalized hitting statistic like OPS+. OPS is On Base Percentage + Slugging percentage, a statistic that has been gaining in popularity over the last decade because it's a quick way to compare both players who walk/hit for average against players who hit for power. OPS+ takes this one step further, it compares the OPS of each player compared to the average in the league, and further normalizes this based on what ballparks the players play in. A league average player will have an OPS+ of 100. In 1967, Yastrzemski's OPS+ was 193 (that's 93% higher than league average!) vs. 2012 Cabrera's 165. So while certainly played great Cabrera's this season, Yastrzemski's 1967 season was phenomenal -- even though the numbers for the triple crown are better for Cabrera.

Why is that you might ask?

Well, back in 1967 life wasn't so good as a batter...pitchers were absolutely dominant. In the early 60s there had been lots of power hitting (1961 is when Mantle and Maris go after the home run title and Maris hits 61). To compensate the did things like expand the strike zone and the result is it swings the other way. It got so bad that in 1969 they changed the rules, lowered the pitcher's mound and shrunk the strikezone. Also even though the rules haven't technically been changing, it's been argued that the strike zone has been effectively shrinking even more since then, based on how umpires are actually calling games.

Long story long, context is everything. One player putting up hitting numbers during the peak of a pitcher dominated era isn't the same as another player doing the same today.

To bring it back to go, you'd need to find a way to normalize each move, perhaps using "relative gain" (profit?), or maybe "points secured vs. total points scored", or perhaps combine the two -- "profit relative to total points scored". After all, the name of the game in go isn't figuring out how to maximize your number of points, it's about maximizing the probability you have more points than your opponent at the end of the game. Generally that means finding ways to make points while your opponent isn't. It might be through forcing them to make life while you secure territory, it might mean forcing them to connect two groups across dame points, etc. Ideally a statistic you develop would be able to quantify this...though the further you go down this line it sounds more and more just like a fancy name for miai counting.

Bill Spight wrote:

You got the empty point classification right.

But what I was musing about was not so specific. SmoothOper pointed out the importance of liberties in tactical situations and then asked about whole board liberties and efficiency. What I am suggesting is that, at the level of the whole board, efficiency is perhaps more related to non-liberty territory.

For tactical stability, perhaps it would be worth quantifying N-th order liberties*, where an N-th order liberty is a liberty you can potentially add to your group with N moves? The simplest example of such is of course a net - reducing the potential to get liberties rather than reducing liberties directly.

Or perhaps more along the lines of your definitions, exclusive liberties - liberties that one side can obtain if needed that are unavailable to the opponent (this seems to me like it would be some function of territory liberties and non-liberty territory?).

*I had originally put secondary and tertiary liberties here, because that is how I had always heard the term used, but, a quick sensei's search shows that the term secondary liberty is used for something else.

Bill Spight · **#19**

Mef wrote:

Bill Spight wrote:

You got the empty point classification right.

But what I was musing about was not so specific. SmoothOper pointed out the importance of liberties in tactical situations and then asked about whole board liberties and efficiency. What I am suggesting is that, at the level of the whole board, efficiency is perhaps more related to non-liberty territory.

For tactical stability, perhaps it would be worth quantifying N-th order liberties*, where an N-th order liberty is a liberty you can potentially add to your group with N moves? The simplest example of such is of course a net - reducing the potential to get liberties rather than reducing liberties directly.

Or perhaps more along the lines of your definitions, exclusive liberties - liberties that one side can obtain if needed that are unavailable to the opponent (this seems to me like it would be some function of territory liberties and non-liberty territory?).

IIRC, Tajima uses the idea of Nth order liberties in his paper about the Possible Omission Number of a group. (The PON is the number of times you can tenuki and still save the group.) Exclusive liberties sound something like outside liberties in a semeai.

Quote:

*I had originally put secondary and tertiary liberties here, because that is how I had always heard the term used, but, a quick sensei's search shows that the term secondary liberty is used for something else.

SL is not a reliable source for English go usage. Nobody who wrote there about terminology was or is a lexicographer, as far as I know. The only place a number of terms appear in the literature is on SL. They are what somebody came up with on their own. (Not that there is anything wrong with coining terminology. But when you do that you are not reflecting actual usage.)

SmoothOper · **#20**

Mef wrote:

SmoothOper wrote:

That is an interesting point that the overall score of the game may bias the results of any evaluation of tesuji if the points per stone metric is used without any adjustment.

Well, with any statistical comparison it is always important to properly normalize your results -- A recent example from baseball: (a digression about the triple crown, stats, and baseball history for those who care to read it).

Miguel Cabrera just won the Triple Crown with a .330 batting average, 44 home runs, and 139 RBIs. This has not been done since Carl Yastrzemski did it in 1967 scoring a .326 average, 44 home runs, and 126 RBIs. You might be tempted to make a direct comparison of these numbers and conclude that, while their seasons were similar, Cabrera's season was a bit better.

If you look beyond those numbers there's a much different story. One "normalized" way of measuring an offensive player's production is oWAR (Wins Above a Replacement Player - isolated for offensive stats only). In 1967, Yaz is said to have produced 9.5 oWAR, while in 2012 Cabrera generated "only" 7.4. This gives us a hint that Yaz's achievement might be better, but even this doesn't capture the whole story. You see WAR looks at the expected production of a "replacement level player", and a replacement leftfielder that Yastrzemski is being compared to is expected to be a significantly better hitter than a third baseman who would replace Cabrera (this because more teams will accept a poor hitting third baseman who has a strong fielding ability).

If you want to properly quantify the difference just for hitting, you can look at a normalized hitting statistic like OPS+. OPS is On Base Percentage + Slugging percentage, a statistic that has been gaining in popularity over the last decade because it's a quick way to compare both players who walk/hit for average against players who hit for power. OPS+ takes this one step further, it compares the OPS of each player compared to the average in the league, and further normalizes this based on what ballparks the players play in. A league average player will have an OPS+ of 100. In 1967, Yastrzemski's OPS+ was 193 (that's 93% higher than league average!) vs. 2012 Cabrera's 165. So while certainly played great Cabrera's this season, Yastrzemski's 1967 season was phenomenal -- even though the numbers for the triple crown are better for Cabrera.

Why is that you might ask?

Well, back in 1967 life wasn't so good as a batter...pitchers were absolutely dominant. In the early 60s there had been lots of power hitting (1961 is when Mantle and Maris go after the home run title and Maris hits 61). To compensate the did things like expand the strike zone and the result is it swings the other way. It got so bad that in 1969 they changed the rules, lowered the pitcher's mound and shrunk the strikezone. Also even though the rules haven't technically been changing, it's been argued that the strike zone has been effectively shrinking even more since then, based on how umpires are actually calling games.

Long story long, context is everything. One player putting up hitting numbers during the peak of a pitcher dominated era isn't the same as another player doing the same today.

To bring it back to go, you'd need to find a way to normalize each move, perhaps using "relative gain" (profit?), or maybe "points secured vs. total points scored", or perhaps combine the two -- "profit relative to total points scored". After all, the name of the game in go isn't figuring out how to maximize your number of points, it's about maximizing the probability you have more points than your opponent at the end of the game. Generally that means finding ways to make points while your opponent isn't. It might be through forcing them to make life while you secure territory, it might mean forcing them to connect two groups across dame points, etc. Ideally a statistic you develop would be able to quantify this...though the further you go down this line it sounds more and more just like a fancy name for miai counting.

Bill Spight wrote:

You got the empty point classification right.

But what I was musing about was not so specific. SmoothOper pointed out the importance of liberties in tactical situations and then asked about whole board liberties and efficiency. What I am suggesting is that, at the level of the whole board, efficiency is perhaps more related to non-liberty territory.

For tactical stability, perhaps it would be worth quantifying N-th order liberties*, where an N-th order liberty is a liberty you can potentially add to your group with N moves? The simplest example of such is of course a net - reducing the potential to get liberties rather than reducing liberties directly.

Or perhaps more along the lines of your definitions, exclusive liberties - liberties that one side can obtain if needed that are unavailable to the opponent (this seems to me like it would be some function of territory liberties and non-liberty territory?).

*I had originally put secondary and tertiary liberties here, because that is how I had always heard the term used, but, a quick sensei's search shows that the term secondary liberty is used for something else.

I was thinking about efficiency of play in couple of different ways. Relating it to another sport basketball, offensive efficiency is the number of points per possession, defensive efficiency is points permitted per possession. The most efficient teams on the season are generally correlated with winning-est teams. In this context efficiency would be related to sente and gote. As a hypothesis maintaining more liberties across the board would help in sente and gote.

Also I am thinking about tempo in go, and what that term means. Is tempo always better? I suspect that fast development is not necessarily the most efficient development, however efficiency ends up defined.

Statistical Approach and Efficiency of Play

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