# The "rectangular measure", a territory size statistic

If you have nothing better to do, take a consecutive portion of your recent scored 19x19 games and, in the final position of each game, find the single largest rectangle you can fit into your own area – that’s area, not territory, meaning that you can include your own living stones (and any captures).

Catalogue the area of the maximal rectangles and average them – this gives you the “rectangle measure”.

I don’t know yet whether the measure is at all meaningful, which is part of the fun.

Here is my result, from ten of my consecutive scored games at mid-SDK.

No. Opponent Rect.
2 GeorgeGu 35
3 MichaelLebl 42
4 brough 50
5 cici 24
6 Koba 78
7 sanderl 20
8 Clossius 42
9 knowing 66
10 alemitrani 35
avg. 43.2
avg. [nearest rect.] 44

So my rectangular measure is 43.2, or 44 to the nearest rectangle.

If I discard Koba 78 as an outlier then I get a measure of 39⅓, rounding to a rectangular 39.

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What I’d like to work out is:

• what is the bound of rectangular measure containing, say, 90% of responding players?

• how does rank correlate to rectangular measure?

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Why are you rounding upwards (43.2 >> 44) and downwards (39⅓>>39)?
Why are you rounding at all?
Why does your new measure RM have to be an integral?

By the way love it that you do some pure fundamental research instead of applied science

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I was rounding them to possible rectangles.

44 is like a 4 x 11 rectangle; 39 is like a 3 x 13.

Being able to envisage an actual rectangle as the average is nice.

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If you add opponent’s rank to your table you would be able to make a rank/RM scatterplot, like the one below.

BTW:

Methodologically not really convincing, but since it is your party

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As much as I would like to participate, there lies my problem - all (or the vast majority of) my games end by resignation.

When Jigo/Offer Draw will be implemented, also a bit of that, I forecast

On what board size is the RM based?

By quickly looking at some of my games, it seems like upper limit on how large area i can naturally build is roughly 25-30 points (like uncontested corner which expands to the side), and everything larger than that does include some quite big dead group of my opponent inside. Its actually kinda interesting to know that i have some sort of limit on what i can realistically expect to have, and when i am just inviting an invasion ^^

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I am asking myself what kind of useful information bring a rectangular mesure compared to a normal counted mesure?
I can see it could be a way to optimize maybe a procedure of normal counting but besides this? Could create a ratio rectangular/normal to evaluate how your territories are well rounded?

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Well, just for fun as @bugcat wrote

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Thanks but not really the answer of the question, sorry. (besides I did read that post too).

Note: “which is PART of the fun”, so not JUST for fun.

19x19, as I said in the OP.

I do have an idea that rank (lower rank = higher RM) and style (more central style = higher RM) could be correlating values.

I’d also expect RM to correlate with winning percentage (the more won games in the set, the higher RM) and, as a result with the ranks of the opponents in the set.

I’d expect RM to also be to some degree inversely proportional to “ORM”, the collective RM of the opponents in the set, which can be worked out by finding their largest rectangle in each game. In hindsight, though, I also wouldn’t be too surprised if that wasn’t the case…

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I wonder if some method could be created based on this to quickly and accurately estimate the score (or, at least, winning percentage) in a running game without having to count each group’s territory. Might be a nice trick to speed up counting in live / blitz games…

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interesting.
In any case, what about considering RMplayer1 - RMplayer2 instead of just RMplayer?

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I just did my last three:

• 30
• 40
• 33
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I would imagine that rectangular measure would not correlate with your rank, since you play against players of various ranks and there are all sorts of variations in each game that may not average out in any meaningful way.

But rectangular measure may be easier to estimate than territory, so I would guess that rectangular measure would be great guide for how you are doing during each game.

Top players are said to keep a running estimate of their exact territory and their opponent’s exact territory, to guide them as to playing safe or taking risks.

If you get convinced that rectangular measure is useful during games, it would be helpful if you published some clear diagrams showing examples of game boards and how to calculate the rectangular measure, as I’m not finding the definition as obvious.

And it would be interesting to see if the same advantage could be gained by evaluating rectangular measure in 13x13 and 9x9 games as well. Myself, I play only 9x9 games due to lack of time and lack of great interest in such aspects of the game as moyos and josekis.

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9x9 without moyos and josekis? I should have a look at your games, sounds interesting.

* spits coffee out in shock *

Blasphemy!!!

To echo what has been mentioned before, I’d be interested in how good of a predictor for who has more points who has the larger rectangular measure is.