Remember the last time JF was ranting about Mickey Mouse time limits? Well this got me to thinking. The question that I puzzled over is, "What is the likelihood that a 'hero' (famous fan favorite, outstanding performer and what not), having won a tournament last year, would repeat as the tournament winner this year?" Unusually, I did not fall back on GoGoD and Kombilo.

Instead I turned to excel... Lots of time later I have more or less simulated all the tournament structures from the reports shown on the Go News site for Japan, Korea, and China. The results of my analysis were a little surprising to me so I offer them here for your enjoyment.

The Basic Story
I assumed a world in which our Hero stands above the crowd. He/She is able to achieve an average 75% winning rate against three tiers of opponents: T1. Those He/She beats 65% of the time, T2. Those He/She beats 75% of the time, and T3. Those He/She beats 85% of the time. The different tiers show a similar pattern among and between them with T1 beating T2 opponents 65% of the time and T3 opponents 75% of the time, etc. Each tier wins 50% of its games against same-tier opponents. I modeled the different tournament structures in excel with random assignment of equal numbers of opponents from the three tiers to fill out the tournament table (note there was no pyramid of skill - I was too lazy). I set up an excel simulation of each tournament structure (see below), ran each simulation 10,000 times, and recorded the results.

Real World Tournament Structures
There are a surprising range of tournament structures in use. I ignored preliminary tournaments, which would add a great deal of additional complexity. Instead I concentrated on the finals.

Challenge Match Structures
The top Japanese tournaments are all structured as challenge matches where the incumbent defends his/her title against a single opponent. Due to the nature of the question that I asked - can last year's winner repeat - these are simple to model. Challenge matches have become rare in Korea and China. In Korea only the Kuktsu and the Female Myeongin retain this structure. In China only the Mingren and the Tianyuan.

Knock-Out Structures
Tournaments based on single-game elimination are the norm. There are a number of varients in terms of size, whether some players are seeded into later rounds, and whether the final is a mini-match or not. (Note that all numbers below for 'seeded' structures assume that our Hero is seeded as deeply as possible into the tournament.)

Other Structures
There are a few tournaments featuring other structures: double elimination, league structures. I skipped those. The only one in CJK that was impacted was the KBS cup, which has a double elimination format.

The Impact of Structure on "Heroism"
The easiest structure to repeat in is a 7-game challenge match like the Meijin in Japan or the Qiwang in Taiwan. In my mythical world, our hero(ine) retains the title about 91% of the time. At the other end of the spectrum is a pure 64-player knock out like the CITIC Cup in China. Despite standing head and shoulders above the competition, our hero has only a 13% chance of repeating. Basically a shorter KO (reducing the number of 'opportunities' to lose along the way) is better, as is being seeded into a later round and having a multi-game final round. The table below shows the impact of these various features.


CJK Tournaments
Below is the list of current tournaments in Japan, Korea, and China per Go News. I have indicated the probability of a repeat winner in my model world beside each one. I have also indicated a "model" that can be traced back to the earlier table. The real take away for me is the huge differences in the probability column for Japan versus Korea and China. Of course most of us were already aware of the fundamental differences in the tournament structures. However, in my case at least, I was not aware of the impact that it would have. It will definitely be one factor in how the Go 'Scene' in each country appears to us fans.


Take Aways
It is an interesting question to me why we see the differences that we do between tournaments in Japan versus Korea and China. Why does Japan have so many challenge matches or alternatively why do Korea and China have so few? The average tournament in Japan is much older than that in Korea or China: Japan 35 years, Korea 17 years, China 10 years (based on the "Holding" column shown on Go News; and yes I know that I am an idiot for deleting the info from my little table! ). Can it be that modern fans within Korea and China prefer the rough and tumble of big knock outs? This would seem like the easiest explanation for what we see and the willingness of sponsors to support it (and also perhaps a big "Hmmm..." regarding the lack of popularity for Go in Japan?). Many of us outsiders looking in have a hard time keeping track of who is who as new winners keep popping up, but presumably local fans do not suffer from this problem to the same degree.

One last warning
All the numbers in my lists are based on a simple theoretical set of competitors. I am not claiming that Iyama has a 91% probability of winning the Kisei next year or that Wang Xi has a 13% probability of repeating in the CITIC Cup. However, I think the relationships between structures are likely to be reasonably appropriate for assessing the impact of choosing one structure over another. As always YMMV!

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

I think there is an interesting research topic related to this idea. There are lots of tournament formats, as we see, but as far as I know even the most basic question isn't answered: how likely is it that the best person wins? You could push a little further and apply some constraints: given that a tournament wants to have at most N rounds/matches, what structure is most likely to result in the best player winning?

Of course there are other objectives in creating a tournament structure, such as trying to create a sense of excitement and story, but I think it's premature to tackle that question before we can even answer the simple one.

Maybe next time I am procrastinating on my actual research I will take a stab at this

I think that a better question is, how likely is it that the winner is not the best player? Isn't the system healthier when there is not a concentration of prizes (and prize monies) in one player or a very few?

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I don't think so, but either way it would be nice to know. If it turns out a tournament format has more luck in it and people decide they like that better, fine.

I don't know whether they do or not, but I'm not sure that it's entirely down to what the fans want. Japanese go has long been based on sponsorship by newspaper companies happy with drip-feed results day by day. At the same time it has been the game of senior politicians who have close links with newspapers, and a feeling has developed that newspapers sponsoring go (and shogi) are somehow preserving Japanese culture - not much of a consideration now but an important one in the soul-searching period after losing the war. By and large it has therefore been a very paternalistic exercise, with fans given what they are given rather than what they want. So long as the number of go players out there is very large, and the quality of what is give is high, there's little incentive to change.

But in Korea, although the Japanese newspaper model was followed initially, the main driving force (especially since the economic crisis there of a decade ago) has been the wealth of digital information companies piggybacking on the new fantastic telecommunications infrastructure put in place. Such companies have no special interest in promoting traditional culture and no relevant political ties, but wanted to showcase their products, preferably on tv. Their tournament formats reflected that, of course, and so again the fans were really just being given what the sponsors wanted. But since this just happened to coincide with the emergence of Korean players as the world's best, the Korean fans had no complaints at all about what they were being given.

The situation in China is more similar to this than to the one in Japan, but political ties still count there and the companies cover a much wider range than telecommunications (tourism organisations are a big component). But getting on tv is still a priority and fans are not consulted too much. They can be vocal on the forums, and are sometimes heeded, but the wishes of the sponsors and the politicians are still the main drivers in determining what the fan gets.

There is also the question of what the players want. KOs perhaps spread the jam better, and it certainly seems to be the case that Korean and Chinese players have much more of Oliver Twist's audacity than Japanese players.

As to why the number of fans in Japan is shrinking, leaving aside the obvious questions "Is it?" (or are they hidden by the internet?) and "Is this not the same in Korea and China?" (probably), I suspect there's nothing that a new Japanese world champion wouldn't fix. The number of people taking up the expensive hobbies of cycling and rowing in Britain has zoomed since Britain's success in the Olympics, and I believe the same phenomenon happens with virtually every other sport and in every other country.

Thanks ez4u, very interesting. You may be interested in using this over Excel (which is horrible for this kind of work): http://www.numpy.org/ (Mathematica or Mathlab are arguably much better but they're not free )

I've been meaning to learn it, so I may do something along these lines perhaps.

When I was setting things up I couldn't help thinking that simulating tournaments and matches seemed ideally suited for a tool that handled recursion well. However, I don't know python well (I had a couple of introductory level courses once) and so went with what I understood.

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Either way we are back to needing an answer to that eternal question, "Who is the best player?" Who wants to kick off a new version of that thread?

_________________
Dave Sigaty
"Short-lived are both the praiser and the praised, and rememberer and the remembered..."
- Marcus Aurelius; Meditations, VIII 21

Yeah, this wouldn't require much Python experience though (unless you wanted a fancy GUI, I'm thinking of just outputting a text file with a table of results in it in CSV here). It's not a very CPU heavy task so you don't need to care about efficiency and you can do much more interesting win %'s using distributions and similar to mimic to some extent differing performance levels for various factors.

Just a though.

What we need is disagreement about who is the best player. So we can argue about it.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.