On March 22 [1972], Ishida Yoshio began his defense of his Asahi Pro Best Ten title [against] the challenger, Iwata Tatsuaki 9d … Rin Kaihō diplomatically and prudently suggested that in his experience, the winner of the first game [of the match] usually won.

So, how good a predictor is the result of the first game?

For this study, I’m going to use all the game-by-game results of the “Big Three” title matches that are available on Go to Everyone.

These are:

the 31st to 46th Kisei

the 31st to 46th Meijin

the 61st to 76th Honinbo

Match

Prediction correct?

31 K

Y

32 K

Y

33 K

Y

34 K

Y

35 K

N (5 matches)

36 K

N

37 K

Y

38 K

Y

39 K

Y

40 K

Y (10 matches)

41 K

N

42 K

Y

43 K

Y

44 K

Y

45 K

Y (15 matches)

46 K

Y

31 M

Y

32 M

N

33 M

N

34 M

N (20 matches)

35 M

Y

36 M

Y

37 M

Y

38 M

N

39 M

Y (25 matches)

40 M

Y

41 M

Y

42 M

N

43 M

N

44 M

N (30 matches)

45 M

Y

46 M

Y

61 H

Y

62 H

Y

63 H

N (35 matches)

64 H

Y

65 H

N

66 H

Y

67 H

Y

68 H

Y (40 matches)

69 H

Y

70 H

Y

71 H

N

72 H

Y

73 H

N (45 matches)

74 H

N

75 H

Y

76 H

Y

Total matches: 48
Predictions correct: 33
% Predictions correct: 69%

Do all of these matches have the same number of games?

It would be interesting to compare with what we would expect to see if each individual game was a coin flip. Even then, the “first game”-prediction will do better than 50%, but the actual number (69%) will be higher than this baseline due to the differing strengths/current forms of the players and also maybe some psychology.

By the way, if they stop playing as soon as the winner is decided, I believe the winner of the last game should be a pretty good “predictor”

Just using a binomial distribution considering the games to be coinflips, being one game ahead gives you an advantage of 75% if its best-of-3, and that should converge down to 50% for best-of-n with increasing n.

So it is always a pretty significant advantage, even if the games are a coinflip. Would be interesting to see how long the series for those title matches were, as I don’t know that. We should expect the actual predictive power of the first game’s result to be a bit higher, since more often than not, the winner of the first game should be the somewhat stronger player.

Thank you, I was just waiting for confirmation on the number of games before doing the math myself, but once again my lazyness has saved me from doing any work

I think (looking at Go News - Go to Everyone!) these are all 7-game matches? In which case the numbers we’re comparing are 65,625% vs 69%. Seems about right.

Now, suppose you are making independent flips of a biased coin (likelihood of heads is greater than 50%). How does that change the likelihood that the first flip matches the mode of a series of N (an odd number) flips.

I wonder if that’s a statistically significant difference, to suggest that these are being win by a definitively stronger player.

Another interesting way to arrange a series, instead of simply setting a fixed “best of N” match, would be to say that the series continues until statistically significant evidence has been gathered that indicates that the better team is ahead.

In that case we would have to argue what our significance bound is. For p=0.05 we might have to play a lot of go: If our null-hypothesis is that both players are equally strong, the only significant result of a 7-game series would be if either player sweeps all seven games.

Also, from a spectator’s perspective, I think this is not the best idea. Assume Ke Jie and Shin Jinseo are playing. It is well established, that the latter is currently somewhat stronger. Wouldn’t it be incredibly dull to have them play until inevitably statistics takes over and gives Shin Jinseo the upper hand, practically eliminating the chance of an upset?
I do see how there can be made a case for that being ‘fairer’, as the actual best player wins, but it makes for a bad sporting event.

If those were all 7-game series, they consisted of at least 4 matches. In hindsight, how do the predictive powers of games 2-4 compare to the first game (independent of previous games’ results that is)?

No, 65,625% vs 69% is not statistically significant.

An easy to remember extremely rough rule of thumb is that the (two standard deviation, i.e. p ~= 0.05) margin of error on N win/loss events is somewhere around sqrt(N). This works okay so long as the chance on each event isn’t too far from 50%.

For example if we had 100 matches, then the margin of error would be sqrt(100) = 10 matches, or 10%.

Or, if we had 400 matches, then the margin of error would be sqrt(400) = 20, or 5%.

Given that we only have 48 matches, and we’re talking about a percentage difference even smaller than that, it is plain to see even without any further calculations that this isn’t even close to statistically significant.