In the database there are 12012 games with 7.5 komi, 19151 games with 6.5 komi. Black player won 47.977% of the games with 7.5 komi, compared with 50.713% when komi was 6.5. Assuming an exponential curve, we can get the following two equations.

0.5^(1 + ( 7.5-x) * y) = 0.4799
0.5^(1 + ( x- 6.5 ) * y) = ( 1 - 0.50713 )

where x is ideal komi, and y is multiplier per point. solving the equations we end up with ideal komi of 6.75929 and multiplier per point of 0.0799152.

Since komi is compensation for half a move. a full move is worth twice that of komi. Meaning, one handicap stone is worth 13.51858 points.

As an example, based on these results the odds of winning an even game against someone 3 stones stronger would be 5.2%, as per 0.5^( 1 + 3 * 13.51858 * 0.0799152 ) = 0.052...

Database with 37380 professional go games.

Prediction performance for elo ranking algorithm (with optimal K), not including first 1/3 of the professional games (which is used exclusively as training data), is 58.0221% when using logistic curve as is the prevailing choice in modern elo implementations. However when using exponential curve the prediction performance increases to 58.0494%. This effectively implies that professional games outcome are based more on the cumulative quality of their moves, and and less on outside factors (than the use of logistic curve would imply).

In the database there are 12012 games with 7.5 komi, 19151 games with 6.5 komi. Black player won 47.977% of the games with 7.5 komi, compared with 50.713% when komi was 6.5. Assuming an exponential curve, we can get the following two equations.

0.5^(1 + ( 7.5-x) * y) = 0.4799
0.5^(1 + ( x- 6.5 ) * y) = ( 1 - 0.50713 )

where x is ideal komi, and y is multiplier per point. solving the equations we end up with ideal komi of 6.75929 and multiplier per point of 0.0799152.

Since komi is compensation for half a move. a full move is worth twice that of komi. Meaning, one handicap stone is worth 13.51858 points.

As an example, based on these results the odds of winning an even game against someone 3 stones stronger would be 5.2%, as per 0.5^( 1 + 3 * 13.51858 * 0.0799152 ) = 0.052...

What does the expression "...not including first 1/3 of the professional games (which is used exclusively as training data)..." mean? Did you segregate your database into two parts based on the dates the games were played or did you randomly select 1/3 for training data? If you used dates, do you get the same result if you choose the oldest 1/3 games as your training data? I would expect this to be the case if no adjustment to the 6.5 komi occurred among professionals. However, I know from studying fuseki trends that around 2002-2003 no major fuseki system for Black won over 50% as (apparently) the pros had not worked out how to play against the increase komi.

A quick and dirty look at even games with 6.5 komi in my database gives the following results by time period:

Yes, I use first 1/3 of the games by date as training data. My intention is to exclude the high variance scenario where lots of new players are introduced into the system and everyones ranks are unreliable.



This fluctuation is probably mostly due to variance from much smaller sample size. Tho just to make sure, Ill run it again, using only more recent pro games.

When we go over professional go games and winning percentages, how do we account for the fact that all pros aren't actually within one stone of each other? Do you only count same dan against same dan? And even then, strengths wax and wane while the dan rank never goes down.

I don't understand this. Are you saying ideal komi is 6.75929 (based on this calculation)? What does multiplier per point mean?

Its a measure of how much chances of winning decrease for each point of komi opponent gets. Using the formula 0.5^(1 + ( opponents_komi - ideal_komi ) * multiplier_per_point) = odds of winning (when opponents_komi > ideal_komi ). So the higher the multiplier the more playing say without komi favors black.

So that's the multiplier.
But don't you think 6.75 komi is, to put it blatantly, a bit of a nonsense?

His result doesn't tell us we should set komi at 6.75; it tells us that 6.5 is not quite enough and 7.5 is a bit too much. We have to translate the continuous value the equations calculate to the .5 increments used for real komi.

So what's the point of the exponential model, or the significance of the value of 6.75?

It sounds like the exponential model was chosen as a nod to other ranking systems. I suppose knowing the "real" value of a continuous Komi might be interesting in some situations (e.g. Predicting the value of each handicap stone in high level games could be used to select an appropriate reverse komi), but I think this is mostly an exercise undertaken because math is fun.

You don't mention your sample sizes, but it looks like you've got a huge case of false precision going on. Unless you specifically give error bars, you should only give the number of significant figures that is warranted by the data, and I think it is unlikely that your data is accurate to within 0.01%