🕸📝Fergus Duniho wrote on Fri, Apr 27, 2018 10:02 PM UTC:
Yes, it would change a lot. 100 draws is mathematically equivalent to each of us winning 50 games against the other. As an experiment, I wrote a modified script that added 100 extra draws between us. My rating dropped from 1715 to 1675, your rating rose from 1477 to 1494, and many other ratings changed by smaller amounts.
Here is what is going on. First, it made our scores against each other more even, so that the maximum change to our ratings from our games together would be less than what it actually is. However, the greater number of games between us would also increase the portion of the maximum change that would actually be made to our ratings. The bottomline is that this caused us to come out with different ratings when our games factored into the calculation, and this continued to have an effect on every subsequent pair of opponents that included one of us. Since ratings are calculated twice, the second time being in the reverse order of the first time, this affected calculations for every opponent either one of us had. As it affected the ratings of other opponents, it affected the ratings calculated from comparing pairs of opponents that did not include either of us. So, the changes this had for our ratings had a chaotic butterfly effect on the ratings of many other players.
Besides this, it added to the number of games we each played, which made our ratings more stable than they would otherwise be. This also affected the calculation of our ratings with other opponents, and this too had a chaotic butterfly effect through the whole network that includes both of us. This is the yellow colored network, which includes most people who have played on Game Courier. The ratings for people in other networks were unaffected.
Yes, it would change a lot. 100 draws is mathematically equivalent to each of us winning 50 games against the other. As an experiment, I wrote a modified script that added 100 extra draws between us. My rating dropped from 1715 to 1675, your rating rose from 1477 to 1494, and many other ratings changed by smaller amounts.
Here is what is going on. First, it made our scores against each other more even, so that the maximum change to our ratings from our games together would be less than what it actually is. However, the greater number of games between us would also increase the portion of the maximum change that would actually be made to our ratings. The bottomline is that this caused us to come out with different ratings when our games factored into the calculation, and this continued to have an effect on every subsequent pair of opponents that included one of us. Since ratings are calculated twice, the second time being in the reverse order of the first time, this affected calculations for every opponent either one of us had. As it affected the ratings of other opponents, it affected the ratings calculated from comparing pairs of opponents that did not include either of us. So, the changes this had for our ratings had a chaotic butterfly effect on the ratings of many other players.
Besides this, it added to the number of games we each played, which made our ratings more stable than they would otherwise be. This also affected the calculation of our ratings with other opponents, and this too had a chaotic butterfly effect through the whole network that includes both of us. This is the yellow colored network, which includes most people who have played on Game Courier. The ratings for people in other networks were unaffected.