What Is the K-factor in the Elo Rating Formula?

Arpad Elo designed his rating system back in the 1960’s (possibly late 1950’s). His system replaced the Harkness rating system because the Harkness system exhibited some serious flaws.

This k-factor resides in front of a difference in the formula. Rather than using cryptic English language, I shall be precise: K*(S — E). The K being in this position acts as an amplifier or a dampener. Elo intended for it to be a variable to adjust it for different circumstances. For youth who could improve rapidly, he wanted K to be larger to boost up their ratings faster. For established ratings, he wanted K to be smaller so that it could track any changes but be more stable while doing it.

I had a debate with FIDE some years ago about the k-factor. I was told that k=40 for youth was correct after I told FIDE that that was a mistake. I was told that many statisticians and ratings experts met and debated for several months about the youth k-factor. After all that discussion, they had concluded that k=40 was correct. I told them it was not correct. I cited that I had done a tournament of teen players, and their was a lot of dispersion in the ratings. I told FIDE that was due to the k=40 factor. I was told, no it was because teenagers have streaky play. Unless I could prove that k=40 was a mistake, then that would end the matter there.

So, what was I to do? How could I prove k=40 was a mistake?

Well, I came up with an idea. I would search for tournaments with only teenagers in it that had a mix of above 2300 and below 2300 players. You see, that is FIDE’s cutoff for turning a youth player’s k-factor from 40 to 10. With such a mixture of players who were all teenagers, I had hoped to find that the k=40 group within that tournament had a greater dispersion in the ratings than the k=10 group.

I found such a tournament, and I processed it with my rating system. I have a book published on Amazon with my rating system in it. It is called The Performance Rating Algorithm and Tournament App: A Faster Algorithm than the Elo Rating System (PRA Theory and Use). The listing page for it on Amazon is here: https://www.amazon.com/gp/product/1099627923/ref=dbs_a_def_rwt_bibl_vppi_i1

So, what did I find? I found that the dispersion in the ratings of the below 2300 group was significantly higher than the above 2300 group. This was exactly what I had hoped to find. But, I didn’t share this with FIDE. Not yet anyway. I found another such tournament with a mixture of players in it. I found the same result in this second tournament. I did this two more times for a total of four major youth tournaments, and the same thing happened all four times. The ratings dispersion was higher in the k = 40 group than the k = 10 group every time.

So, now with four full tournaments that I found and processed, I discussed these matters with FIDE. The Federation president I was communicating with was so impressed that he put together a hiring package for me. But, Makropoulos (the president of all of FIDE at the time) shot down my hiring. That was too bad, because FIDE could have benefited from my powerful rating system.

Some things can be said about these four tournaments. The first and foremost is that these boys were honestly battling it out to their abilities. If they were cheating or sandbagging, I would not have been able to detect what was going on. If they were streaky players as was claimed by FIDE, then I also would not have been able to get a bead on what was going on. So, I applaud these youthful warriors of the mind.

Next, my rating system must be pretty powerful to be able to detect that k=40 was a mistake. How many rating systems can check up on other rating systems? Well, mine can do this. Incidentally, I have found that Elo is actually a bit better than Chessmetrics, contrary to the claim that it is an “improved” system over Elo. But, I have processed many historical tournaments using Chessmetrics as a starting point and corrected mistakes and omissions by it — just as I have done with the Elo rating system. This is why I say Elo is better than Chessmetrics — from my perspective, Elo seems to have fewer errors that I have to fix to get to the bottom of a historical tournament than Chessmetrics.

In computer science, we learn to optimize an algorithm. What does this mean? It means we tweak it until we get it to go as fast as it can. This kind of thing applies to the Elo system. Where Elo has his K-factor, there is some value of K that optimizes his algorithm. My Basic system is kind of like Elo’s system, and where Elo’s K-factor is, I have found that my Basic system optimizes at a 9.0. This value provides the fastest convergence of the population of ratings while introducing the least amount of dispersion. There exists some value of K in the Elo rating system that optimizes his rating system as well.

In Elo’s system, he has it set to 10 for established ratings. This is not far from the 9.0 I found for my system. Is K = 10 correct? Probably not. But, it is close enough that it works well enough. If FIDE wanted to find the optimized and correct value of K, they could up it to say 12 and do what I did with those four youth tournaments and measure the dispersion after leaving it at that value for several months. Then, lower K to maybe 8 and measure the dispersion after it being there for maybe 2 to 3 months. If there’s equal dispersion then K is somewhere between 12 and 8. If K = 8 shows less dispersion than either K = 10 or K = 12, then it looks like K should be lower than 8. One would have to run such an analysis to find out what K should be. But, it most certainly should not be 40, and someone posted on facebook that FIDE has set K back to 40 for youth.

Shortly after my debates with FIDE, they got rid of K = 40, which I took to be an admission that I was right (and the statisticians and ratings experts were wrong). But, FIDE has reset K to 40 again, which is still a mistake. FIDE paid those people to have those meetings on what K should be, and they were wrong. I was right, and FIDE didn’t pay me a cent or even acknowledge me.

Thus, Elo’s assumption that K is a variable is incorrect. K should be a fixed value, and this is a mistake that Elo made in his rating system.