Lately, I am examining a new statistic concept or issue in which I can trust to better accuracy not only about my analysis, but also about determining the possible cheater conduct of one player. It is not one tool which I realized it works not only to analyze cheaters factors, it is a tool which may help me to better accuracy of my analysis and can also helps me in this way.

Probably in following articles I will write more about this. But for now I can share a range of results about my mistakes in the last month. In the first column we have my Elo, and the second column, which is what matters now, we can see my mistakes in that game. The following columns are the result in the game. First of all, we can see games in which I made 6 mistakes or less and I lost. This means that I play versus very good players.

Second, what I am trying to explain. If we take into account the numbers in the red circle: 8,6,8,9,9,4,7,10,7,7 and 6. This sequence, is the sequence of my mistakes in these games. The most usual, should be take all serie, but if for example we analyze these numbers, we can obtain the standard deviation through the formula we have in Excel. The standard deviation is the variance squared to 0,5.

The result if I am not mistaken, it is 1,69. This should mean that I can deviate from the mean around +-1,69 points. This is not true at all if we can see that I made since 4 till 10 mistakes, but helps us to understand some matters about our precision game. To better adjustment, I should take all series. Right now I am ready to post some conclusion, at first glance, about that.

1-If we need to judge about if one player is a cheater, we should take too many games about him. At most games we have, better conclusion we can draw. In the same way as the mistakes. Because one practically perfect game of him, may indicate luck or even better concentration in that game. Likewise, may indicate a good opening game. Other players may take (pen-written) notes about one opening, (magics about online game in which we cannot see our opponent). But as we cannot analyze a hundred games of our opponent, we should be ready to judge only 3 or 4 games about him, in the same way I did with the tables in which we try to sort our rival according to one or two single games, in a very biased way.

2-According to logics or simply a huge data of games analyzed about my own games played.. I am not ready to analyze hundreds of rival's games. But, in fact, I have been analyzed hundreds of my own games. So I can draw some conclusions about that. This means that the larger is the number of mistakes we make in one single game, the larger would be the standard deviation number we will obtain. For example: One player which make 10 mistakes in mean, can make 6 mistakes in the following game, or even 15 mistakes. But one player which make 5 mistakes in mean, can make 3 mistakes in the following game, or even 7 mistakes.** This means: The standard deviation should be larger for novice players, or for players who make more mistakes in one game.**

**Conclusions:**

When I made 10 mistakes as a mean, I had an Standard Deviation of +-3,6 points. Right now, my standard deviation it is around +-1,8 points, according to my mean of 7,5 mistakes per game. This means that one player which made a mean of 5 or 4 mistakes, should be one Standard Deviation of +-1 point. And the best player of the world should have an Stantard Deviation lower, according that they made around 2 to 3 mistakes, should be understandable. The best players of the world often made the same number of mistakes, 2 or 3. (Although the difference between the top 100 best players of the world is best explained for the fact that the top 10 best players, lose less points per mistake than the other, holding the same number of mistakes in each case. This could be a good topic about discussion and analysis in the future).

According to Tamenori, the best known player who play in Playok and which ranking is higher, in the World Othello Federation Ranking list, he has 2427 points of Elo, but in Playok.com he has only 2170 at the time in which I am writing this (july 2016). 257 points less than his official score. Why? Why practically all people in Playok.com has less Elo score, than the score we can see in official ranking? unfortunately, in Playok.com exist too many cheaters who impairs his score, and this applies for all players in this room. Seeley has in Playok.com 1983 points and his official score it is 2327; 344 of difference. (Probably best fitted to Tamenori, due to better selection of his rivals in Playok.com, according to his games). A mean of +250 points correction to our own score in Playok.com should be warranted, in order to be able to judge our score. So, when we analyze according to my table, we should add 250 points to each Elo in each player we analyze with my table. You can ask me why I do not update. In fact, my table try to explain the "real factor", this means, the real mistakes according to one real Elo, not the Playok.com games. The table is based in Playok.com games, but was made with intent to work for real games. (I made according to Playok.com because I have not many games in other site).

So, in my opinion, I do not like to update the full table only because exist cheaters who impairs the score of all people in Playok.com. I think that it s most fair that when we go to table, simply add +250 points to our Elo rival. For example, if our rival has 1450 points of Elo and he made 6 mistakes. We can go to table and add +250 points, this means, he should have 1700 points of Elo, and the table, will allocate him a likelihood of 40% of do 6 mistakes, rather than 20% which would be in case of 1450 points.

Anyway, I posted a mean of mistakes which make Playok.com players according to their Elo. I added a column in which we can also see the mean of their points lost. Finding the real numbers implies working with a sample of more than thousand games and finding a complementary Wzebra software which for now I think that does not exist. In any case, the numbers should exist.