The Elo rating system is a method for calculating the relative skill levels of players in two-player games like chess. It was named after its creator, Arpad Elo, a Hungarian-born American physics professor and chess enthusiast. The system is based on the idea that a player's skill can be represented by a single number, called the Elo rating. The higher the rating, the better the player is.

Here's a simplified explanation of how the Elo rating is calculated:

1. Each player starts with an initial rating. In chess, a common starting point is 1200, but it may vary depending on the organization or platform.

2. When two players face each other, the system calculates the expected probability of winning for each player using their current ratings. The probability is calculated using a logistic function, specifically:

E(A) = 1 / (1 + 10^((R(B) - R(A)) / 400))

Where E(A) is the expected probability of winning for player A, R(A) is the rating of player A, and R(B) is the rating of player B.

1. After the game, the system updates each player's rating based on the outcome (win, loss, or draw) and the expected probability of winning. The rating change is determined using the formula:

ΔR(A) = K * (S(A) - E(A))

Where ΔR(A) is the change in rating for player A, K is a constant factor (typically between 10 and 40, depending on the player's rating and the specific implementation), S(A) is the actual result of the game for player A (1 for a win, 0.5 for a draw, and 0 for a loss), and E(A) is the expected probability of winning for player A.

1. The new rating for player A is calculated by adding the change in rating to the previous rating:

R'(A) = R(A) + ΔR(A)

This process is repeated for each game played, and the ratings are continuously updated to reflect the players' relative skill levels. The Elo rating system is widely used in various competitive games and sports, with some modifications to suit the specific context.

Yes, there has been some degree of Elo rating inflation in the 2000s, particularly in chess. Elo rating inflation refers to the phenomenon where the average rating of players in a rating pool increases over time without a corresponding increase in their actual skill levels. Several factors have been attributed to this inflation:

1. Increased access to resources: In the 2000s, there has been a surge in the availability of chess resources such as books, software, and online platforms. Players can study and practice more efficiently, leading to overall improvements in skill levels. As players improve, they may gain rating points from others, resulting in a gradual increase in the overall rating pool.

2. Growing player base: As chess has become more popular and accessible, the number of players participating in rated competitions has increased. New players usually enter the rating pool with lower ratings, and as they improve, they "inflate" the rating pool by taking points from established players.

3. Rating floors: Some chess organizations have implemented rating floors, which prevent a player's rating from dropping below a certain threshold. This can lead to an accumulation of rating points in the system, as players who would have lost points due to poor performances are instead protected by the rating floor.

4. Inclusion of lower-rated players: Many online chess platforms have broadened the range of players included in their rating systems, which can lead to higher-rated players gaining more points when playing against weaker opponents. This can also contribute to rating inflation.

5. Changes in the K-factor: The K-factor is a constant used in the Elo rating system to determine the weight of each game in updating a player's rating. Some chess organizations have made adjustments to the K-factor over time, which can impact rating inflation.

It's worth noting that the extent and impact of Elo rating inflation remain subjects of debate among experts. Some argue that the inflation is a natural consequence of an evolving and growing player base, while others believe it undermines the accuracy and value of the rating system.

Rating floors primarily affect lower-rated players, as they prevent their ratings from dropping below a certain threshold. However, these rating floors can have an indirect impact on the scores of Super Grandmasters as well.

When lower-rated players have their ratings artificially maintained by a rating floor, they are essentially "retaining" rating points that they would have otherwise lost. As these players continue to participate in competitions and face higher-rated opponents, they can pass these rating points along to the stronger players who defeat them. This can lead to an overall increase in the ratings of higher-rated players, including Super Grandmasters.

In this sense, rating floors can contribute to rating inflation throughout the entire rating pool. However, it's important to note that rating floors are just one of several factors that may contribute to rating inflation. The overall impact of rating floors on the scores of Super Grandmasters is likely to be relatively small compared to other factors, such as increased access to resources, changes in the K-factor, and the growth of the player base.