When I played in tournaments, at the start of a game, my opponent would ask my rating. I knew he was forming an opinion about my playing strength based on my rating. But performance and strength are two different things. If rating determined the outcome of the game then no player rated higher than his opponent would ever lose.
At the chess club I hear comments by wood pushers that told me they sized up a player's strength by their rating. This is a faulty way to approach such an assessment. A chess players performance can be reduced by several factors. A divorce, job change or a move are considered the highest three sources of stress. I am a chronic pain patient and I know my performance ability is dramatically affected by pain.
An example is former World Champion Mikhail Tal (RUS). He was a brilliant player and he could beat anyone in the world on one of his good days. But he suffered kidney problems for years that eventually culminated in his death. Obviously this illness caused his tournament performance to suffer. When Tal's FIDE rating dropped below the top 10 in the world, did that mean he was not a dangerous player anymore?
On days when he felt good, his chess genius was capable of destroying any opponent. A few years before his death, he won the World Blitz Championship! In that tournament Gary Kasparov was eliminated.
Next time you are paired in a tournament, your opponent may not be at his best. Play each round and ignore your opponents ratings.
Especially if your opponent is a stranger and you don't know your history. Remember ratings are a reflection of past performance. I once played an A class opponent who usually defeated his opponents before the endgame. My game with him did go into the end game and the position ended up with his having a rook pawn and of course we each had our kings. I knew that if I could get my King in front of his pawn the game was a draw. To my surprise he let that happen and then spent a very long time thinking on a position that was a book draw. The longer he thought, the larger the crowd grew around our table. The crowd was confused as to why the game continued. Finally, my opponent offered a draw and indicated he had not studied basic endgame positions.
This is another example of performance strength diminishing based on no other factors except a lack of knowledge of endgames. So the rating assessment based on prior performance is not so simple as a rating from past performance. I understand Apraid Elo's statistical formula anf all things being equal it is accurate. But it does not include certain other factors. That is why it is a performance rating.