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The chess one isnt quite right. There’s been experiments where if a woman player didn’t know her opponent was a man she would perform better. It’s called stereotype threat phenomenon.
It also happens when a male player knowingly goes up against someone higher in the league than himself and he performs below his own standard average.
Basically people in general psyche themselves out of their best performance when going against someone they perceive to be better than them whether that’s factual or not. Confidence and undermining confidence can change a whole lot about how a person does in any given game or task.
It’s a phenomenon that’s been observed across multiple sports, not just between men and women chess players. It’s particularly poignant in men vs women’s chess… because of people repeatedly telling women they are inherently worse than men. Like you are doing right now.
There’s been multiple studies on this. So yes, I side with the data that stereotype threat phenomenon has a significant impact on women’s performance in chess against men.