How much does stress affect sports-related performance, and why???

There’s an old saying in sports, “keep a cool head, and all will come your way”. Is it true?

I realise that different people are affected in different ways by stress (and therefore some cope better, and may even do better under stressful conditions), but is it generally true that the more calmer (for lack of a better word - I think “cool” desribes it better) you are, the better your overall performance in a game? Are there any studies that have been done on this subject, and if so, what were their findings?

Tied to this is the phenomenon of “choking”. Basically this is when you lose it (both your concentration and cool i.e. nerves get the better of you). But are there any sports athletes that have been studied (or studies that show people) who actually perform better under these types of conditions?

To recap: Do lower stress levels actually help an athletes performance? If so, why?
And what causes people to react so differently under pressure?

PS: As an aside, have there been any athletes that physically (and mentally, though I guess this ones harder to measure) show phenomenal resilience to stress, or are basically “extremely cool” under pressure?

Cortisol is what you want to know about. It’s a hormone the body produces in response to stress, and it has a negative impact on pretty much anything you’re interested in.