Disagree totally castrolgtx. Sports days should only be competitive if children are allowed some say over whether/what they compete in. Even if say everyone has to be in at least one race, but keen/sporty children can be in as many as they want.
At our school sporting achievement, effort and success is rewarded all the time. Those in school teams are praised and get certificates, as well as writing reports on matches for newsletters etc. They sometimes get photos in the local paper etc.
Would you be as keen if all children were FORCED to take part in a music or maths or spelling or whatever competition, with parents and other sundry adults invited to watch this? My kids would have loved some of the above, but I wouldn't force anyone else to do them. Instead, we have concerts and other events for musical children to take part in - as well as those who frankly aren't that musical but love to have a go, and that's great. The key thing is choice.
Our sports days are non-competitive in the sense that they are team games with different activities and children moving around the field, but the competitive element is that points are awarded and the 4 school house teams compete for a cup. And believe me, they do think that matters!
I've had this debate numerous times in recent years, so out of interest I've asked my mum and others of her generation and even earlier generations, and they were almost unanimous in all hating sports days, both when they were at school and as parents. So I don't think the old-style ones were all they are now cracked up to be.