Database design event timing

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MySQL

Goodnight,

I tell you what I have in mind and I would need the vision of more people to design/organize the database in the best possible way.

As a first note, I need a database to control the times of the participants during an event which can be divided into several days.

Starting from that first note, the minimum tables I would need:

EVENTS (id, name, start_date, end_date, location..........)
STAGE (id, id_event, name, date..............)
PARTICIPANTS (id, name, surname.....)
PARTICIPANT_EVENT (id, id_participant, id_event)
CATEGORIES (id, name..........)
PARTICIPANTS_CATEGORIES (id_participant_event, id_category)
TIMES (id_event_participant, stage_id, start_time, end_time)
PENALTIES (i_:participant_event, time)

I plan to do something like this with the tables, although if you see any improvement correction to be made, I would appreciate it if you told me.

All this will be to exploit it with PHP, what interests me is:
- A classification per day event (this has no major problem)
- If it consists of several stages, on the second stage and later see if it has advanced or not some position of the classification of the previous day (to do this I do not know what would be the best way to do it, I would need a little help)
- A history per participant of all the events where he has taken part and his position in that event (I don't know how to guide him either quite well to be able to do it)

Any help, recommendation will be welcome.

Thank you :)

What I have tried:

I am in full analysis of how to do what is described