Sort values in two column and insert order position into another column in mysql

Question

I have a database about sports event that contains:
*User ID
*Amount of Points that the user got on that event
*Time (HH:MM:SS) that took the user to complete track.

How can I first sort them by no. of points, then if two users have same amount of points, by time (shorter is better); and then insert the places to rows?

I have database like that:

ID    No. of Points   Time     Place
------------------------------------
1        15          00:56:00
2        13          00:55:15
3        17          01:00:00
4        17          00:57:00
5        19          00:52:15

I need to have it with places:

ID    No. of Points   Time     Place
------------------------------------
1        15          00:56:00   4
2        13          00:55:15   5
3        17          01:00:00   3
4        17          00:57:00   2
5        19          00:52:15   1

I hope, you understand that. Sorry for bad English.

Best regards,

Answer 1

You can do this with update statement as follows. 

SET @placeValue:=0;

UPDATE [Table Name] SET Place=@placeValue:=@placeValue+1 ORDER BY 
[Amount of Points] DESC,Time ASC