There is a record whose value is expressed by a natural number. (The value is strictly discrete, not only continuous and then rounded to a natural number.) However, after the record is once established, any other person to topple the previous record-holder will break it by at least 2. The value of the record can be expressed by both odd and even numbers.
For instance, if the current score is 505, the next record-holder's score may be 507, 508, 509, etc., but it may not be 506.
What record is this?