Order by fields after searching
Not really feasible without a plugin – fortunately, there's the excellent SuperSort:

{% set results =  craft.entries.section('player').search('team:"thenameoftheteam"') %}

{% set resultsByPlayerPosition = entries|supersort('sortAs', '{playerPosition}') %}
{% set resultsByPlayerHeight = entries|supersort('sortAs', '{playerHeight}') %}
{% set resultsByPlayerBirth = entries|supersort('sortAs', '{playerBirth}') %}


If you need the sorted results in the opposite order, you can just apply the |reverse filter, i.e. 

{% set resultsByPlayerHeight = entries|supersort('sortAs', '{playerHeight}')|reverse %}


If e.g. playerPosition is a relational field (a category, perhaps), you'll need to do something like this:

{% set resultsByPlayerPosition = entries|supersort('sortAs', '{{ playerPosition.first.title }}') %}