Get related entry data within a plugin (ElementCriteriaModel) without extra queries
I fixed this now by using the method buildElementsQuery, like so:

    $query = craft()-&gt;elements-&gt;buildElementsQuery($criteria, $contentTable, $fieldColumns);


After that, I was able to add custom joins to the query:

$query
    -&gt;addSelect('sport.title sportTitle')
    -&gt;leftJoin('relations sportRelation', 'sportRelation.sourceId = elements.id AND sportRelation.fieldId = 71')
    -&gt;leftJoin('content sport', 'sport.elementId = sportRelation.targetId')


This gave me access to the data I need, without running extra queries. Thanks go out to Bob Olde Hampsink for showing me this.

I'd love to hear though if there is a simpler way that won't require custom SQL, but for now this will do the trick.