13 personnel means that there is one running back, three tight ends, and one receiver. 13 personnel is typically a run-heavy grouping and forces the defense to match with larger personnel themselves. Having three tight ends can help overload one side of the formation, add extra gaps to defend, and challenge the defense to guard bigger bodies in the pass game. With such a heavy run emphasis out of this grouping, defenses often stack the box and leave the single receiver in man coverage. That can give the offense options to create matchups outside if they feel like they have a receiver that can win vertically.
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Most teams run out of this personnel grouping, but coordinators will also counter by running play-action and exploiting the defenses’ over-commitment to the run. Often, teams don’t have three tight ends that they feel are strong plus’ in both run blocking and pass catching, so the grouping isn’t seen very often. However, it has great utility in setting the strength of the defense and creating a predictable look to run plays against.