Woods attended West Monroe High School where he played at wide receiver as a freshman. He moved to defensive back as a sophomore and intercepted 6 passes, including 2 returned for touchdowns. He helped his team win a football state championship in his junior year, posting 43 tackles, 5 interceptions, 6 receptions for 233 yards and 2 punt returns for 60 yards. In his last year, he received All-state, All-Northeast Louisiana and All-district honors. He also practiced basketball.
College career
Woods accepted a football scholarship from Louisiana Tech University. He started 10 games out of 12 as a true freshman at free safety, tallying 61 tackles and 2 passes defensed. The next year, he posted 71 tackles, 7 passes defensed and 3 forced fumbles. He also had 6 interceptions, including one returned for a touchdown in a win over the University of Illinois in the 2014 Heart of Dallas Bowl. As a junior he took a step back, recording 56 tackles, 3 interceptions and 3 passes defensed. As a senior, he registered 89 tackles, 5 interceptions and 6 passes defensed. He left after starting all but two games, making 181 tackles, 14 interceptions, 18 passes defensed, 4 sacks, 6 forced fumbles, and 325 interception return yards.
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Professional career
Woods was one of 60 defensive backs invited to the NFL Scouting Combine in Indianapolis, Indiana. He performed all of the combine and positional drills, finishing seventh among safeties in the 40-yard dash. Woods also tied for second in the three-cone drill, tied for third among his position group in the bench press, and sixth in the broad jump. On March 23, 2017, he participated at Louisiana Tech's pro day, along with Carlos Henderson, Trent Taylor, and 12 other prospects. Woods beat his times at the combine in the 40-yard dash, 20-yard dash, and 10-yard dash while also performing positional drills for scouts and team representatives from all 32 NFL teams. At the conclusion of the pre-draft process, Woods was projected by NFL draft experts and scouts to be selected anywhere from the fourth to sixth rounds. He was ranked as the seventh best strong safety in the draft by NFLDraftScout.com. The Dallas Cowboys selected Woods in the sixth round of the 2017 NFL Draft. On May 11, he was signed to a four-year, $2.55 million contract that includes a signing bonus of $159,888. Throughout training camp, Woods competed for a roster spot against Robert Blanton, Kavon Frazier, and Jameill Showers. Head coach Jason Garrett named him the backup free safety to Byron Jones to begin the regular season. He made his professional regular season debut in the Dallas Cowboys' season-opening 19-3 victory over the New York Giants. On September 25, Woods recorded three solo tackles and deflected a pass in the Cowboys' 28-17 victory at the Arizona Cardinals. He recorded his first career tackle on the opening kickoff on Cardinals' running backKerwynn Williams after a 21-yard kick return. On November 12, he collected four combined tackles, defended a pass, and made his first career interception off a deflected pass from Atlanta Falcons'quarterbackMatt Ryan during a 27-7 loss. The following week, Woods earned his first career start at strong safety after Jeff Heath suffered a concussion the previous week against the Falcons. He recorded five combined tackles as the Cowboys were routed by the Philadelphia Eagles 37-9. In Week 11, Woods earned the starting strong safety job and recorded three combined tackles during a 38-14 win against the Washington Redskins. Because of injuries to other players he was moved between safety and slot cornerback during the season, and although he had some problems tackling, he finished with 41 tackles and one interception. In Week 9 of the 2019 season, Woods recorded an interception and a forced fumble in a 37-18 win over the New York Giants, earning him NFC Defensive Player of the Week.