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Hetmyer has withdrawn for personal reasons while Paul is out because of an injury, and Motie has failed to recover from the hand injury he sustained while playing against India last month.
The three games are West Indies' last of the Super League. They are currently in sixth position with 80 points, having won eight and lost 13 of their 21 fixtures so far. Depending on how many points they take from this series there is a chance they could slip out of the top eight - direct-qualification positions - for next year's World Cup, to be played in India.
"The pressure has been on from the beginning to try and win cricket games but this team has been together for a while now," captain Nicholas Pooran said. "We knew that this series was for points. The pressure, I don't think we are looking at it from that perspective, in terms of we have to win and must get points. The guys know what's at stake here and we know what we have to do to be successful."
Jermaine Blackwood, who played his only two previous ODIs back in 2015, and uncapped legspin-bowling allrounder Yannic Cariah have been called into the squad for the three games in Barbados, with Odean Smith travelling as a reserve. Cariah, 30, was recently a part of the West Indies A side that played two four-day games against Bangladesh A.
"Hetmyer has to attend to a family matter in Guyana. Unfortunately, Motie is not yet able to rejoin the squad and Keemo is struggling with an injury," West Indies' lead selector Desmond Haynes said. "However, it provides an opportunity for Yannic Cariah to get a chance. He is someone that has been performing well on the regional circuit and we feel now is the right time to integrate him into the senior team set-up."
Kevin Sinclair, the offspinner who is uncapped in ODIs, is also a new face in the squad. Roston Chase had earlier been ruled out through injury and Fabian Allen for personal reasons.
"We are looking to broaden the pool of players and we have decided to give Sinclair an opportunity," Haynes said. "He has been in the system for a while and was also in the A team to play against Bangladesh A in the upcoming series. We believe with his calm approach and skills he will do well in the matches against New Zealand."
West Indies ODI squad: Nicholas Pooran (capt), Shai Hope, Jermaine Blackwood, Shamarh Brooks, Yannic Cariah, Keacy Carty, Jason Holder, Akeal Hosein, Alzarri Joseph, Brandon King, Kyle Mayers, Jayden Seales, Kevin Sinclair.