On December 13, 2023, the Boston Red Sox signed Criswell to a one year, $1 million contract.

Trophies 
Milestones
Former Youth Teams 
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| SO/BB | MLB | 2025 | 1.80 |
| SO9 | MLB | 2025 | 4.6 |
| BB9 | MLB | 2025 | 2.5 |
| HR9 | MLB | 2025 | 1.5 |
| H9 | MLB | 2025 | 11.7 |
| WHIP | MLB | 2025 | 1.585 |
| Fielding Independent Pitching | MLB | 2025 | 5.17 |
| ERA+ | MLB | 2025 | 117 |
| Batters Faced | MLB | 2025 | 80 |
| Wild Pitches | MLB | 2025 | 0 |
| Balks | MLB | 2025 | 0 |
| Times Hit by a Pitch | MLB | 2025 | 0 |
| Strikeouts | MLB | 2025 | 9 |
| Intentional Bases on Balls | MLB | 2025 | 0 |
| Bases on Balls/Walks | MLB | 2025 | 5 |
| Home Runs Allowed | MLB | 2025 | 3 |
| Earned Runs Allowed | MLB | 2025 | 7 |
| Runs Allowed | MLB | 2025 | 10 |
| Hits Allowed | MLB | 2025 | 23 |
| Innings Pitched | MLB | 2025 | 17.2 |
| Saves | MLB | 2025 | 1 |
| Shutouts | MLB | 2025 | 0 |
| Complete Games | MLB | 2025 | 0 |
| Games Finished | MLB | 2025 | 5 |
| Games Started | MLB | 2025 | 1 |
| Games Pitched | MLB | 2025 | 7 |
| ERA | MLB | 2025 | 3.57 |
| Win-Loss Percentage | MLB | 2025 | 1.000 |
| Loss | MLB | 2025 | 0 |
| Wins | MLB | 2025 | 1 |
| Wins Above Replacement for Pitchers | MLB | 2025 | -0.1 |
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| SO/BB | MLB | 2024 | 2.35 |
| SO9 | MLB | 2024 | 6.6 |
| BB9 | MLB | 2024 | 2.8 |
| HR9 | MLB | 2024 | 0.9 |
| H9 | MLB | 2024 | 9.3 |
| WHIP | MLB | 2024 | 1.349 |
| Fielding Independent Pitching | MLB | 2024 | 4.15 |
| ERA+ | MLB | 2024 | 102 |
| Batters Faced | MLB | 2024 | 424 |
| Wild Pitches | MLB | 2024 | 2 |
| Balks | MLB | 2024 | 0 |
| Times Hit by a Pitch | MLB | 2024 | 7 |
| Strikeouts | MLB | 2024 | 73 |
| Intentional Bases on Balls | MLB | 2024 | 0 |
| Bases on Balls/Walks | MLB | 2024 | 31 |
| Home Runs Allowed | MLB | 2024 | 10 |
| Earned Runs Allowed | MLB | 2024 | 45 |
| Runs Allowed | MLB | 2024 | 52 |
| Hits Allowed | MLB | 2024 | 103 |
| Innings Pitched | MLB | 2024 | 99.1 |
| Saves | MLB | 2024 | 0 |
| Shutouts | MLB | 2024 | 0 |
| Complete Games | MLB | 2024 | 0 |
| Games Finished | MLB | 2024 | 4 |
| Games Started | MLB | 2024 | 18 |
| Games Pitched | MLB | 2024 | 26 |
| ERA | MLB | 2024 | 4.08 |
| Win-Loss Percentage | MLB | 2024 | .545 |
| Loss | MLB | 2024 | 5 |
| Wins | MLB | 2024 | 6 |
| Wins Above Replacement for Pitchers | MLB | 2024 | 0.7 |
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| SO/BB | MLB | 2023 | 2.45 |
| SO9 | MLB | 2023 | 7.4 |
| BB9 | MLB | 2023 | 3.0 |
| HR9 | MLB | 2023 | 1.6 |
| H9 | MLB | 2023 | 10.9 |
| WHIP | MLB | 2023 | 1.545 |
| Fielding Independent Pitching | MLB | 2023 | 5.35 |
| ERA+ | MLB | 2023 | 74 |
| Batters Faced | MLB | 2023 | 151 |
| Wild Pitches | MLB | 2023 | 2 |
| Balks | MLB | 2023 | 0 |
| Times Hit by a Pitch | MLB | 2023 | 4 |
| Strikeouts | MLB | 2023 | 27 |
| Intentional Bases on Balls | MLB | 2023 | 1 |
| Bases on Balls/Walks | MLB | 2023 | 11 |
| Home Runs Allowed | MLB | 2023 | 6 |
| Earned Runs Allowed | MLB | 2023 | 21 |
| Runs Allowed | MLB | 2023 | 23 |
| Hits Allowed | MLB | 2023 | 40 |
| Innings Pitched | MLB | 2023 | 33.0 |
| Saves | MLB | 2023 | 0 |
| Shutouts | MLB | 2023 | 0 |
| Complete Games | MLB | 2023 | 0 |
| Games Finished | MLB | 2023 | 4 |
| Games Started | MLB | 2023 | 0 |
| Games Pitched | MLB | 2023 | 10 |
| ERA | MLB | 2023 | 5.73 |
| Win-Loss Percentage | MLB | 2023 | .500 |
| Loss | MLB | 2023 | 1 |
| Wins | MLB | 2023 | 1 |
| Wins Above Replacement for Pitchers | MLB | 2023 | -0.4 |
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| SO/BB | MLB | 2022 | 4.00 |
| SO9 | MLB | 2022 | 10.8 |
| BB9 | MLB | 2022 | 2.7 |
| HR9 | MLB | 2022 | 0.0 |
| H9 | MLB | 2022 | 5.4 |
| WHIP | MLB | 2022 | 0.900 |
| Fielding Independent Pitching | MLB | 2022 | 1.61 |
| ERA+ | MLB | 2022 | 152 |
| Batters Faced | MLB | 2022 | 13 |
| Wild Pitches | MLB | 2022 | 0 |
| Balks | MLB | 2022 | 0 |
| Times Hit by a Pitch | MLB | 2022 | 0 |
| Strikeouts | MLB | 2022 | 4 |
| Intentional Bases on Balls | MLB | 2022 | 0 |
| Bases on Balls/Walks | MLB | 2022 | 1 |
| Home Runs Allowed | MLB | 2022 | 0 |
| Earned Runs Allowed | MLB | 2022 | 1 |
| Runs Allowed | MLB | 2022 | 1 |
| Hits Allowed | MLB | 2022 | 2 |
| Innings Pitched | MLB | 2022 | 3.1 |
| Saves | MLB | 2022 | 0 |
| Shutouts | MLB | 2022 | 0 |
| Complete Games | MLB | 2022 | 0 |
| Games Finished | MLB | 2022 | 0 |
| Games Started | MLB | 2022 | 1 |
| Games Pitched | MLB | 2022 | 1 |
| ERA | MLB | 2022 | 2.70 |
| Loss | MLB | 2022 | 0 |
| Wins | MLB | 2022 | 0 |
| Wins Above Replacement for Pitchers | MLB | 2022 | 0.1 |
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| SO9 | MLB | 2021 | 0.0 |
| BB9 | MLB | 2021 | 0.0 |
| HR9 | MLB | 2021 | 0.0 |
| H9 | MLB | 2021 | 40.5 |
| WHIP | MLB | 2021 | 4.500 |
| Fielding Independent Pitching | MLB | 2021 | 3.17 |
| ERA+ | MLB | 2021 | 28 |
| Batters Faced | MLB | 2021 | 10 |
| Wild Pitches | MLB | 2021 | 0 |
| Balks | MLB | 2021 | 0 |
| Times Hit by a Pitch | MLB | 2021 | 0 |
| Strikeouts | MLB | 2021 | 0 |
| Intentional Bases on Balls | MLB | 2021 | 0 |
| Bases on Balls/Walks | MLB | 2021 | 0 |
| Home Runs Allowed | MLB | 2021 | 0 |
| Earned Runs Allowed | MLB | 2021 | 3 |
| Runs Allowed | MLB | 2021 | 3 |
| Hits Allowed | MLB | 2021 | 6 |
| Innings Pitched | MLB | 2021 | 1.1 |
| Saves | MLB | 2021 | 0 |
| Shutouts | MLB | 2021 | 0 |
| Complete Games | MLB | 2021 | 0 |
| Games Finished | MLB | 2021 | 0 |
| Games Started | MLB | 2021 | 1 |
| Games Pitched | MLB | 2021 | 1 |
| ERA | MLB | 2021 | 20.25 |
| Win-Loss Percentage | MLB | 2021 | .000 |
| Loss | MLB | 2021 | 1 |
| Wins | MLB | 2021 | 0 |
| Wins Above Replacement for Pitchers | MLB | 2021 | -0.2 |
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