Most Improved Player of the Year
This award seems pretty easy. Thomas has put himself in the MVP discussion in just one season after not being in it at all last season. He has improved his shooting by 6.7 points a game and has improved his shooting percentage in every shot category (2P%, 3P%, and overall FG%) all while attempting 91 more shots this season. Going more into the advanced stats, Thomas has increased his win shares by 2.8 games. Win shares are simply an estimate of the number of wins that a specific player contributed. Thomas has been the most improved player this season obviously, but the runner-up would have to be Marcus Smart. Smart had a bundle of game-winning plays on both ends of the floor.
Most Underrated Player of the Year
This award could be given to a numerous amount of players on this Celtics team, but Johnson stuck out the most. Johnson is the player who is depended on to defend all the league's best posts. Boston as a team isn't very good in the post, but if you take Johnson off this team, they might not stand a chance against any team with a dominant post. Besides Al Horford, Johnson is the only player Boston relies on for post offense. Most of these Celtics players are underdogs and overlooked, so you could give this award to basically anyone.
Defensive Player of the Year
This should come as no surprise. Avery Bradley has been the cornerstone of the Celtics defense pretty much since he got to Boston. He has shut down the league's best guards and should be on the All-NBA Defensive First or Second Team. As you can see from the video above, he shuts down Kyrie Irving, which will be huge if these teams are to meet in the Eastern Conference Finals. While his defense is the main part of his game, his offensive game has come along very well, as he is the best 2-way player on the Celtics. Bradley might also be the most important player besides Thomas when it comes to being successful in the playoffs.
Most Valuable Player
Yet again, another award where it shouldn't take much thinking. As well as being the leader and MVP of this Celtics team, he has propelled himself to the top 5 in the MVP race. Thomas has had himself one of the best single seasons ever by a Celtic since Larry Bird back in the day. As Thomas leads the Celtics in the NBA Playoffs, he still looks to prove doubters wrong, even though they are the top seed in the Eastern Conference.