Z and Miller need the ball to affect the game. Z is more a shooting center than defender or rebounder. Miller needs to ball to be effective so I have to disagree with your assessment on these two, Roy.
Ilgauskas especially is not known for rebounding, shotblocking or defense but he is 7'3" at the end of the day. He may get an offensive rebound here or there but he is primarily a jumpshooter from mid range. While he won't create shots and will require dishes from his team mates to score. I think he is a good center for MIA's offense, he plays a lot of high post with will allow them to penetrate from the wings. He might muck with Bosh's game but he will help LeBron and Wade. But he isnt a good rebounder or defender and has had many health issues with his feet. MIA may be a very poor offensive rebounding team. I can see them being one and done on a lot of possessions.
Miller often dominated the ball on past teams he is a versatile all around player who had decent stats across the board but needed the ball. I thought both of these signings were ones that defied the logic of not needing the ball.
This is definitely true of Haslem and Anthony however, they don't need the ball.
Over the last two seasons Mike Miller has become far more passive offensively. He has only been taking 8.5 shot attempts per 36 minutes which is in line with what Kendrick Perkins takes for the Celtics and lower than every other rotation player on the Celtics roster.
Ergo, Miller only requires a small amount of touches and shot attempts. A low usage player.
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I agree with your description of Zydrunas Ilgauskas.
Where we differ is that I consider players who finish plays
(for example, a stand still shooter like Jason Kapono or Troy Murphy) and allow others to spend their time on the ball and make the key plays
(like Wade or Bron setting up the shooting opportunity) ... I consider those players (offensively orientated players) to be players who do not need the ball in their hands to be effective. They spend most of their time without the basketball allowing others to create the opportunity and only step up to finish a play.
In contrast to role players like Jannero Pargo or Leandro Barbosa or Al Harrington who (1) spend a lot of time on the basketball (2) and/or like to create their offense and/or (3) take a lot of shot attempts.