Tim knows in his heart of hearts, he doesn't matter. He's known all along that he is not Jason and he certainly isn't Dick. Somehow he became Robin, but he himself doesn't matter. Tim Drake the Star Trek nerd, who followed Batman and Robin at night, who is tiny, once failed p.e. because of tennis, and does not matter in the grand scheme of things.
He knows this in the way that Bruce is Batman. Tim is glad he was able to curb Bruce's destructive tendencies after Jason's death. He played a minor role that helped him get back on the road he was. He probably would have found it eventually, anyway. Tim had faith in that, he just had to make sure it was sooner rather than later.
Robin matters.
Well, Jason and Dick as Robin mattered. They were needed and wanted. He was a poor replacement for the real sons. Tim knew that in the way Batman taught him things, in the way that Alfred greeted him, and the look in Dick's eyes that seemed to say you aren't good enough.
He tries so hard, but it never is enough. He knows.
So if he gets hit with a baseball bat so Batman doesn't, it doesn't matter. His ribs ache, oh they hurt so fiercely, but it's better him than Batman. When a pregnant woman is held hostage at a bank robbery and he gets her to safety with the other hostages while only suffering a slight stab wound, it doesn't matter. She matters more. Bruce never openly berated him getting hurt to help someone else, Tim can't help, but think that Bruce is okay with it because he knows what Tim has known all this time, he doesn't matter.
His being Robin is ultimately replaceable.
Bruce wonders whether Tim knows how much it hurts him to see him injured. Dick as Robin was so energetic but mindful of his actions. Jason was so reckless, but in an incalculable way, not even Jason planned for. Tim was so smart, he thought out and knew the consequences of his actions before he did them. Tim had taken a baseball bat to the chest so he wouldn't be injured. He had laughed it off, even when Alfred wrapped his broken ribs that had already started to turn dark blue.
Bruce often wondered if he was a masochist. But then Bruce noticed that Tim would allow himself to be hurt if he knew that he was saving someone else from it, like the time Tim saved a pregnant woman and a lot of other people at a bank robbery, that night had been one of the longest of Bruce's life. Tim had saved all the hostages and stumbled out to meet him with a lopsided smile and a knife in his stomach. Tim assured him that, he would be fine, he kept the knife in to slow the bleeding. Bruce had been so worried, but Tim was losing to much blood to notice. Alfred and Leslie had done emergency surgery. Bruce would never forget the surprise on Tim's face when he saw that Bruce was waiting for him to wake up.
Bruce wondered if the small child knew just how much he mattered. He was going to tell him many times, but it never seemed like the right time. Tim had to know how much he was loved and mattered to them all.
Bruce never was that good with communication, after all.