It is called an Inverted-U graph and it shows the relationship between performance and arousal levels. Arousal levels are determined by a players blood pressure, heart rate, breathing rate, etc. As the graph indicates, as arousal levels increases, so does his performance. This is why many players seek to get "psyched up" prior to a competition. Increasing arousal levels gets the body going which prepares it for performance tasks. However, the down side of all this is that sometimes a player's arousal levels can get too high due to nerves, anxiety, fear of failure, perfectionism, etc. As the graph shows, too much arousal sends performance downward. As I stated in the previous post linked above, different types of tasks require different levels of arousal. The arousal level of a football lineman is going to be different than a starting pitcher when it comes to peak performance.
Now let's apply all this to "playing favorites." One of the most important jobs of any leader is figuring out where his people are on the Inverted-U. A coach need to know the personalities of his players. Once he does, he can tailor his interactions accordingly. If a player is by nature a bit sluggish and to the left of the peak on the graph, the coach may need to introduce some stress for this player in order to move the player's arousal levels higher. It might take the form of getting in a player's face and telling him he better start picking up the pace a little. In turn, the player's performance will improve as it moves upwards towards the peak of the Inverted-U. If a player is naturally high-strung or someone who puts a lot of pressure on himself may typically be on the right or downside of the graph. Introducing more stress by yelling at the kid is just going to make the player's performance even worse. This is the kid who needs a pat on the back or some words of encouragement in order to get him to relax and move back and up to the left towards his optimal level.
Of course, the problem in some peoples' minds is that the coach is not treating his players equally. The player who needed stress introduced may say "Wait a minute. Coach yells at me but pats him on the back when he makes mistakes. He's playing favorites." It is true. The coach is not treating the two players equally. But he is treating them fairly. He is doing what is necessary to get the most out of each player. Always yelling at mistakes only serves those players who are motivated by that. Only patting them on the back may get players to call the coach a nice guy but he too is only reaching the players who respond best to a pat on the back.
Good coaching requires a coach to be fair, not necessarily equal. It also requires them to know the players well enough to understand where each player typically falls on the graph in order to interact with them properly. It's not always easy but it's the reality of coaching.
