Why does the "this" keyword not refer to the Player instance after it is created? Why does it point to the window obj?

function Counter(props) {
    return (
        <div className="counter">
          <button className="counter-action decrement" onClick={function() {props.onChange(-1);}}> - </button>
          <div className="counter-score"> {props.score} </div>
          <button className="counter-action increment" onClick={function() {props.onChange(1);}}> + </button>
        </div>
    );
}

function Player(props) {
  return (
    <div className="player">
      <div className="player-name">
        {props.name}
      </div>

      <div className="player-score">
        <Counter score={props.score} onChange={props.onScoreChange}/>
      </div>
    </div>
  );
}

Player.propTypes = {
  name: React.PropTypes.string.isRequired,
  score: React.PropTypes.number.isRequired,
  onScoreChange: React.PropTypes.func.isRequired
}

const Application = React.createClass({
    propTypes: {
        title: React.PropTypes.string,
        initialPlayers: React.PropTypes.arrayOf(React.PropTypes.shape({
            name: React.PropTypes.string.isRequired,
            score: React.PropTypes.number.isRequired,
            id: React.PropTypes.number.isRequired
        })).isRequired
    },

    getDefaultProps: function() {
        title: "My Scoreboard"
    },

    getInitialState: function() {
        return ({
            players: this.props.initialPlayers,
        });
    },

    onScoreChange: function(index, delta) {
        console.log('onScoreChange', index, delta);
    },

    /*
     * Confused as to why we use bind here... Why wouldn't "this" refer to the Player once the instance of the Player is created?
     * I think what's going on here is that the "this" is instead bound to the enumerated instance of the Player, meaning
     * that once the function is done with the particular instance it no longer exists and as a result points to the Window?
     */

    render: function() {
        return (
            <div className="scoreboard">
                <Header title={this.props.title}/>

                <div className="players">
                  {this.state.players.map(function(player, index) {
                      return (
                        <Player
                            onScoreChange={function(delta) {console.log(this)}}
                            name={player.name}
                            score={player.score}
                            key={player.id}/>
                        );
                    }.bind(this))}
                </div>
            </div>
        );
    }
});