beat to the draw

Napoleon HillのThink and Grow Richを読んでいます。
The sponsor! That unfortunate victim who now pays the cost of all radio "entertainment," soon will become idea conscious, and demand something for his money. The man who beats the sponsor to the draw, and supplies programmes that render useful service, is the man who will become rich in this new industry.
この本の話は古いのでメディアの主体がラジオになっています。今やテレビもピークを過ぎ、まだ落ちぶれてはいませんが、インターネットに抜かれている面も増えてきていますね。
"The man who beats the sponsor to the draw" はスポンサーにどう対処して番組を売り込んだのでしょうか？　辞書で調べます。
OneLook Dictionary Searchでは "beat ... to the draw" を見出しにした辞書は見つかりませんでしたが、次の辞書に "beat someone to it" とも言うとあり、以下の説明がありました。
・American Heritage Dictionary of Idioms: Also, beat to the draw or punch. React more quickly than someone else. For example, The new salesman tried to serve one of my customers, but I beat him to the draw and Bill was determined to get there first and beat everyone else to the punc0h. The variants imply aggression to get ahead, draw alluding to the drawing of a pistol and punch to hitting with the fists.
なるほど、最近は余り見かけませんが、西部劇の早打ちの決闘ですね。