According to recent research performed by Twitch’s own research department, livestreaming a game on Twitch often leads to better sales of said game. It seems a bit biased as well as self-serving, especially since this report suggests that game publishers and developers should invest in the Twitch community.
Danny Hernandez, the Twitch data scientist who compiled the report, studied how much exposure Twitch can do for a game regarding sales. He found that 25% of game sales for Punch Club and The Culling were directly due to Twitch streaming. He also noted that Twitch is responsible for increases in player interest weeks after a game releases as much as 15%. 

I found that when a Steam connected viewer watched a game on Twitch, their odds of purchasing the game within 24 hours went up substantially. So I attribute purchases that fit this ?watch then buy? pattern to Twitch.
His biggest example of how Twitch can boost sales is from TinyBuild’s launch of Punch Club, where the developer set up a Twitch channel for viewers to play Punch Club. Once they completed the game, they would release it. Once the game launched, TinyBuild handed out several Steam keys to Twitch streamers to keep building the momentum from the Twitch Plays session. In six weeks, 1.2 million users tuned in to watch Punch Club on Twitch, and 2.8% of the Steam-connected viewers bought the game after viewing the broadcasts. Hernandez further estimates that 25% of all Punch Club sales are due ...