The Hawks averaged 32.6 SF/60 and 26 SA/60. The Blues averaged 28.8 SF/60 and 27 SA/60. Averaging those has the Hawks taking 29.8 ES shots a game and the Blues 27.4.
The Blues took more penalties than the Hawks (293 to 248). The Hawks average more shots per power play (1.44 to 1.30). The Blues give up fewer shots per penalty kill (1.24 to 1.44). Net effect is the Hawks being expected to take about one more power play shot per game than the Blues (5 to 4). It's not quite a full 1.0 shot difference, so I'm going to round the 27.4 ES shots up to 28 to compensate.
Ryan Miller has a career ES save percentage of 0.923. Corey Crawford is 0.924. Miller has a career PK save percentage of 0.881 which is pretty much exactly league average. Crawford is at 0.865.
Have the Hawks take 30 ES shots and 5 PP shots. Flip a weighted coin to determine if each shot is a save or a goal. Count the goals. Have the Blues take 28 ES shots and 4 PP shots . Flip a weighted coin to determine if each shot is a save or a goal. Count the goals. Blues goals > Hawks goals then Blues win. Repeat 10,000 times.
Hawks win 56.6% of the games. Hawks win the series 63.8% of the time
In his 19 games in St. Louis, Miller has a Ondrej-Pavelec-like ES save percentage of 0.913 and PK of 0.855. If he plays at that level, Hawks win 64.7% of the games and 80.6% of the series.
In his 3 years in St. Louis, Elliott has an ES save percentage of 0.932 and PK of 0.898. If the Blues play Elliott and everything else is equal, Blues win 51.0% of the games and 52.0% of the series.
Turning to Elliott
If Miller loses the first two games and the Blues stick with Miller, they come back to win the series 10.5% of the time. If they are down 2-0 and turn to Elliott, they come back and win 18.7% of the series.