I'm sure there's a more accurate way to do estimates... Been a long day and my brain power is sapped, so I'm not going to attempt to get more advanced for now.
However you could, as a starting point, compare a players GF/GA to his teams GF/GA using the teams total TOI (GF/GA per minute)
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EX: (chosen because he came up first when I went to check plus/minus stats)
Patrice Bergeron on ice for 90GF 51GA
He played 81 games
Boston 260 GF 199 GA
Boston on ice 5002 minutes in 2011/2012
Therefore every GF is worth 19.238 minutes of playing time
every GA is worth 25.136 minutes of playing time
Using this simplistic method, and averaging the GF estimate and the GA estimate, Bergeron can be estimated to have played 18 minutes and 36 seconds per game.
In reality, he played 18 minutes and 34 seconds per game.
Undoubtedly it was lucky that the estimated and actual were this close in this example.
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EX #2: Chara (because hes on the same team, and this way I don't need to look up new team stats

)
115 GF 85 GA in 79GP
Comes out to an estimated TOI of 27 minutes 32 seconds per game.
He actually played 25 minutes and 0 seconds per game.
This one was further off, but still semi-reasonable for a rudimentary estimate.
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Keep in mind that this simple formula does not take into account the higher rates of GF/GA on the PP/PK - and probably several other factors that I am not considering. Part of the reason for the discrepancy in Chara's numbers could be related to the higher PK/PP time he had last year.
Seems to be somewhat accurate in the two example I tried though.