Inspired by this post at Russian Machine Never Breaks, I decided to do my own simulation, since a mean of 42 goals looked pretty light, given the lowest point in his data set so far is 46. Results and methodology after the jump.
Since I don't know enough R or J to write the simulation myself, I enlisted the help of my brother, Erik. The J code used to run the simulation is his, so if you use it, be sure that the attribution is to him and not me. Also, don't ask me to debug it, because this code is at least as hard to read as a PERL inquiry you didn't write yourself.
Standard Deviation: 7.46
Neil's original method was to gather all of games that the Capitals have played while Alex Ovechkin has been a member of the team, count the shots in each game, then assign a probability to Alex taking a given number of shots in the game given his prior performance. Since the Caps had played 414 games with Ovechkin on the roster when we compiled this data, I divided the frequency count of each number of shots in a game by 414 to arrive at a probability that Ovechkin takes a given number of shots in a game. The cumulative probability column was used in conjunction with a random number generator to assign the number of shots for a given game. It should be noted that games missed with injury or suspension were counted as zero shot games.
Each shot is treated as a Bernoulli trial, which is to say a weighted coinflip with AO's career shooting percentage to that point in time: 12.5%. If the random number generator gets a number between .125 and 1, then the shot missed. Anything lower than that and the shot resulted in a goal. That was replicated 82 times to form a season, then that was replicated 10,000 times to form a dataset based on AO's career goal scoring.
Since the original question was 50 in 50, I have a mean of 32.76 and a standard deviation of 5.87 goals for 50 games, reaching 50 or better 36 times out of 10,000 trials, or .36% of all the seasons.
For the total 82 game season, the results were a mean of 53.62, much more in line with AO's historical goal scoring rate and a standard deviation of 7.39 goals, so the 95% confidence interval is 38.9 goals to 68.4 goals.
Going forward, this seems high considering the wear that AO is putting on his body and the pattern of production that other elite goalscorers have exhibited as they reached their middle and late 20s; he's probably not going to produce at the same rate, but if he were going to, this is what it'd look like.
No pretty pictures, because my system chokes on trying to bubble sort 10000 data points in Excel, so I'm sorry about that.