As of this season, Alexander Ovechkin must score 237 goals in order to better The Great One's all time goalscoring record. In this thread I do some back of the envelope calculations to estimate with what probability that will happen, and plot the results.
Key assumptions: I assume that he will play 5 more seasons. One could of course assume more or fewer. There are two main sources of uncertainty with this calculation: how many games will he play, and at what rate will he score. In each case a distribution must be assumed. For each distributional assumption you will get a different result.
To model his scoring rate, I draw samples from a Gaussian distribution fit to his GPG in his 14 seasons in the NHL. First, a line of best fit is found to model the trend of scoring throughout his career. This is slightly negative and likely underestimates the effect of ageing. For each year, a sample is drawn from a distribution with the mean given by this trend, and standard deviation given by the year to year variance of his goal scoring.
To model the number of games he will play I use a triangular distribution with its peak at 78, max at 82 (obvs) and minimum at 67, which is 5 fewer than the smallest number of games Ovi has played in a full length season. Ovechkin has been an extremely healthy player during his career, but obviously this could change.
The two are multiplied together and rounded down to give an estimate of goals scored in a given year. This process is repeated for each of his remaining 5 years, and 10,000 montecarlo trials are done.
Results: Here is the normalized histogram for 100,000 trials and the empirical CDF.
TL;DR: There's about a 4% chance that Ovechkin scores 895 or more under these assumptions. In this case, we can pretty safely conclude that a severe injury or a lockout would basically eliminate the possibility of Ovechkin setting a new record.
However, the total isn't the only record up for grabs. Also in jeopardy is the number of 50 goal seasons record. Under these assumptions, Ovechkin has about an 18% chance of setting the new record (10). However, under these assumptions, it is almost a certainty that Ovechkin will eclipse Gordie Howe for 2nd all time on the scoring list. Given league scoring trends and games missed to lockouts, I don't think it's a stretch to say that Ovechkin very well may be the greatest goalscorer who ever lived.
Key assumptions: I assume that he will play 5 more seasons. One could of course assume more or fewer. There are two main sources of uncertainty with this calculation: how many games will he play, and at what rate will he score. In each case a distribution must be assumed. For each distributional assumption you will get a different result.
To model his scoring rate, I draw samples from a Gaussian distribution fit to his GPG in his 14 seasons in the NHL. First, a line of best fit is found to model the trend of scoring throughout his career. This is slightly negative and likely underestimates the effect of ageing. For each year, a sample is drawn from a distribution with the mean given by this trend, and standard deviation given by the year to year variance of his goal scoring.
To model the number of games he will play I use a triangular distribution with its peak at 78, max at 82 (obvs) and minimum at 67, which is 5 fewer than the smallest number of games Ovi has played in a full length season. Ovechkin has been an extremely healthy player during his career, but obviously this could change.
The two are multiplied together and rounded down to give an estimate of goals scored in a given year. This process is repeated for each of his remaining 5 years, and 10,000 montecarlo trials are done.
Results: Here is the normalized histogram for 100,000 trials and the empirical CDF.
TL;DR: There's about a 4% chance that Ovechkin scores 895 or more under these assumptions. In this case, we can pretty safely conclude that a severe injury or a lockout would basically eliminate the possibility of Ovechkin setting a new record.
However, the total isn't the only record up for grabs. Also in jeopardy is the number of 50 goal seasons record. Under these assumptions, Ovechkin has about an 18% chance of setting the new record (10). However, under these assumptions, it is almost a certainty that Ovechkin will eclipse Gordie Howe for 2nd all time on the scoring list. Given league scoring trends and games missed to lockouts, I don't think it's a stretch to say that Ovechkin very well may be the greatest goalscorer who ever lived.
