Let’s not forget to see the forest through the trees. The purpose of the post was to have some fun with Ovechkin getting 50 in 50. Agree or disagree with how my numbers were reached, the bottom line is: The chances are slim to none. Maybe it is .0002%, maybe it is .0016%, maybe it is (n+1)^(ln(y)-e^3), but we should all agree that unless the odds are 14 trillion to one we should not take the bet.

As for projecting an 82 game season, again, let’s not lose sight of the message: “A 37-goal season looks light. I would take the over.”

You know what would be refreshing? A comment that starts with “I did my own simulation and came up with…”

]]>Secondly, KHtaD is correct. If your simulation is deviating from the observed results that much, something is most likely wrong. Both KHtaD and I understand standard deviation, but the mean is just too low for this to be correct. You didn’t describe any factors you used in your Monte Carlo to account for regression to the league mean, injuries, or aging (though, seriously, Ovie is still in his prime, he’s not going to age negatively this season).

]]>So what I’m saying if anything at all is that individual seasons will see big changes from one to the next but if you were to look at his career it would look more normal

]]>My objection has nothing at all to do with the results of the projection – 50 is a very difficult plateau to reach and you need either unprecedented volume (Ovechkin) or absurd accuracy (Kovalchuk) or some of each and some luck (Crosby). Any number of factors, including age, injury, or bad luck, can prevent a player from hitting 50.

Rather, the problem is this; if you’re running a simulation of Alex Ovechkin’s next season BASED ON THE DATA FROM THE PAST FIVE YEARS and you’re arriving at a mean of 91% of the prior low-water mark, you’ve screwed up your simulation somewhere. Your mean is 42. The prior low in the data is 46. If the simulation is based on the past data, then the simulation is wrong.

If you’ve included correcting factors for age and/or injury in your simulation, then the result makes sense, but I still think it’s a little strong. If you haven’t, and what’s in the article, a Monte Carlo based on observed shots-in-a-given-game and observed-shooting-percentages-in-a-given-game is all there is, you probably have a binning error and the first place you want to start looking is the shooting percentage. I think you’d be far better served with a Bernoulli simulation – you could still use the shots-in-a-game methodology, but you’d use a set shooting percentage for each shot; a weighted coin flip, in the parlance of Vic Ferrari. Figure out what you think Ovechkin’s true shooting percentage is, keep the shots/game, then apply that shooting percentage to each event. Much cleaner, no binning problem.

You could also use a reverse binomial distribution, the distribution of the number of trials it takes to get to the Kth event, to figure out what AO’s chances of making 50 in 50, or 50 in 82 are in a symbolic way.

In sum, I have no problem with the conclusion, but I do have a problem with how you got there, and I definitely have a problem with all the strawmen.

]]>If you expect Ovechkin to score 50 goals a year forever, that is flawed logic. Just because someone “always” scores x goals doesn’t mean the following season they won’t score y goals. And I am not saying he “won’t” score 50 goals. In fact, I am saying with 95% certainty he will score somewhere between 28 and 58 goals.

“when the mean is well below all previously observed data used to make the simulation parameters, it’s a red-flag; something’s wrong.”

So players don’t age? They don’t get injured? Fluky things don’t happen? NOTHING happens that could cause even a dynamic player like Ovechkin to have an off year? The chances of that happening are ZERO? I am curious: why is Ovechkin immune to the laws of nature and physics every other person seems to be influenced by?

I am sure people in 1987 thought the odds of Gretzky scoring less than 50 goals were just as far fetched, yet he came in with a “clunker” season of 40 goals. Things happen.

Now another explanation:

1. I am not saying he is going to average 42 goals over the next 82 games. I AM saying if we took 10,000 simulated seasons, each with 82 games in them, we can expect Ovechkin to score on average 42 goals, PLUS OR MINUS 8. In some of these alternate universes he scores 34, maybe due to “injury” or a teammate getting hacked to death by the Boogeyman – whatever – but things happen.

2. This is a 82 game SIMULATED season. Ovechkin cannot be expected to play every game every season – and even if he did chances are he will not score a goal in every game, nor even get a shot on goal every game. Granted, it is rare when he is held without a shot, but it CAN and DOES happen. The model takes this into account. And in reality, if he doesn’t get a shot on goal or doesn’t play the game, the net result is the same: 0 goals, so it works out.

]]>I’d be interested to see what the results were with his career shooting percentage applied to his distribution of shots on goal, rather than the very chunky per-game shooting percentages.

]]>These are averages and the plus/minus is the standard deviation. Meaning, we expect 68% of the time for Ovechkin to score 34 to 50 goals. We expect him to score 26 to 58 goals 95% of the time.

So when I say “Ovechkin scoring on average 42 goals, plus or minus 8″ what I am really saying is “If we had an Ovechkin playing in each of the 10,000 alternate universes there would be different results from each. Some Ovechkins will see longer/shorter shooting slumps, some will see injury, some will see his teammates get injured/traded, etc. So when we look at the 10,000 Ovechkins as a whole, 65% should score on average 42 goals, plus or minus 6 goals.

]]>Using his numbers from the last 2 years, out of 10,000 seasons he hits 50+ goals 6 times, 49 goals 3 times and 48 goals 4 times. Averages 27 goals, plus/minus 6.

Using last 3yrs: out of 10,000 seasons he hits 50+ goals 14 times, 49 4 times, 48 8 times. Avg 28, plus/minus 6.

Better, but not enough for me to pack our bags and head to Vegas. :-)

Again, great suggestion!

]]>