I don’t think it would be an overstatement to suggest that the 2011-2012 season was a precocious one for Ryan Nugent-Hopkins (RNH). Though common media opinion before the season was that the physicality of NHL play would challenge the androgynous-y 18-year-old, he silenced his critics early and often, finishing the season with 18-34-52 in 62 games. Simple.

As I mentioned in a previous article, it seems the Oilers’ main plan to compete coming into the 2013 is to let the kids mature one more calendar year and leave everything else exactly the same. I took a look at how I thought the 3rd year Oilers would do yesterday, and today will concentrate on RNH, the lone impact sophomore on the team.

When analyzing the third year players, I was able to draw on two previous years of performance to run a multiple regression model. Obviously the more years of data we have, the more confidence we can have that a model will be able to reflect a true level of ability. The issue with sophomores like RNH is that we only have one prior data point to draw on. I had to come up with some means of projecting performance using a similar population of players.

I first compiled a list of all players who played in at least 20 games in both their rookie and sophomore seasons at any point since the first 1994-95 lockout, with their rookie seasons occurring between the ages of 18 and 21. This created a population of 87 players that I could harvest for information. The basic idea is that I want to use their rookie seasons to come up with a method for how they did in their sophomore seasons. I started using similar methods as I did for the 3rd years yesterday, namely regressing current year points per game (PPG) against previous season PPG (in this case, using only the one season I have).

This produced ok results, but when I graphed the data I noticed that there seemed to be a lot of non-linearity in the relationship between first year PPG and second year PPG. That is, the relationship between first year PPG and second year PPG didn’t seem to increase in a straight line, it had many periods where the slope of the relationship slowed or accelerated considerably. It was at this point that I decided to use a method of non-linear regression, or polynomial regression. MATH!!!!!!

I’ll spare the gory details, but I fit a line using a sixth-order polynomial equation to minimize the errors between my forecast value and the actual 2nd year dependent variable. There are 7 terms in the equation (6 exponential terms and the 1 constant intercept). Check it out nerds:

y = 19.435×6 – 85.219×5 + 141.41×4 – 110.55×3 + 41.821×2 – 6.239x + 0.5913

-or-

2nd year PPG forecast = 19.435*1st year PPG ^6 – 85.219*1st year PPG^5 + 141.41*1st year PPG^4 – 110.55*1st year PPG^3 + 41.821*1st year PPG^2 – 6.239*1st year PPG + 0.5913

This equation creates a lovely curved line that fits the data much better than a straight one would. It also has a decent correlation (R-squared) of 0.563. Here’s the plot:

You can see all 87 players in my population plotted above, with their 1st year PPG on the x axis and their 2nd year PPG on the y axis. I’ve named a few notable outliers, along with a couple of Oilers in Gagner and Comrie. If you fell below and to the right of this line, you underperformed where the model thought you would, and if you were above and to the left of the line, you overperformed (ie, you Eric Staal’ed the joint). RNH is plotted in the top right of the chart, and you can see him in the neighbourhood of other highly-touted centres such as Toews, B Richards, Backstrom, Kopitar, and Gomez.

Here’s a table that shows the expected performance of RNH and other 2nd year NHL centres this year:

So what does this data suggest? It suggests that if RNH follows the performance progression of past players, he is due to take a fairly large step up in performance, from 0.84 PPG to 0.93 PPG. This would translate to 45 points over the 48-game shortened season, or 76 points over a full 82 game schedule — as an absolute total, this is much higher than the 52 he tallied in his rookie season. Of the three impact rookies I’ve looked at, my rankings of who will have the largest positive impact in terms of points per game growth over last season is 1. RNH, 2. Hall, and 3. Eberle.

As an aside, I highly doubt Lander gets 14 points this year, unless he somehow plays the whole year and gets >0 mins off the 4th line. Considering the Oilers’ injury history, I suppose this has a greater than zero chance of happening.

Here’s the full list of players included in my sophomore study:

## 3 Comments

Hmm… I can’t be bothered to strip your data from the image and analyze it, but I don’t see what the 6th order polynomial is really giving you. What is the marginal gain in r^2 as you add terms to the linear relationship? It looks like very little. In fact, you’re probably getting weird residuals due to those extra inflections which are undoubtedly not “real”.

Also, I’d be more interested in this if you looked at it by game state and normalized by TOI. What does 1st yr ES pts/60 min look like vs. 2nd yr ES pts/60 min?

Regardless, I am not sure this is really that important. At least in terms of individual contributions to the team winning. RNH’s influence on the Oilers’ ability to win hockey games will be based on his production normalized by the opportunity afforded him. The opportunity is related to where he starts his shifts, what his ES/PP/SH TOI breakdown looks like and his total TOI, and how the Oilers choose to use him in matchups. I suppose this is pretty cool for fantasy stuff though.

Hey RQ,

The increase in R2 was from about 0.52 in the linear relationship to 0.56 in the nonlinear relationship. In this exercise my primary interest was to squeeze out as much predictive power as I could, so I tried literally a half dozen techniques and this provided the best correlation. I’m a quick and dirty kind of guy, but the residual plot looks decent to me, randomly distributed, etc.

And yes, I do believe scoring rate per 60 is more useful to judge a player’s usefulness, but since this is the one time I get to throw the gauntlet down for seasonal point predictions, I’m taking advantage. In any case, I’d just like to show different ways about thinking about generating projections. And yes, it is kind of just a bit of fun !

The performance of Ryan Nugent-Hopkins in previous season was excellent. Really he has been deserved to enter in the World Junior Hockey Championship. Hope the Canadian team management will consider him very eagerly.