# Diminishing Returns – The Prelude

#### By Unknown author

I’ve been working on some interesting data involving the Chicago Blackhawks and the relationship between player salaries and overall performance. Before I can go into detail about the results I need to explain what I am doing. So the first part of these articles are my attempt to explain my “chickenpox” graphs.

An XY splatter graph, or Scatter plot is used when you want to look at the relationship of one variable with another. In our case we want to look at the correlation of the salary cap cost of a player and his various performance statistics. To create the graph each player is mapped to a specific data point. The player’s salary cap cost is plotted in the X direction and one of the player’s production stats is plotted in the Y direction. So there will be one graph for each of the 4 stats I am investigating.

Once all the data is mapped I can then create a “trendline” to view the relationship between the specific performance stat and the player’s salary cap cost. Using this technique the curve of the trendline is important. Trendlines that increase quickly show a strong relationship between the two variables. Trendlines that increase slowly do not.

Finally we can look at the R squared value to determine how closely the data “fits” the trendline. An R squared value of 1 means the data fits the trendline closely.

**Now about the data**

So what I did here to obtain the data is combine the information from two sites. I’m using 5on5 min 50 gp player’s stats from behindthenet. And combining that information with capgeek.com’s salary cap information.

If you click on the thumbnail above you will get my first graph. This graph shows player’s goals/60 values over player’s salary cap costs. I ended up using logarithmic trendlines for this data because that gave me the best “r-squared” results. Even with that the r-squared values were not very good.

That is because there really isn’t a strong correlation between salary costs and overall performance. As an example, 821K player Claude Giroux scores more frequently per time on ice than 9.538M Alex Ovechkin. And that happens all over the salary cap spectrum. In both positive and negative directions.

There is however, some correlation between salary cap costs and performance. The trend does go up as salaries increase. It is just that the growth slows as salaries increase which is why a logarithmic trendline is most appropriate.

This means that high priced players are generally less cost effective than mid range players. And Entry Level and Restricted Free agent contracts tend to be the most cost effective per overall performance. Well the good ones at any rate.

And in fact the best use of salary cap space is to try and keep your team from relying on 500K players. The biggest bang for the buck (or where the trend-line rises the quickest) is between the 500K player and the 750K one. And the next biggest is between the 750K player and the 1M player. Looking at the top end, players at the top of the 800K range have 10 more goals and 25 more points than players in the 500K range.

In fact the costs are almost exponential. The trend-line jumps up ~.25 goals/60 between the 500K player and the 1M player. That same increase is not seen until you go from the 1M player to the 2M player. And that increase is not seen from the 2M player until you reach the 4M player. And that same increase from a 4M player is not seen until you reach the 8M range.

So this leads to an interesting observation. One of the biggest reasons the Hawks struggled last year was because of the need to rely on 500K players like Nick Boynton, Jassen Cullimore, Fernando Pisani and Jake Dowell. One of the most significant differences between last year and this year is the increase in Blackhawk’s salary cap. This means the Hawks won’t need to rely on min contract players for as many positions as the 2010/11 season.

**Playoff vs non Playoff Team Players**

In looking at this data I couldn’t decide whether I should use all the players who met my criteria or just the players from playoff teams. That got me thinking that I should first compare the playoff team players with the non playoff team players to see if there was actually any difference.

In this graph the playoff team players are in blue and the non playoff team players are in yellow. From the two trend-lines you can see that the overall expected performance of playoff team players was better than the overall performance of non playoff team players. And that was true throughout the entire salary cap range.

I was a little bit surprised by this. I was expecting the Entry Level Contract range of non playoff teams players to actually have a better performance than the playoff teams. They are getting the better draft picks after all.

One of the possible explanations of this is that unrestricted free agent 4th line players (who are also in this price range) get to choose who they sign with. If those players are outperforming non playoff team prospects then it is possible that these free agents have a bigger impact on the league than I originally thought.

Also if you look at the comparisons of blue to yellow you see that there are more non playoff team players in the 1.5-4M range and many more playoff team players in the 4.5M and above range. The NHL is clearly a “have and have not league”

I also found it interesting that the top paid non playoff team players can compete in goals/60 with playoff team’s top players.

However those same top end non playoff team players can not compete with top end playoff team players in points. Is that because they do not have as good of teammates?

The Goals For/60 information gave me similar results to points.

However, I was really not expecting the significantly larger difference in Goals Against/60. Non playoff team players can somewhat compete in scoring goals with their playoff team counterparts. They just can’t match them defensively. Of all the data, this was the most interesting to me because it was the least expected.

So that is my presentation of my data. Now that I have done that I am going to compare the Chicago Blackhawks players with the overall performance values of the Playoff team players. I then am going to look at how the Blackhawks compared specifically to the two Stanley Cup Finalists. Finally, I am going to look at the Hawks top 4 paid forwards against the top 25 – 5M and above players.

In the conclusion of my intro, I found this data and the observations from it to be really interesting and I hope you will too.