When trying to choose a topic to research I tried to find one that interests me. I decided that I wanted to look at nhl players' statistics in some way



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Introduction:

When trying to choose a topic to research I tried to find one that interests me. I decided that I wanted to look at NHL players' statistics in some way. Since I am a goalie myself I choose to look at goalies in particular. From looking at all of the statistics I decided to look at salaries more thoroughly since I believe that professional athletes are severely overpaid. When coming up with a question I decided to look at what factors affect NHL goalies' salaries since I had a lot of statistics that I could use to answer that question. The sampling technique I used was convenience sampling because once I found a website with most of the information I needed I only used those goalies to research further. The goalies I looked at were the top forty-five goalies with the highest salaries. There was possibly some sampling bias in the information I gathered because it is from the 2009/2010 season, which is after the salary cap was implemented, so the salaries aren’t an accurate representation of the years previous to the salary cap.


The following positively skewed box plot shows that the majority of goalies are paid between 1 and 5 million dollars a year, while very little are paid less than 1 million and a significant amount are paid between 5 and 7 million. The summary chart also shows that the average salary of an NHL goalie is 3.0173 million dollars per year and the box plot shows that the median salary is 2.6 million dollars a year. I could not find the average salary for all goalies in the NHL for the 2009/2010 season so that I could compare the average I found of the top 45 highest paid goalies in the NHL. However, the overall average salary for all NHL players including goalies is about 1.9 million dollars for this season. Even though I only looked at the top 45 goalies, there are only 73 goalies total who have played a game this season in the NHL, so the average wouldn’t be too much different than the average I found for the top 45 goalies. From this information it is clear the NHL goalie typically get paid more than NHL players; probably a about one million dollars more on average. With salaries that high I knew there would have to be many factors that affect the salaries of goalies and I was intrigued to find out which ones had the largest effect.



Question: What factors affect an NHL goalie's salary the most?
Hypothesis:

Based on my knowledge of hockey, I believe that years in the NHL, games played last year and goals against average last year will be the three factors that affect NHL goalies' salaries the most.


The following data shows all of the factors that I looked at to determine what affects NHL goalies' salaries:

The factors that I looked at were; birthplace, current team, age, height, weight, year drafted, round drafted, overall draft pick, games played last year, wins last year, losses last year, shootout losses last year, shutouts last year, goals against last year, save percentage last year, goals against average last year, minutes played last year, years in the NHL, total games played, total save percentage and total goals against average. (For definitions and calculations of the factors looked at refer to glossary at the end).

The first factors I looked at were birthplace and current team, however I did not compare them directly to the average salary, I just looked at the frequency of goalies that came from each country or played for each team that were in the group of goalies with the top 45 average annual salaries.

This graph shows that Canada has by far, the highest frequency of goalies that make it into the NHL and have a salary ranked in the top 45 highest salaries. This does not however mean that Canadian goalies make more money than goalies from different countries, it could just mean that there are more Canadian goalies in the NHL. I was surprised that the United States did not have a very high frequency of goalies with the top 45 highest salaries since hockey is so big in the states.



This graph shows that most teams either have only one or two goalies with high salaries and their third string goalie has a low salary. The teams with only one goalie in the top 45 highest salaries only pay their starting goalie a high salary which makes the most sense since they are the ones playing the majority of the games, however it is beneficial to have a backup goalie who is good enough to pay a large amount to, incase your starter goalie gets hurt, this is why many teams have two goalies with high salaries. However, the two outliers in this graph are the New York Islanders and the Atlanta Thrashers, whose goalies are all paid an amount high enough to be ranked in the top 45 highest salaries.

Next, I choose to examine the physical characteristics of goalies to see which of them had the greatest impact on salary.



The graphs above showing height and weight being the explanatory variables and average salary being the response variable, indicate that as your body size increases, the amount of money you make decreases since both slopes are negative. The slope of the line of least squares for the graph comparing height and average salary indicates that for every inch taller a goalie is, his salary goes down by $329 000. The correlation of -0.30867281 between height and average salary shows that they have a negative, weak correlation, meaning that height has little effect on an NHL goalie’s salary. The slope of the line of least squares on the graph comparing weight and average salary shows that for every pound heavier a goalie is, their salary decreases by $2 150. The correlation of -0.015385332 between these two variables shows that weight has virtually no impact on an NHL goalie’s salary. I found this information interesting because I assumed that bigger goalies would make more money since they would take up more net and probably get less goals scored on them , which would in turn allow them to make more money since they are doing a better job. Since I am a goalie I decided to check what my salary would be according to my height and weight by extrapolating. Using the equation of the line of least squares from the graph comparing height and average salary, I plugged in my own height to fins out what my salary would be. From that equation I found that based on my height I would have a salary of 5.257 million dollars if I was an NHL goalie. Next, I did the same thing for my weight. From that equation I found out that based on my weight I would only make 3.142 million dollars if I was an NHL goalie. I found this information interesting because my salary based on my height was significantly higher than what my salary would be based on my weight.


Below are the graphs showing the relationship between goalies’ save percentages and their average salary. I found that there were outliers in this information as well so I removed them and created new graphs. These outliers were goalies with no saves last year, meaning they didn’t play any games and therefore had no stats to influence their salary for this year. In the graph showing the relationship between total save percentage and average salary there was a weak, positive correlation (0.3135), however after the outliers were removed, the correlation went from weak to moderate (0.4756) meaning that a goalie’s total save percentage does have a fairly significant effect on his salary. The slope of the line of least squares from this graph indicates that a goalie’s salary goes up by 137.2 million dollars for every 1 their save percentage goes up. However, it is impossible for a save percentage to be above 1, so I divided the slope by 100 to find out how much their salary increases for every 0.01 or 1% their save percentage increases. According to the calculation I made, for every 0.01 higher a goalie’s total save percentage is, his salary will go up by $137 200 in the next year. As for the graph showing the relationship between last years save percentage and average salary, the correlation between the two went from 0.3153 to 0.2626 after outliers were removed. This means that last years save percentage only has a weak correlation with a goalie’s average salary and therefore has little effect on his salary. The slope of the line of least squares from this graph indicates that a goalie’s salary goes up by 34.1 million dollars for every 1 their save percentage goes up. However, I had to divide the slop by 100 again since a save percentage cannot be over 1. From this calculation I determined that for every 0.01 higher a goalie’s save percentage from last year, his salary will be $34 100 more the following year. This set of graphs demonstrated that a goalie’s overall save percentage is more important than his save percentage just from last year when it comes to determining their average annual salary.






Below are the graphs showing saves last year and comparing saves last year to average salary. The graph comparing saves last year with average salary has a correlation of 0.5592, meaning that the correlation is moderate and positive. This indicates that the amount of saves a goalie makes each year has a fairly significant impact on their salary in the following year. The equation of the line of least squares line on the graph comparing saves last year and average salary indicates that for each additional save a goalie makes his salary will go up by $1570 from 1.2 million dollars if he made no saves at all. The graph strictly looking at saves last year shows that the average amount of saves a goalie with a salary ranked in the top 45 makes in a year is about 1152. I decided to plug this average into the line of least squares equation to find out much the average goalie would make a year based on the amount of saves he makes. From that equation I determined that if a goalie made the average amount of saves (1152) in a year he would receive a salary of 3.008 million dollars in the following year. Based on how strongly correlated the explanatory variables are correlated to the response variable (average salary), this information shows that the amount of saves a goalie made last year effects their salary more than their save percentage. I believe this is because it is likely that goalies with more saves over the course of the year played more games and were likely their teams starting goalie and generally starting goalies get paid the most. Where as a goalie could play only one game and have a high save percentage and not get paid as much because he is just a back up goalie.





Next I chose to look at each goalie’s record from last season in comparison to their average annual salary to see if the amount of games their teams win or lose has an effect on their salary. All three of the explanatory variables looked at in the graphs below had a positive, moderate correlation with average salary meaning that they probably al have somewhat of an impact on a goalie’s salary. Wins had the strongest correlation (0.5801), next was losses (0.4844) and the variable with weakest correlation out of the graphs below was shootout losses (0.4302). The slope of the line of least squares from the graph comparing wins last year to average salary was 0.0849 and the y-intercept was 1.3. This means that if a goalie didn’t win a single game in his season, his salary the following year would be 1.3 million dollars and his salary would increase by $84 900 for each additional game he won that season. The equation of the line of least squares from the graph comparing losses last year and average salary means that for every extra game a goalie loses in a season he will get $107 000 added to his salary for the next year. The equation of this line also shows that if a goalie didn’t lose any games in a season his salary would only be $1.5 million as shown by the y-intercept. Lastly, The equation of the line of least squares from the graph comparing shootout losses to average salary indicates that for each additional game a goalie loses in a shootout his salary will go up by $264 000 from $ 1.8 million if he doesn’t lose any games in a shootout. The information I gathered from these graphs didn’t really make sense to me since the line of least squares on the graphs showed that goalies make more money from losing more games then winning. The only rational conclusion I could draw from this information was that a goalie’s record actually had very little to do with his salary despite the moderate correlation coefficients. However the more wins, losses and shootout losses a goalie has, the more games he has played in so games played is actually the variable that affects a goalie’s salary. To further explore this prediction I decided to look at games played compared to average salary next.







The graphs below show data on the total number of games goalies have played and total games played compared to the average salary in millions a goalie makes. In the graph showing total number of games played, the median was found to be 46 which I found interesting because most teams usually have a starting goalie that has as a large salary and plays in at least 55 games and a backup goalie who has a lower salary and only plays in 20 or so games. When I looked back on my data on teams in the NHL, I noticed that a few teams had two goalies in the top 45 highest salaries and I figured that this median number must have come from one of those teams who have two goalies with high salaries who split the amount of games fairly evenly. When comparing games played last year and average salary, there correlation was found to be positive and moderate (0.5621), meaning that games played is pretty influential regarding the amount of money a goalie in the NHL makes each year. The equation of the line of least squares from this graph indicates that if a goalie played in no games at all in the previous season his salary would be 1.15 million dollars and for every additional game a goalie plays in, his salary will go up by $46 300 the next season. Based on this information I can predict that the more games a goalie plays in his current year, the higher his salary will be the next year. This conclusion was not only drawn from the graph comparing games played and average annual salary but from analyzing the rest of the graphs above as well. The graphs above showed that the more games a goalie lost the previous year, the higher their salary would be the next year which doesn’t really make sense. From this information I determined that the reason a goalie who had more losses had a higher salary is because he played in more games. For example, a goalie may have only lost 1 game and have a low salary, while a goalie who had 25 losses may have a higher salary because the goalie with 1 loss only played 3 games whereas the goalie with 25 losses played 65 games, probably meaning he was a starter goalie and would be paid more. I decided to see if my prediction that goalies who play more games in the year previous get a higher salary next year by interpolating and extrapolating. I took a small number from the graph (30) and the most amount of games a goalie could play in a season (82) and plugged them into the line of least squares equation, then found the difference between the two numbers to find out how much more money a goalie would make if he went from playing 30 games one season to 82 games the next. I found that if a goalie who played in 30 games and was likely a backup goalie got promoted to a starting goalie and played in all 82 games in the NHL season his salary would increase by 2.4076 million dollars!





The next set of data I decided to look at was comparing age, years in the NHL, and total number of games played to average annual salary. All of the following graphs have a positive correlation meaning the older the goalie, the longer they’ve been in the NHL and the more games they’ve played, the higher their salary should be. Age has a moderate correlation with average salary (0.4261) meaning that it is likely a factor that mildly affects a goalie’s salary. The equation of the line of least squares from this graph indicates that every year a goalie’s salary will increase by $162 000 based on their age. However if you look at the histogram the mean age of goalies in the NHL with high salaries is 28, so it seems as though goalies in the middle of their career receive higher salaries as well since I only looked at goalie’s with the top 45 salaries. The number of years in the NHL and also had a moderate, correlation with average salary(0.5299), meaning that it likely does have an impact on the amount of money a goalie gets every year. The equation of the line of least squares from this graph indicates that in a goalie’s first year in the NHL he will make $1.4 million and then each year his salary will increase by $226 000. When looking at the graph comparing a goalie’s total games played to their salary, the correlation is also moderate (0.6358) but it is higher than years in the NHL and age, meaning that out of these three variables, total games played seems to be the most influential on how much money a goalie makes per year. The equation of the line of least squares from this graph indicates that if a goalie hasn’t played any NHL games his salary will be $1.6 million and it will go up by $5 530 the next year, for each additional game the goalie plays in this year. Since the data comparing years in the NHL to average salary and the data comparing total games played both give different information for a goalie’s starting salary I decided to try and find an explanation for the discrepancy. Since goalies can be drafted into the NHL and receive a salary without playing in any games, a goalie could technically receive $1.4 million in his first year without playing any games and could make $1.6 million the next year. Also, if you refer to the slope of the line of least squares comparing years in the NHL to average salary, it is about $0.2 million so my prediction would make sense because that would mean if a goalie started with a salary of $1.4 million he would get $1.6 million the next year, just as my prediction stated. In conclusion, these graphs show that the more experienced the goalie, the more his contract will be. I decided to determine what my salary would be based on my age and how long I have been playing hockey as well. Since I am only 17 years old and the youngest goalie in the NHL is 19, I had to extrapolate to find this data, however I was able to interpolate to find my salary based on the number of years I’ve been playing hockey since I have played for 6 years. From these calculations I determined that my salary would be $1.05 million based on my age if I was an NHL goalie and $3.89 million based on how many years I’ve been playing hockey. The discrepancy in this information is due to the fact that I have been playing hockey since I was 6, however NHL players cannot start playing in the NHL until they are 18, so my information isn’t really correct.





In the top left graph goalies’ total goals against averages are being compared with their average salary and a very weak, positive correlation was found between the two variables (0.1644). The goalies who hadn’t played any games in the NHL and therefore had no goals against average were then removed as outliers and the correlation changed from being weak and positive to being moderate and negative (-0.4313). The graph on the right with the outliers removed is much more accurate and makes more sense because as a goalie a lower goals against average is better, so there should be a negative correlation between goals against average and average salary. The equation of the line of least squares from this graph indicates that a goalie with a goals against average 1 higher than another goalie would have a salary that is $3.4 million lower than that goalie! The two graphs below show the same thing except just the goals against average from last year instead of total and that correlation with average salary is much weaker (-0.2422) than when total goals against average was compared (-0.4313), meaning that the total goals against average is more important than last years goals against average when determining an NHL goalies’ salary. The equation of the line of least squares from this graph indicates that for every 1 a goalie’s goals against average goes up or gets worse, his salary in the following year will go down by $1.22 million. This seems like a dramatic number, however for a goalie’s goals against average to go up by one, he would have to let in one more goal than last year in every single game he played in and it would be very unlikely for a goalie to get that much worse in one year. I decided to plug in my goals against average from ball hockey last season (2.54) since I had access to it to see what my salary would be based on my goals against average. From this calculation I determined that my salary would be $3.564 million based on my goals against average.






Next, I decided to look at draft numbers and compare them to goalies’ average annual salaries. The first graph shows the year the goalie was drafted into the NHL compared to the average salary they make and it has a moderate, negative correlation (-0.411). This means that goalies just coming into the NHL are starting off with lower salaries than goalies who have been playing in the NHL for years. The equation of the line of least squares from this graph indicates that a goalie just coming into the NHL will make $173 430 less than a goalie drafted one year before him. The next graph shows the correlation between the average salary and the round the goalie was drafted in, which is very weak and positive (0.1216). This means that the round the goalie was drafted has a very small impact on the salary the goalie receives if it has any impact at all. The equation of the line of least squares from this graph indicates that a goalie drafted one round after another goalie will make $84 400 more than the goalie drafted before him. This doesn’t make sense because the best goalies are usually picked in the earliest rounds, so it is pretty clear that these two variables are unrelated. Lastly, the overall draft pick has virtually no correlation (0.0646) with average salary as shown by the bottom graph. This means that the overall draft pick has basically nothing to do with the salary an NHL goalie receives so I did not bother to analyze this variable any further. In conclusion, of these three graphs relating to drafting, the year drafted is the only factor that proves to have an impact on goalies salaries.





Lastly, I decided to look at how goals against and shutouts affected NHL goalies’ salaries. The first graph shows the total goals against compared to average salary and they have a moderate and positive correlation (0.5298). The equation of the line of least squares from this graph indicates that if a goalie did not let in any goals last year his salary would be $1.15 million and it would increase by $18 000 for every goal he let in. Since the graph indicates that the more goals a goalie lets in, the higher their salary will be I believe that the relationship has more to do with the more goals a goalie lets in, usually they will have played more games, making them a starting goalie, which would indicate a higher salary. Lastly, shutouts from last year was compared with average salary and was found to have a moderate, positive correlation (0.4154), meaning it should have some impact on determining an NHL goalie’s salary. This makes sense since a shutout is essentially a perfect game for a goalie and every coach wants a goalie who can handle the pressure of keeping a shutout. The equation of the line of least squares from this graph indicates that if a goalie got no shutouts, his salary in the following season would be $2.2 million and would go up by $313 000 for every additional shutout he earned. Finally, in the graph showing the frequency of shut outs last year the average is under 3. I found this to be interesting because the average amount of games a goalie plays is 40, as shown in the graph showing games played last year above, however they only get less than 3 shutouts out of all those games. Being a goalie I know it is difficult to get shutouts, however I expected the numbers of NHL goalies to be a little bit higher than that. I wanted to find out the reason for this discrepancy and u remembered that just recently they made goalie’s change to smaller equipment. For example, pads went from being 12 inches wide to being 11 inches wide and this is probably a big contribution to the low numbers of shutouts goalies are getting now. Since shutouts last year had a pretty high correlation with average salary I decided to extrapolate to see how much money a goalie would make if he got 20 shutouts in one season. From this calculation I determined that if a goalie got 20 shutouts in one season he would have a salary of $8.46 million in his next season!




Conclusion:

The five factors that I found to have the most impact on an NHL goalies salary based on the strength of their correlations in order are; total games played (0.63585762), wins last year (0.58015612), games played last year (0.5620546), saves last year (0.55917401) and years in the NHL(0.52985582).I based my conclusion on correlations because I was trying to find out which variables had the most impact on an NHL goalie’s salary and correlations describe how closely related two variables are. All of the factors listed above still only have a moderate correlation, some are just stronger than others, this means that there are very many factors that influence an NHL goalies salary, not just a few really strong influential factors. Before gathering my information and analyzing the graphs, I hypothesized that years in the NHL, games played last year and goals against average last year would have the biggest impact on an NHL goalie’s salary, therefore two of my hypothesized factors were correct. I guessed that years in the NHL would be a big factor because I know that rookies can only make up to a certain amount of money each year and generally the more experienced you are, the more money you make, or if you aren’t good enough to make a lot of money, you probably won’t stay in the NHL for many years. I figured that the amount of games played last year would have a big impact on goalies’ salaries because I know that starting goalies usually make more money and starting goalies would have played the most games on their team. Lastly, I thought that goals against average last year would have an impact because generally coaches want goalies with a low goals against average and goalies who did well in their last season and they’re willing to pay them more. I think the reason why goals against average from the previous year didn’t have as much of an impact as some other factors because if a goalie isn’t on a good team then their goals against average will be lower but that doesn’t mean they should be paid less. I think the top five factors with the largest impact on goalies’ salaries have the most impact because they are all either related to how long the goalie has been playing or if he is the starting goalie or not. In conclusion, goalies who have been playing in the NHL for a longer time are going to have higher salaries than guys just coming into the NHL and starting goalies are going to be paid more than backups. There are many factors that affect an NHL goalie’s salary but they mostly have to do with experience.




Goals against average: (GGA) is calculated by dividing the total amount of goals scored on the goalie by the total number of games the goalie has played.
Overall draft pick: The actual number, in order the goalie was drafted out of every player and goalie drafted into the NHL.
Round drafted: Refers to which of the five rounds in the NHL entry draft the goalie was drafted.
Save percentage: Is calculated by dividing the amount of saves made by the goalie by the amount of shots taken on net.
Shutout: Is when a goalie does not allow any goals in a game.
Year drafted: The year the goalie was drafted into the NHL by an NHL team.

“NHL Salary Database.”< http://static.fantasysports.ca/NHLSalaryData/globe/top100avg-G-salary.html> updated September 9th, 2009.


“NHL.com, The National Hockey League” <http://www.nhl.com/ice/app> updated January 19th, 2010.
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