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General Discussion on Hockey Scoring

Over time, statistics have become a bigger and bigger part of the professional game of hockey. When the NHL was created in 1917, the only statistics that were kept were the extreme basics; goals for and against per team, and wins, losses, and ties. More over, only one person, the sports editor of a Montreal newspaper, kept this data. Throughout the years, the types of data recorded grew slowly. By the early 1960's, the NHL had a statistician for the league, and the different types of statistics collected became quite impressive.

Today, these statistics can be quite important, since many players have certain clauses in their contracts that depend on these statistics. For example, many defencemen can receive bonuses based on their plus-minus ratings (the number of even strength goals scored when that player is on the ice minus the number of even-strength goals scored against), while other players also have bonuses based on the more conventional individual goal and point totals. Also, teams as well as the league, can examine the statistics to try to determine certain trends in the game, and use the information to develop means to influence these trends. For example, a "hot" issue in the sports media right now is the number of head injuries that occur in the NHL. Because of the comprehensive statistics kept by the NHL, the public is aware that there has been an alarmingly increasing trend in the number of head injuries in the past decade, and is putting pressure on the league to address this issue.

With this impressive collection of data, we feel that the next natural step is to try and forecast the data. However, there are certain problems that arise when considering this. First, the main problem is that the data has not been collected over a long enough time period. Statistics on injuries have only been collected for the past two decades. Data that has been around since the early sixties, which includes plus-minus, power play goals, and penalty minutes, still only have about 30 yearly data points, which is usually not a large enough quantity when trying to develop a predictive forecasting model. The most reliable data that has been collected for a relatively long period of time is goals scored. So, although the NHL houses an impressive array of different types of data, it is probably going to be a while before predictive models can be used with a high degree of reliability.

The final model that we use to predict future values for average number of goals per season is the ARIMA (0,1,0) model. This is simply the "naive forecast". Although it does appear to provide reasonably good statistical results, we expected to be able to find a model that did better than the naive forecast. Thus, our goal was only partially achieved.

One would probably think, when trying to predict average number of goals per game, that the changes in the average number of goals scored per game in a season is fairly easy to explain, and thus fairly easy to forecast (we certainly did at the start of this project!). However, this is completely untrue. We believe the reason behind this is that there are many contributing factors to the number of goals scored in a season, although, how these factors contribute to the number of goals scored, and how these factors are correlated with one another, can only be determined in hindsight. A perfect example of this is the introduction of the crease rule in the 1991-1992 season. This rule states that, "a goal is disallowed if puck enters net while a player of the attacking team is standing on the goal crease line, is in the goal crease or places his stick in the goal crease" (The National Hockey League Official Guide and Record Book, 1993). There were no other significant rule changes, and no other major changes to the makeup of the game (one expansion team was introduced into the league, the San Jose Sharks). Rationally, one would assume that the average number of goals per game would decrease significantly, especially since the rule was designed to stop players from crashing into the goalie, trying to bang the puck into the net. However, not only did the average goals per game not go down, they actually increased slightly! The only conclusion that can be reached is that there were other, more invisible factors contributing to the increase in goals.

There are many situations like this. In the 1998-1999 season, the league specifically sought to try and increase goal output, and to do this they restricted the size of goalie equipment, since the league felt goalies were gaining an unfair advantage from oversized equipment. Also, the size of the crease was decreased to cut down on the "in-the-crease" infractions discussed earlier. However, at the end of the 1998-1999 season, goal averages had not changed at all from the season before.

The most probable explanation is that the rules do have a slight effect on the average number of goals scored per game, however, there is a more overriding factor. We surmise that this factor is simply the general trend that the game of hockey is going through. For example, without looking at the average goals per game, the late seventies and most of the eighties are generally regarded by hockey analysts as an era of extremely offensive-minded hockey, with perhaps even weak goaltending (Total Hockey, "The Evolution of Hockey Strategy", 1998). The fifties are generally regarded as a defensive minded, almost boring era. In the mid-nineties, many teams were coping with an overall lack of talented players, and as such the "neutral zone trap, clutch and grab" type hockey became extremely popular (Total Hockey, 1998). This style of hockey did not require extremely gifted players, and its purpose was to basically slow down the talented opposing players. Obviously, this style of hockey is not very committed to goal scoring.

Looking back on the average goals per game, you can clearly see that these trends existed. The problem is that these trends are really only visible in hindsight, and are practically impossible to predict (especially by any statistical means) into the future. For example, we may be in the midst of a change in trend right now. In 1998-99, under a new coach, the Toronto Maple Leafs tried a more offensive approach to hockey that hasn't been seen in a while. The results were extremely positive, and they vaulted from 20th place in the 1997-1998 season to 5th overall in the 1998-1999 season. The next year some some teams started switching their style to a more open, offensive type of hockey. This trend though did not last for long.

There probably are certain statistics that help explain the average number of goals in a season, such as number of penalty minutes, power play goals, and number of man-games lost to injuries. However, this data occurs at the same time as the average goals per game, so there is little predictive value in them. A correlation can be determined by looking at past data, but is of no use for forecasting.

Although our initial aims were achieved to a point, it is disappointing that we were not able to help explain the average number of goals per game with a relevant explanatory variable. It appears that this is the nature of the data, similar to the data observed in the stock markets. Based on this, it is logical that our best predictive model was similar to a "random walk". Unless someone in the future can uncover a hidden relationship between another factor and average goals per game, it is unlikely that a better predictive model will be created. The only improvement may be simply the benefit of more data, where perhaps more robust parameters may be determined.

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