Trevor Hardy
CFL.ca
Okay. Raise your hands – both of you – that had Hamilton over Montreal, BC over Calgary and Edmonton over Saskatchewan this past weekend.
But really – should we be surprised? I mean, the only predictable thing about the 2010 season has been its unpredictability.
Going all the way back to Week 1 of this season, you may remember Winnipeg beating Hamilton by 20 points. And just two weeks later? Hamilton beats Winnipeg by 21!
Or how about those crazy Montreal and Calgary backtoback games in early October? Calgary looked like the far superior team in the first game, but then Montreal comes back with a huge game in the second.
Sure, I’ll admit it – I didn’t expect Toronto to lay a beating on Montreal back on August 14 (especially after having Montreal beat them by 31 points just two weeks earlier). Nor did I expect Toronto to go into Mosaic Stadium and hand the Roughriders their first loss at home in over a year.
And how about Winnipeg? Up to this weekend, they had scored more points than they had allowed – but somehow had managed a record of 4 wins and 11 losses. This almost defies logic!
All these crazy results got me thinking: Is 2010 the most competitive CFL season ever? Let’s do some math and find out!
MEASURING COMPETITIVE BALANCE
I’ve decided to answer the question of whether the 2010 season is the CFL’s most competitive ever by comparing historical endofseason winning percentages. To do this, I will calculate the spread of winning percentages leaguewide. This calculation will result in a statistic known as “standard deviation”. Don’t worry – I will describe this in a moment.
I’ve also chosen to compare the CFL to other professional sports leagues using the same calculation.
And while I acknowledge that there are plenty of other ways to assess competitive balance (margin of victory, championships won), I’ve chosen to look at the historical spread of leaguewide winning percentages because I believe the results are easy to compare – not just from year to year, but even from sport to sport.
SCOPE OF REVIEW
Before we begin, let’s first disclose the information I’ve looked at in order to arrive at my conclusions:
 Each CFL team’s season ending wonloss records for the period 1980 to 2009, inclusive, plus each CFL team’s wonloss record for the 2010 season up to and including games played to October 23, 2010.
 Each NFL team’s season ending wonloss records for the period 1980 to 2009, inclusive.
 Each NBA team’s season ending wonloss records for the period 1980 to 2009, inclusive.
 Each MLB team’s season ending wonloss records for the period 1980 to 2009, inclusive.
You might be wondering why I’ve decided to exclude the NHL from my analysis. Well, I’ve found that the existence and prevalence of tie games in the NHL (prior to the adoption of the shootout beginning in 2005) unnecessarily complicates the comparisons among leagues and has the potential to skew the results and conclusions. And quite frankly, after compiling all of those other results I was just flatout tired!
THE STANDARD DEVIATION MEASUREMENT
I understand that the term “standard deviation” may be a term many of you may not be familiar with, so I’ll spend a bit of time introducing it to you.
Okay, before we go ahead and calculate “standard deviation”, we first need to calculate something called the “mean”.
Now, when we use the word “mean” in statistical analysis, we’re not describing Rob Murphy’s attitude toward opposing defensive linemen. Instead, the word “mean” in statistics is simply another word for “average”.
Most of you are probably already quite familiar with calculating averages, or “means”. If so, you’re already half way to knowing how to calculate a standard deviation. For those of you that don’t know how to calculate a mean, I’ll use some recent CFL data to illustrate:
TABLE 1  
CLUB  2009 Winning Pct. 
Montreal  .833 
Saskatchewan  .588 
Calgary  .588 
Hamilton  .500 
Edmonton  .500 
B.C.  .444 
Winnipeg  .389 
Toronto  .167 
To calculate the average leaguewide winning percentage in 2009, you would need to add up all the winning percentages in Table 1 above (4.009) and then divide this number by the number of teams (8), which results in an average leaguewide winning percentage of .500.
In fact, it should be no surprise that the average leaguewide winning percentage for the CFL in 2009 was .500. This is because the average leaguewide winning percentage is ALWAYS .500. This is because every time one team wins, another team must lose.
I will use this “mean” of .500 to perform our standard deviation calculation next. And it’s probably best to illustrate the concept of deviation with another example, so here goes:
Imagine a perfectly competitive season, one in which your team had the same record as every other team. If you were to look at the standings, the winning percentages would look like this:
TABLE 2 

CLUB  Imaginary Winning Pct. 
Montreal  .500 
Saskatchewan  .500 
Calgary  .500 
Hamilton  .500 
Edmonton  .500 
B.C.  .500 
Winnipeg  .500 
Toronto  .500 
Once again, our “mean” leaguewide winning percentage is .500, as it always will be. And since every team’s winning percentage is exactly the same as the leaguewide “mean”, there is no “deviation” from the mean. That is, in this extremely unlikely scenario, the standard deviation of winning percentages would be nil (zero). And it is this scenario that would appear to represent the most competitive league – every team has the exact same record (don’t get us started on the tiebreaker rules).
The standard deviation of nil we just calculated would increase under a scenario which the CFL had at least one team with a winning record (and, by association, at least one team with a losing record).
For example, if we were to change the imaginary results presented in Table 2 above by just one game, we would see that the standard deviation would increase. Let’s assume that, instead of every team having a .500 winning percentage, only six teams have a .500 winning percentage and the two other teams have 10 – 8 and 8 – 10 records:
TABLE 3 

CLUB  Imaginary Winning Pct. 
Montreal  .556 
Saskatchewan  .500 
Calgary  .500 
Hamilton  .500 
Edmonton  .500 
B.C.  .500 
Winnipeg  .500 
Toronto  .444 
Once again, the “mean” leaguewide winning percentage is .500. However, now we have two teams which have “deviated” from the “mean”. In fact, the standard deviation of the winning percentages in Table 3 above is .028.
At this point, you might be wondering about two things:
 How to calculate standard deviation; and
 The maximum standard deviation of leaguewide winning percentages.
With respect to the standard deviation calculation – well, it’s not a particularly difficult calculation – it just takes a bit of time to do manually. It may be easiest for you just to use the automatic Microsoft Excel or calculator function rather than explain it here.
And having learned that the minimum standard deviation of leaguewide winning percentages is nil, you might be surprised to learn that the maximum standard deviation of leaguewide winning percentages is .500. Let me explain:
The maximum standard deviation of leaguewide winning percentages would occur under a scenario where the league was at its least competitive. This would be where four teams would have perfect records and the other four would have no wins. Of course, the chances of this ever happening in the CFL are impossibly small, but let’s suspend our disbelief just for a moment and imagine the following:
TABLE 4 

CLUB  Imaginary Winning Pct. 
Montreal  1.000 
Saskatchewan  1.000 
Calgary  1.000 
Hamilton  1.000 
Edmonton  .000 
B.C.  .000 
Winnipeg  .000 
Toronto  .000 
The reason that the maximum standard deviation of leaguewide winning percentages is .500 is because the deviation is measured beginning at the “mean”. Since our “mean” winning percentage is .500, and we know that a team’s winning percentage can never be more than 1.000 or less than 0.000, the most a team could ever “deviate” from the mean is .500.
THE RESULTS
Okay, now that we’re all experts on how to calculate standard deviation, let’s see in Figure 1 below how competitive the CFL has been over the last 30 years, based on our calculation of standard deviations of leaguewide winning percentages.
You will notice that, based on our standard deviation calculations, the competitiveness of the CFL has varied significantly over the last 30 years. Based on a cursory viewing of Figure 1 below, the CFL appears to have been at its least competitive in 1981 (when the standard deviation of leaguewide winning percentages was highest), and at its most competitive in 1990 (when the standard deviation of leaguewide winning percentages was lowest). There appears to have been an extended era of relative competitive imbalance in the mid1990s, which was followed by a noticeable increase in competitiveness in the late 1990s and early 2000s.
Anyway, how do these historical results compare with what we’ve seen so far in 2010? Well, up to October 23, 2010, the standard deviation of leaguewide winning percentages was slightly less than 15%. Which when you compare to Figure 1 above will reveal that 2010 has, indeed, been a very competitive season. A standard deviation of 15% is well below the average, indicating a more competitive season than normal.
While I was at it, I thought it might be interesting to compare the CFL to other professional sports leagues. These results are presented in Figure 2 below, which plot the standard deviation of leaguewide winning percentages of the CFL, NFL, NBA and MLB. Figure 2 appears to show us that the CFL is, on average, about as competitive as the NFL. The NBA appears to be slightly more competitive than the CFL, while MLB is significantly more competitive than any of the professional sports leagues studied.
We could hypothesize a whole bunch as to why MLB appears to be so much more competitive than other sports leagues. Why do you think this is so?
And while MLB appears to be a lot more competitive than the CFL based on the standard deviation measurement, the good news for fans of the CFL is that our league appears to be getting more competitive over time. And this is occurring at a time when it appears that the other professional sports leagues studied may be getting less competitive, based on our standard deviation measurement. The average standard deviations of leaguewide winning percentages for each decade have been calculated and summarized in Table 5 below:
TABLE 5  
Avg. Standard Deviation  19801989  19901999  20002009 
CFL  .187  .195  .166 
NFL  .185  .185  .193 
NBA  .147  .167  .147 
MLB  .065  .066  .071 
The NFL’s standard deviation is trending upward over time, indicating that it may be becoming less competitive. In the three decades studied, the NBA was at its least competitive in the ‘90s, with its results in the last decade reverting to levels seen in the ‘80s. Meanwhile, MLB has seen its clubs’ winning percentages show increasing deviation, possibly indicating a league that is becoming less competitive over time.
The good news for CFL fans is that our league appears as competitive – and unpredictable – as ever! Should be an exciting road to the Grey Cup!