Here is a step-by-step guide as to how to calculate the Noll-Scully measure of competitive balance. Note that I will include both the case where a team can have only two outcomes (a win or a loss) and where a team can have three outcomes (a win, a loss or a tie). I will also report both calculations of the actual standard deviation of winning percent using a sample and using a population. They will also help for comparison purposes.
Remember the Noll-Scully measure of competitive balance is calculating how far a particular sport or league's distribution of wins deviates from the purely random outcome (i.e. equal playing strength).
Step 1: Get League Standing Data. Download the league standings data - typically at the end of the regular season - and insert it into a spreadsheet. (If you are having trouble getting the standings data from a webpage to paste easily into Excel, I suggest that you use the Mozilla Firefox browser and copy the data from the data using Firefox to Notepad (can be found under All Programs | Accessories on a Windows computer) and paste the data into Notepad, then copy all of that data from Notepad and paste into Excel - works great for me, though I don't know why).
Step 2a: Calculate Actual Standard Deviation. For leagues with only wins and losses, such as basketball or baseball, to calculate the actual standard deviation of winning percentage in Microsoft Excel if the winning percent data is in Column C and there are 30 teams, then for a sample you will use the formula =stdev(C2:C31) and for a population use the formula =stdevp(C2:C31).
Step 2b: For leagues with wins, losses and ties, first calculate winning percent as (# of wins * 2 + # of ties)/(# of games played * 2), and then in Microsoft Excel if the winning percent formula is in Column C and there are 30 teams for a sample you will use the formula =stdev and for a population use the formula =stdevp. (I will let the statisticians argue which is more appropriate of the two).
Step 3a: Calculate Idealized Standard Deviation. For leagues with only wins and losses, such as basketball or baseball, to calculate the idealized standard deviation of winning percentage in Microsoft Excel if the winning percent data is in Column C and there are 30 teams, you will use the formula =average(C2:C31)/SQRT(B2), where B2 is the number of regular season games played.
Step 3b: For leagues with wins, losses and ties, [(1-p)/4n]1/2, where p is the probability of a tie under the equal playing strength assumption and n is the number of games played. Richardson's Eastern Economic Journal paper suggests using playoff series games that went six or seven games and calculating how many were tied at the end of regulation. That seems reasonable to me, so this will need to be figured out separately for the league you are using. Once that is done, use the probability of a tie for (p) and the number of regular season games played for n, and this is the idealized standard deviation of winning percent for a league that has wins, losses and ties.
Step 4: Calculate the Noll-Scully Competitive Balance Measure. For both types of leagues, if the actual standard deviation of winning percent is in cell D2 and the idealized standard deviation is in cell D3, then in cell D4 insert the following formula: = D2/D3, and that is the Noll-Scully competitive balance measure.