Strength of Schedule calculations changed

Editors Note: Adjustments made to this blog to account for slight changes in the women’s SOS calculations as well.

2013 NCAA Basketball ChampionshipFor many of our mathematicians and number crunchers on the D3boards have been struggling with one thing since the Regional Rankings came out: they couldn’t get the SOS numbers the NCAA released to jive with their calculations. After all, there isn’t anything overly complicated with the calculations. The basics are this: a team’s Opponent’s Winning Percentage (OWP) x 2/3 + the Opponent’s Opponent’s Winning Percentage (OOWP) x 1/3. Another key is the fact that a multiplier of 1.25 is used for road games, 1.0 for neutral games, and 0.75 for home games in the OWP and OOWP for the men’s side of things.

For the mathematicians and the number crunchers, they break out their Excel sheets, paper, pencil and calculator, or whatever they use and they plug in the results for all Division III games into that and they come out with the overall SOS. However as I mentioned, they couldn’t figure out why their numbers weren’t adding up this past week.

Well, it turns out that is because the NCAA changed one simple thing in how they crunch the numbers and, well, forgot to tell everyone. (When reading through the 2013 Division III men’s pre-championship handbook it appears the change has not been rewritten in this material – but that is for others to figure out.)

The decision was made by the Championships Committee back in September and was apparently made because the original SOS calculations was coming up with some screwy numbers, especially in Division II where some provisional members were not playing a majority of their games in the division and that resulted in smaller win/loss numbers and thus, maybe, some inflated win-loss percentages. The previous means of calculating the SOS was apparently then causing what was perceived as inflated or deflated SOS’s.

To explain the change, let’s start with how they originally did the math for a men’s team. Here is Team A’s schedule over eleven games:

Opponent W L WP Mult. Average
Team B 9 1 .900 1.25 1.125
Team C 9 3 .750 1.25 0.938
Team D 5 2 .714 1.25 0.893
Team E 7 4 .636 1.00 0.636
Team F 6 4 .600 1.25 0.750
Team G 6 4 .600 0.75 0.450
Team H 6 4 .600 1.25 0.750
Team I 4 5 .444 0.75 0.333
Team J 4 6 .400 1.00 0.400
Team K 4 8 .333 1.00 0.333
Team L 1 7 .125 1.25 0.156
        Total: 6.764
        SOS (total/games): .6149

However, here is the change. They are now calculating based on each raw number, not the overall percentage. So here is Team A’s exact same schedule with this raw number calculation instead:

Opponent W L Mult. Raw Ws Raw Ls
Team B 9 1 1.25 11.25 1.25
Team C 9 3 1.25 11.25 3.75
Team D 5 2 1.25 6.25 2.50
Team E 7 4 1.00 7.00 4.00
Team F 6 4 1.25 7.50 5.00
Team G 6 4 0.75 4.50 3.00
Team H 6 4 1.25 7.50 5.00
Team I 4 5 0.75 3.00 3.75
Team J 4 6 1.00 4.00 6.00
Team K 4 8 1.00 4.00 8.00
Team L 1 7 1.25 1.25 8.75
      Total: 67.50 51.00
      SOS (WP): .5696

Certainly the difference between .6149 and .5696 looks large (.05!), but this is just 11 games and obviously by this point in the season we are looking at give or take 20-plus games on a team’s schedule, so the amount of data is greater and the numbers are probably a bit closer. Of course the biggest difference will come for teams that play teams with less regional results than others who maybe play all of their games in region.

Now for the women, they do not use the multiplier the men do, but if we are talking about adding just the numbers and not averaging the averages… there is a slight change. Below is a table for Team A’s opponents:

Opponent W L WP
Team B 9 1 .900
Team C 9 3 .750
Team D 5 2 .714
Team E 7 4 .636
Team F 6 4 .600
Team G 6 4 .600
Team H 6 4 .600
Team I 4 5 .444
Team J 4 6 .400
Team K 4 8 .333
Team L 1 7 .143
 Totals:  61 48
 SOS:  .560 .556

The .560 would be the new SOS… the .556 would have been the old SOS number. Yes, the number is ever so slightly different especially compared to the men, but it is an adjustment.

This doesn’t look initially like it will have a large or dramatic impact on Division III. I am sure our mathematician friends can say more about this, but it appears the NCAA is breaking down the numbers in more detail to get more accurate information than in the old system.

I hope that helps, but I will let our math friends be the ones who can break this down further on the merits of the decision.

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