A Broken Tie

by Maine Basketball Rankings

At first, it was a 3-way tie. When you look at as many playoff scenarios as I do, ties stand out. But 3-way ties? Oh man.

The model runs a different final standings every day, and most of them disappear. Upsets happen. Help points change. But 8 days later (an eternity!), there’s still this tie.

Only…it isn’t a tie. The numbers look identical, but Excel is putting one team ahead of the other. At first, I thought it was a mistake. There’s not a lot of variety in what numbers get put into the Heal Points, so it’s very unlikely that 2 teams in the same class could get so close and not be a tie. In the Power Rankings, sure. But not in the Heals. It had to be a mistake.

It isn’t.

The tie is broken at the 11th decimal place.

When the Heal Points were created, we didn’t have Excel or other programs that calculated the Heal Points for us. They were done by hand. And I think what’s happening here is a limitation of that era is going to determine a playoff spot.

Oh, and the teams are rivals. And they still could both get in. So no drama. None at all.

Let’s look at the A North Girls.

Oceanside and Medomak Valley are no strangers. You might be familiar with the recent history of their boys’ teams. And now they might be separated by the thinnest of margins.

First, we need to look at how the MPA calculates Heal Points. From the website:

In the first step, the preliminary index of the school is ascertained. This is computed by assigning forty-two (42) points for each Class AA victory, forty (40) points for each Class A victory, thirty-eight (38) points for each Class B victory, thirty-six (36) points for each Class C victory and thirty-four (34) points for each Class D victory. These points are added and the total divided by the number of scheduled games. In all cases a minimum divisor is established by the appropriate sports committee. A team with no victories is assigned a preliminary index of 1.000. [Example: If a school team had two victories over class B schools, two victories over class C schools and two victories over class D schools, their total would be reached by adding 38 + 38 + 36 +36 + 34 + 34 + 220. If the school team played an 18 game schedule, the 220 points would be divided by 18, giving a preliminary index of 12.2222222222 and would be reported as 12.222.]

There’s an important distinction here that each team’s Preliminary Index is calculated first. In the example above, that 12.222222 goes on for infinity. But…

For purposes of computing the Heal Points, the preliminary index is carried out to ten (10) places and the tournament index is carried out to twelve (12) places. For reporting purposes, these indices are rounded to three (3) places and four (4) places, respectively.

So we cut off the Preliminary Index after 10 places. 12.22222222222222222 becomes 12.2222222222. 6.6666666666666666 becomes 6.6666666667. And so on. This is likely because when you’re doing this by hand or with one of those calculators that prints out on a roll of paper, you don’t have the ability to let it keep going forever. You just can’t.

The tournament index for the team used as an example would be determined by adding the preliminary indices of the schools from which it had defeated. This total would be divided by the number of games on the schedule (18 in this case). If the two B schools had 33 preliminary indices of 8.000 and 5.000; the two C schools 6.000 and 5.400; and the two D schools 4.400 and 4.200; the total of these would be 33.000. This total of 33.000 divided by the 18 games on the schedule would give the team a figure of 1.833333333333, reported as 1.8333. Finally, the tournament index is computed by then multiplying that figure by 10, giving the reported figure as 18.3333.

The key here is “adding the preliminary indices of the schools from which it had defeated.” Remember that cutoff of 10 decimal places? 1/3 + 1/3 = 2/3. But 0.333 + 0.333 < 0.667.

Here’s where you say, “well, that’s dumb. Clearly not the intent. etc, etc.” But I think it is. You’ll recall from above that the Preliminary Index is calculated to 10 places, but the Tournament Index is calculated to 12. Why? What possible reason could there be to go out 2 more spots than if you wanted to create an opportunity for separation? If it was just a question of your ability to calculate numbers, you’d cut them both off at 10. If it was the hassle of dealing with it, you’d cut it off at 5 or 6. Almost every PI is a number that goes on for infinite decimal places. There’s not any nuance once you get past 2 or 3 spots.

You also might not get this if you don’t set up Excel (or whatever you’re using) correctly. Excel will assume those numbers go on forever. You have to tell it otherwise with something like a ROUND() function.

So back to Oceanside and Medomak Valley. Let’s assume the following:

  • Medomak Valley beats Belfast
  • Gardiner beats Oceanside
  • Erskine beats Cony
  • Morse loses to Waterville
  • Morse loses to Winslow
  • Brewer loses to Lawrence
  • Brewer loses to Hampden
  • Mt. Ararat loses to Edward Little

And you get this:

Brewer complicates this a little, as there’s scenarios where both Medomak Valley and Oceanside could jump ahead of Brewer, the original third team in the 3-way tie. I don’t think we can get the 3-way tie back, but I’m hoping. Because that would be super chaotic.

But you can see that the Heal Points, if correctly calculated according to the MPA’s stated rules, would put Medomak Valley in ahead of an Oceanside team that beat them twice. That’s a bitter pill to swallow if you’re Oceanside, but as I always like to say when people talk about bubble teams that get snubbed for March Madness: you can’t really complain unless you go undefeated.

This is also the place where I note that changing the class weights from 5 to 2 is absolutely a determining factor here.

I’ve gone over the MPA’s webpage a dozen times, and I don’t see a different way to do this that doesn’t ignore the fundamental laws of math, which wouldn’t be a great look for an organization made up of educators.

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