# Feet, inches, and averaging

March 19, 2023 at 3:56 PM by Dr. Drang

After Purdue’s historically embarrassing loss to Fairleigh Dickinson on Friday night, many sportswriters awakened to Purdue’s longstanding poor performance in the NCAA tournament and wrote articles like this one in *Slate*. As I read that article, I saw one error that should embarrass *Slate* and then saw another statement that seemed like an error but wasn’t. I figured they were worth a short blog post.

The embarrassing error concerns the height difference between Purdue and FDU. Purdue’s top player, Zach Edey, is 7′ 4″. According to Slate, FDU has “nobody taller than 6-foot-6.” *Slate* apparently doesn’t know how to use foot and inch marks, but I don’t consider that an error. And even though a quick perusal of FDU’s roster clearly shows a 6′ 7″ player, I’m going to give them a pass on that, too, as Pier-Olivier Racine doesn’t get much court time and didn’t play at all in the Purdue game. No, the error comes later when, after establishing that Edey is 7′ 4″ and the tallest players on FDU are 6′ 6″, the article says

Edey is 8 inches taller than anyone who guarded him.

My guess is that the writer, Alex Kirshner, did the calculation in his head this way,

74 – 66 = 8

and everyone at *Slate* who read the article before publication just went along with it. I’m also pretty sure that all my non-American readers are nodding their heads and congratulating themselves on not using those awful and confusing US customary units. But honestly, is it really that hard to see that 7′ 4″ is actually 10″ taller than 6′ 6″? I bet even Purdue’s engineering students would get that one right.

Here’s the thing that seemed like a mistake but wasn’t:

There are 363 Division I men’s basketball teams. FDU is the shortest one of them all, according to Ken Pomeroy’s data, with an average height of 6-foot-1.

This wasn’t the first time I’d heard that Fairleigh Dickinson’s team had an average height of 6′ 1″—it’s in several of the Purdue-excoriating articles. And it wasn’t the first time I thought *that can’t be right.* I don’t need KenPom to tell me the team’s average height (and a good thing, too, because it’s behind a paywall), all the heights are on the afore-linked roster.

Scrolling through the list of players, there are only two under 6′ 1″, one who is 6′ 1″, and ten others who are taller. Even without doing a single calculation, I knew the average had to be over 6′ 1″. And it is. To the nearest half-inch,^{1} the average height of the thirteen players on FDU’s roster is 6′ 3″.

The thing is, while I can believe that *Slate* would make a mistake in calculating a team’s average height, I can’t believe Ken Pomeroy would. So how did he come up with 6′ 1″? The answer is on his site, and it’s a good one:

Overall average height is computed by taking the average listed height of every player on the team, weighted by minutes played. Players that have played less than 10% of their team’s minutes are not included.

Pomeroy wants to give his readers the average height of the team *on the court*, and weighting the players’ heights by minutes played is probably the best way to do that. And dropping out those who play in “garbage time” makes sense, too.^{2}

So I made a little spreadsheet with the FDU players, their heights, and the minutes they played in the Purdue game. Here’s a screenshot:

As you can see, the team’s shorter players, Roberts and Singleton, also got the most minutes, so the time-weighted average, rounded to the nearest half-inch, for this particular game was 6′ 1½″. Close enough. I wouldn’t be surprised to learn that FDU had its taller players on the court more than usual in this game.

The spreadsheet also includes the naive average of 6′ 3″ and the 6′ 2″ average of the nine FDU players who played in the Purdue game.

By the way, I didn’t enter the heights in feet and inches as shown in the second column. I entered the heights in inches in the third column and converted to feet and inches for presentation with this formula for the player heights

```
FIXED(FLOOR(C2÷12,1), 0) & "′ " &
FIXED(MOD(C2, 12), 0) & "″"
```

and this formula for the average heights.

```
FIXED(FLOOR(C16÷12,1), 0) & "′ " &
FIXED(MROUND(MOD(C16, 12), 0.5), 1) & "″"
```

I needed the `MROUND`

function in the latter formula to get the results rounded to the nearest half-inch.

The “played average” was calculated this way:

```
AVERAGEIF($D$2:$D$14,">0",C$2:C$14)
```

I’m not a big spreadsheet user, and I think this is the first time I ever used `MROUND`

or `AVERAGEIF`

. So thanks to *Slate* and KenPom for that.