Stat geeks

[Phil]

I was working on something and wanted to look at the distribution of points scored per game per team as well as the overall average points scored.

I also wanted to look at the distribution of points given up and the overall average.

Obviously, by definition the averages must match.

I used this site:
NCAA Statistics

To get the numbers (go to scoring offense, change the entries from the default to 345 and copy and paste in Excel; rinse and repeat for scoring defense

The problem is I get an average number of points scored per game as 67.4

But I get an average number given up as 65.0.

I initially looked at the average of the averages which would necessarily match but it was too far off to make sense so I calculated the aggregate averages (rather than the average average). While doing so I saw that the database has 4575 games for both offense and defense so that matches, but the aggregate points scored are 308362, While the aggregate points given up are 297412.

Those should match.

If they were off by a handful I might've guessed some reporting glitch although even that doesn't make sense but they differ by over 10,000 points.

Before I write to the NCAA, can someone help me figure out if I'm missing something stupid which seems likely?

As an aside, while looking at this I happen to sort the data by points scored and I was initially surprised to see that 74 teams have scored more than 1000 points to date, but UConn is not one of them (obviously, this is prior to today's game).

I won't share the reason here to give someone something to do if they are interested but once the trivial answer is reveal that be interested in discussing why it is the case.

 

[Puppy Love]

I think the problem is because teams have played different numbers of games so points given up and points scored have differences in how the are weighted. You need a weighted average (with number of games played as the weight) to get to meaningful numbers.

 

[Suebird10fan]

Wouldn't 345 be all and only D1 schools? But many D1 schools have played D2 teams. So the two stats comprise different sets of teams. I.e. Points scored is points scored by D1 teams. Points given up includes points scored by some D2 teams (playing vs D1 teams) and would be expected to be a bit lower. Right?

 

[Phil]

I think the problem is because teams have played different numbers of games so points given up and points scored have differences in how the are weighted. You need a weighted average (with number of games played as the weight) to get to meaningful numbers.

No.

As mentioned, I originally was lazy and took at average of averages, knowing it could be off a bit, but knowing it should be close enough. It wasn't so I recalculated. You can call it a weight average, but it is total points divided by total games. The game count is the same, but the points scored and points given up are very different.

 

[Phil]

Wouldn't 345 be all and only D1 schools? But many D1 schools have played D2 teams. So the two stats comprise different sets of teams. I.e. Points scored is points scored by D1 teams. Points given up includes points scored by some D2 teams (playing vs D1 teams) and would be expected to be a bit lower. Right?

Yes, 345 is D1.

I have to think about whether that's the answer.

 

[Suebird10fan]

Yes, 345 is D1.

I have to think about whether that's the answer.

Extreme example: say it's early November and only 1 D1 school has played a game. It's against a D2 school and the D1 school wins 80-60. In that case total games is 1. Total points scored would be 80. Total points given up would be 60.

 

[Glenn]

As Sue bird says it reflects the fact that D1 teams play d2 teams. That is consistent with the fact that points scored is higher than points given up as the d1/d2 games would generate a bunch of points scored

 

[Phil]

Extreme example: say it's early November and only 1 D1 school has played a game. It's against a D2 school and the D1 school wins 80-60. In that case total games is 1. Total points scored would be 80. Total points given up would be 60.

Yep. that must be it.

Thanks.

 

[Plebe]

Yes, 345 is D1.

I have to think about whether that's the answer.

Not that it affects your question, but aren't there 349 teams in D1?

 

[Phil]

Not that it affects your question, but aren't there 349 teams in D1?

Four teams:

• Abilene Christian University
• Grand Canyon University
• University of the Incarnate Word
• University of Massachusetts Lowell

are transitional and not counted in the stats. (And not eligible for post-season, I think).

So both 345 and 349 are correct numbers, depending on the context.