Size Does Matter, from Alston Mabry

March 29, 2009 |

A little NCAA Tournament counting:

If you go to Yahoo Sports you can grab data on each team in the NCAA basketball tourney. For any team, determine an average weight and average height for the players that are actually playing.

Take the average minutes per game for each player and multiply this stat by the player's weight, and also by his height (in inches) to create two new stats that show an aggregate value of the weight and height that player contributed during the team's total time on the court per game.

Total these stats for the entire team and divide by the total of the average minutes played for all the players, and you have essentially an overall average weight and average height for the five players the team had on the court during games.

Here is an example:

University of Oklahoma

Player   GP Min HT WT min*HT mi*nWT
Allen    18   4.7 83 267 7,022   22,588
Cannon    9   6.8 80 230 4,896   14,076
Crocker 35 29   78 206 79,170 209,090
Davis    34 14.9 77 208 39,008 105,373
Franklin 12   2.2 71 161 1,874    4,250
Gerber   13   2   80 228 2,080    5,928
Griffin 34 33.1 82 251 92,283 282,475
Griffin 35 29.8 79 238 82,397 248,234
Johnson 35 31.3 75 176 82,163 192,808
Leary    33 10.2 71 173 23,899   58,232
Pattillo 18 13.7 78 216 19,235   53,266
Warren   35 31.2 76 207 82,992 226,044
Willis   16   6.4 78 172 7,987   17,613
Wright   32   8.1 81 234 20,995   60,653

total team min: 7020.5
total height: 546,001
total weight: 1,500,630

Avg Team Height: 77.8 in
Avg Team Weight: 213.7 lbs

These calculations were done for the 32 teams that made it out of the first round.

Then the point differential was calculated for each of the 28 games that those 32 teams played in rounds 2, 3 and 4.

In 18 of 28 games, the team that won also had the heavier average player. In 19 of the 28 games, the team that won had the taller average player.

To run a correlation, a winner/loser score ratio was calculated for each of the 28 games (i.e., Big State beats Western U by a score of 100 to 80, then the score ratio is 100/80, or 1.25), as well as a difference between the two teams playing in average height and average weight.

Example:

Louisville 79, Siena 72

Louisville
avg wt: 211.7
avg ht: 77.0

Siena:
avg wt: 201.2
avg ht: 76.3

score ratio: 1.097
weight diff: +10.5
(i.e., winner heavier than loser by 10.5 lbs)
height diff: +0.712
(i.e., winner taller than loser .712 inches)

Running a correlation of the score ratio and height difference for the 28 games produced a surprising p of -0.24. So while the winning team was taller in 68% of the games, there were shorter teams that won by big margins, and taller teams that won by small margins.

The correlation between score ratio and weight difference was initially even more surprising - to me, at least, because I was certain a priori that weight mattered significantly. But the correlation was only +0.08. So, the winning team was usually heavier, but more bulk affected the margin of victory only slightly

The Final Four looks as follows:

Team / avg ht / avg wt

North Carolina 77.2 / 216.1
Villanova 77.1 / 207.7

Connecticut 79.0 / 215.5
Michigan State 77.2 / 212.2

So, it looks like Carolina beats Villanova on weight (though Pitt weighed in at 217.3), and UConn beats Michigan State on height. Then it looks like it's UConn on height again in the final against Carolina (with their weights being too close to matter).

All 32 schools, sorted by average weight:

SCHOOL / AVG HT / AVG WT

Xavier 78.1 221.5
Pittsburgh 76.3 217.3
USC 78.4 217.1
Gonzaga 78.4 216.7
North Carolina 77.2 216.1
Connecticut 79.0 215.5
Syracuse 77.0 215.3
Memphis 78.7 214.7
Oklahoma 77.8 213.7
Arizona State 76.7 212.4
Michigan State 77.2 212.2
Wisconsin 76.9 211.8
Louisville 77.0 211.7
Duke 77.6 209.6
Marquette 75.6 209.1
Maryland 77.5 208.1
Texas 76.2 208.0
Villanova 77.1 207.7
LSU 77.7 207.5
Washington 75.5 207.5
Missouri 77.8 207.1
Dayton 77.2 207.1
Arizona 76.8 206.4
Oklahoma State 75.6 206.0
Texas A&M 78.0 205.8
Kansas 76.6 205.2
UCLA 77.2 204.7
Purdue 76.7 204.0
Siena 76.3 201.2
W. Kentucky 76.6 200.4
Michigan 76.1 197.7
Cleveland State 76.1 197.3

All 32 schools, sorted by average height:

SCHOOL / AVG HT / AVG WT

Connecticut 79.0 215.5
Memphis 78.7 214.7
Gonzaga 78.4 216.7
USC 78.4 217.1
Xavier 78.1 221.5
Texas A&M 78.0 205.8
Missouri 77.8 207.1
Oklahoma 77.8 213.7
LSU 77.7 207.5
Duke 77.6 209.6
Maryland 77.5 208.1
UCLA 77.2 204.7
Dayton 77.2 207.1
North Carolina 77.2 216.1
Michigan State 77.2 212.2
Villanova 77.1 207.7
Syracuse 77.0 215.3
Louisville 77.0 211.7
Wisconsin 76.9 211.8
Arizona 76.8 206.4
Purdue 76.7 204.0
Arizona State 76.7 212.4
Kansas 76.6 205.2
W. Kentucky 76.6 200.4
Siena 76.3 201.2
Pittsburgh 76.3 217.3
Texas 76.2 208.0
Cleveland State 76.1 197.3
Michigan 76.1 197.7
Marquette 75.6 209.1
Oklahoma State 75.6 206.0
Washington 75.5 207.5

Comments

2 Comments so far

Nelson on April 1, 2009 11:18 am
Interesting analysis but I do think it needs to be weighted by minutes played. It is not clear that those who play at a high level (usually only 8 or 9 per team), look like those who ride the pine.
Tom Sproul on April 28, 2009 2:01 pm
A statistical note: The correlations are not really comparable across height and weight because they have not been scaled. Height and weight differences should be converted to ratios or percentage differences if the correlation coefficients are to be compared in a meaningful way. It would also be helpful to know the correlation of height and weight with each other… then an instrumental variables technique could be used to get the average effect of height difference independent of its correlation with weight difference, and vice versa. Just a thought…

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