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