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Statistically Speaking: Rating the Coaches

Saturday, June 16, 2007

Rating the Coaches


Which coaches earned their clipboards last season and which should be forced to hand in their headsets? Everyone’s got an opinion on which coaches did well and which did not last season. In playing around with the numbers, I’ve developed a simple rating system to rate each of the NCAA coaches. First we need to come up with a reasonable preseason expectation for each team. To do this, we could peruse numerous preseason magazines and come up with an average, or we could save some time and come up with a simple formula like this:

Win % Last Season (50%) + Win % 2 Yrs Ago (20%) + Win % 3 Yrs Ago (10%) + .500 (20%)

The four components are winning percentage for the previous three seasons; with each season decreasing in importance as the distance from the current season increases and the final component is a winning percentage of .500 as teams tend to trend towards .500. Including this component ensures we don’t penalize coaches coming off undefeated seasons because improving upon a 100% winning percentage is impossible. Additionally, we don’t reward coaches who go winless because we assume they will improve at least marginally. Next we just subtract the team’s expected winning percentage from their actual winning percentage. This number is the coach’s rating.

Here's an example of the formula at work for Jeff Tedford of the California Golden Bears:

In 2003 the Bears went 8-6 (.571 win %), in 2004 the Bears went 10-2 (.833 win %), in 2005 the Bears went 8-4 (.667 win %), and in 2006 the Bears went 10-3 (.769 win %). The 2003 win % gets multiplied by .5. The 2004 win % gets multiplied by .2. The 2005 win % gets multiplied by .1. Then we multiply the standard .500 win % by .2.

(.667*.5)+(.833*.2)+(.571*.1)+(.500*.2)=.657 is Cal's expected win % for 2006. Cal actually won at a .769 clip so Tedford's coaching rating for 2006 is +.112 (.769-.657). This means Cal won a little more than 11% more games than was reasonably expected at the beginning of the season. This figure was the fourth best coach rating in the Pac 10 in 2006.

Before we get into the coaching rating portion, it’s important to find out if this expected winning percentage is at least a decent predictor of a team’s record. If it’s not then the coach rating is not a valid statistic. Fortunately it is quite valid. The r squared value for the expected winning percentage predictive power in 2006 was .3437. This means that expected winning percentage explained a little more than 34% of the variation in actual 2006 winning percentage. If we break this number down by BCS and non-BCS schools we find that it is a much better predictor for a BCS school’s record than for a non-BCS school. The r squared value for BCS schools (including Notre Dame) was .4254 in 2006. For non-BCS schools it was only .1705. This is still a decent relationship, but it shows that the records of non-BCS schools tends to vary more from year to year than the records of BCS schools. Consequently, we should not be quite as shocked when non-BCS schools see a substantial jump in their winning percentage. BCS schools live in a more caste-dominated society where the divisions between upper, middle, and lower classes are rigid and defined. Non-BCS schools on the other hand reside in a more socially unpredictable society where the lines between the three classes are much less defined. With that out of the way, here are the best coaches from 2006.

Dick Tomey (San Jose State) +.392

Jim Grobe (Wake Forest) +.389

Bronco Mendenhall (BYU) +.372

Greg Schiano (Rutgers) +.340

Rich Brooks (Kentucky) +.309

Todd Graham (Rice) +.296

June Jones (Hawaii) +.290

Chris Petersen (Boise State) +.278

Urban Meyer (Florida) +.276

Frank Solich (Ohio) +.271

At worst, this rating seems to be a solid predictor of coach of the year award winners. Petersen won the Paul 'Bear' Bryant Coach of the Year Award, Jim Grobe won the Bobby Dodd Coach of the Year Award, and Greg Schiano won the Walter Camp, Eddie Robinson, and Home Depot Coach of the Year Awards.

Now here are the worst coaches from 2006.

Tom Amstutz (Toledo) -.263

Gregg Brandon (Bowling Green) -.268

Pat Hill (Fresno State) -.289

Chuck Amato (NC State) -.294

Jeff Genyk (Eastern Michigan) -.297

Jack Bicknell (Louisiana Tech) -.329

Walt Harris (Stanford) -.354

Dan Hawkins (Colorado_ -.367

Tommy West (Memphis) -.427

Shane Montgomery (Miami, Ohio) -.467

Three of these gentlemen were axed after the season (Amato, Bicknell, and Harris) and several others are on the hot seat heading into 2007 (Genyk and Montgomery). Of course, some are also good coaches who just had poor seasons (Amstutz, Hill, Hawkins, and West). Now here are the best coaches by conference.

ACC
Jim Grobe (Wake Forest) +.389

Big East
Greg Schiano (Rutgers) +.340

Big 10
Bret Bielema (Wisconsin) +.235

Big 12
Dennis Franchione (Texas A&M) +.215

Pac 10
Mike Riley (Oregon State) +.208

SEC
Rich Brooks (Kentucky) +.309

Conference USA
Todd Graham (Rice) +.296

MAC
Frank Solich (Ohio) +.271

Mountain West
Bronco Mendenhall (BYU) +.372

Sun Belt
Larry Blakeney (Troy) +.166

WAC
Dick Tomey (San Jose State) +.392

And finally the worst coaches by conference.

ACC
Chuck Amato (NC State) -.294

Big East
Randy Edsall (Connecticut) -.203

Big 10
Pat Fitzgerald (Northwestern) -.205

Big 12
Dan Hawkins (Colorado) -.367

Pac 10
Walt Harris (Stanford) -.354

SEC
Mike Shula (Alabama) -.185

Conference USA
Tommy West (Memphis) -.427

MAC
Shane Montgomery (Miami, Ohio) -.467

Mountain West
Chuck Long (San Diego State) -.181

Sun Belt
Darrell Dickey (North Texas) -.127

WAC
Jack Bicknell (Louisiana Tech) -.329

Obviously this system is not meant t0 be the end-all, be-all of coaching ratings. I don't think Rich Brooks is a better coach than Steve Spurrier, but in accordance with exceeding preseason expectations, Brooks was better in 2006.

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