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Written March 18, 2021


Paul Keller was a high school coach in his hometown of Prospect, Ohio, from 1933 to 1942.  His basketball teams won 76% of their games, and his track teams won 49 meets without a loss.

But let's consider the final week of January, 1960.  I was in the seventh grade in nearby Richwood.  Paul was teaching math at Delaware Hayes High School, also not far away.

And all of Central Ohio was following the fortunes of a 35-year-old rookie basketball coach, Fred Taylor.  Like me, he had been born in Zanesville.  Now his Ohio State Buckeyes had a 12-2 record, and seven weeks later, they would go on to win the NCAA basketball championship!

Led by Jerry Lucas, Larry Siegfried, and John Havlicek, Ohio State was outscoring its opponents by a ridiculous-sounding margin of 92 to 71.  Paul Keller wondered what that meant, really.  Therefore he devised a chart that he called his Offensive Efficiency Rating System.

“The first game that Keller charted,” we learn from a 1967 Kansas State master's thesis by Robert Francis Knight (no, not that Bobby Knight), “was the Ohio State-Michigan State game on January 30, 1960.  In this game, Ohio State scored 111 points on 98 possessions for an Offensive Efficiency Rating of 1.13.  This means that Ohio State scored 1.13 points every time that they had possession of the ball.  On the other hand, Michigan State scored 79 points on 94 possessions for a rating of 0.84 points per possession.”

Ohio State's defense allowed a whopping 79 points?  Should they be worried?  No, it was a fast-paced game, and the Buckeyes' Defensive Efficiency Rating of 0.84 was actually quite good.

Keller said that “points in a game actually mean nothing, but points per possession mean everything.”  He wasn't the first to notice this.  In 1959 the soon-to-be-legendary coach Dean Smith — who majored in mathematics at Kansas and claimed he would have been happy to be a high school math teacher — had started to emphasize possession-based analysis.

Knight's master's thesis included sample charts like this.

According to The Ohio State Lantern of March 7, 1961, Paul Keller's son Dick was helping him chart.  And in the fall of 1960, Dick enrolled at Ohio State as a first-year engineering student.

Paul looked up Coach Taylor and showed him the Keller numbers, explaining that “an efficiency rating of less than 1.00 indicates that a team has shown a weakness in one or more of the factors controlling the rating.”  That was a weakness which might require attention from the coaches.  Thereafter, following each game, Paul sent a report to the coach, as well as to Eddie Lane for his play-by-play broadcasts and sports shows on WMNI radio.

This photo from the Delaware Gazette shows Keller using statistics from Ohio's State's 79-45 defeat of Northwestern on January 14, 1961, to illustrate his top factors.  All four turned out to be +  for Ohio State.

 In that game, the Buckeyes shot better from the field, 55.0% to 48.6%.  They were almost perfect from the free-throw line, 92.9% to 78.2%.  They lost the ball in 16 of their 66 possessions for a slightly better turnover percentage than their opponent, 24.2% to 25.2%.  And they pulled down 42 rebounds; dividing that number by possessions shows Ohio State better at rebounding, 63.6% to 59.5%.

Of course, we can't simply calculate an OER from percentages.  However, we can estimate the number of possessions from four raw numbers:  field goal attempts, free throw attempts, offensive rebounds, and turnovers.  Jeffrey Haley from Texas suggests that for college basketball, the formula should be FGA + 0.475 x FTA – ORB + TO.

Keller's stats turned out to be useful in comparing a team's performance from game to game (“much better job tonight”) and in certain isolated parts of a particular game (“we got sloppy after halftime”).

For example, keeping control of the ball is important.  In that defeat of Northwestern, Ohio State had an excellent 1.20 OER with 79 points on 66 possessions.  But let's break down those possessions, which included 16 turnovers (when the Buckeyes failed to get off a shot) and only 50 kept possessions.  So the 79 points were scored on 50 kept possessions, an “OER Potential” of 1.58 during that turnover-free time.  Had they been able to maintain that 1.58 for an entire turnover-free game of 66 possessions, they could have scored 104 points!

Other aspects to be broken out might be the times that a team is playing a certain defense, or the last ten minutes of a half (were the players tiring?), or maybe “garbage time” when the starters have been removed from the game.  The Lantern reported that during the 100-68 blowout at Wisconsin on January 30, 1961, Ohio State had an unbelievable 1.47 OER while the regulars were on the court, but only 1.18 for the game as a whole.

Paul started marketing his innovation to high school and college coaches around the country.  I was in high school by that time, and as a manager for the Richwood Tigers I was in charge of statistics.  Coach Frank Zirbel showed me Paul's letter.  I responded, and I may have paid $15 to receive the full kit.  However, for me the OER was merely a curiosity.  I did get to meet Paul when he was one of the officials at a local track meet.

Sports Illustrated, February 5, 1968

Paul R. Keller of Delaware, Ohio is the originator of a statistical measure for basketball that he calls the Offense Efficiency Rating (OER). To help analyze their play, 769 high schools and colleges employ the Keller system, for his figures are both more logical and valuable than the rudimentary conventional offensive and defensive indices.

Last year Keller's figures showed conclusively that UCLA won the national championship primarily on account of its defense. This year his analysis indicates that Houston — a team whose defensive prowess often has been maligned — beat UCLA in the Astrodome at the Bruins' own best game, defense. In fact, both teams had such bad Offense Efficiency Ratings that Keller assumes that the unusual Astrodome setting played a responsible role.

The figures also show that the UCLA press has lost none of its power. Houston's OER was not only significantly lower when the Bruin press was on, but UCLA was much more potent offensively following the press. The Bruins scored 1.22 points every time they took the ball off the press, but only 0.76 points each time they got the ball in more normal fashion.

When I was program director of my college radio station, I asked sophomore Lee Beckett to keep track of the OER during our WOBC broadcasts of Oberlin's away games.  He referred to those numbers during his halftime studio show.

Nowadays points per possession, both for offense and defense, are frequently analyzed by pundits.  For example, here's Craig Meyer in the Pittsburgh Post-Gazette for February 19, 2021:  “In Pitt's first six games against opponents from college basketball's six major conferences, five of which were against ACC teams, it allowed an average of 0.95 points per possession.  In its past seven games, it is giving up 1.16 points per possession.  If that gap seems insignificant, it's not.  Based on the Panthers' average tempo of 69 possessions per game, it's the difference between allowing 65.6 and 80 points per game.”

How offensively efficient is your rating?

POSTSCRIPT:  Nowadays, another Ohio math teacher's idea is slowly working its way into basketball.  This one was invented in 2007 by Nick Elam of Northridge High School, near Dayton.  He's currently an assistant professor of educational leadership at Ball State University.

Six years ago I wrote, “One thing I like about hockey is that the game ends when it's supposed to end.  In the final minutes, a losing team can't delay the inexorable countdown.  The coach can call a single timeout for a 30-second discussion at the bench, but only after the official has already stopped play.  In college basketball, however, each team can interrupt the action by calling five timeouts.  The teams often use all ten opportunities.  Also, late in the game, the trailing team can stop the clock another ten times or so by fouling an opponent.  There seems to be a whistle every 1.9 seconds.  Last month, blogger Bob Smizik reported, ‘It took 14 minutes to play the final 34 seconds of the Pitt-St. Bonaventure game Saturday.  There were no commercials during those 14 minutes.’”

Earlier this month James Herbert of CBS wrote, “When a 3-pointer from Wisconsin's D'Mitrik Trice cut Illinois' 12-point lead to nine with 2:09 on the clock last Saturday, it took 22 minutes to reach the final buzzer.”

Dr. Elam's research indicates that late-game deliberate fouling occurs in approximately half of all games, but only one percent of the time does it accomplish its purpose (enabling the trailing team to win).  Endless free throws and sideline huddles are not very entertaining.  He's promoting a better way, which has been tried out recently at the NBA All-Star Game:  the Elam Ending.

The parameters vary, but typically the rule would be activated when less than four minutes remain in the game.  On the next whistle, the final media timeout is called and the game clock is shut off.  A target score is established:  eight points more than the leading team has tallied.  If Hometown is ahead of State 75-70 at that moment, the target becomes 75+8 or 83 points, and that number is prominently posted.

The winner will be the first team to reach 83.  Since only one team at a time can score, there's no danger of overtime.  In this case, Hometown obviously has a better chance, needing only eight points before State can tally thirteen.  But the teams will be playing real basketball, and the climax will be marked by the ball going through a hoop — a walkoff score that sets off an immediate victory celebration!



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