Tuesday, August 23, 2011

The Worst All-Ivy First Teamer (UPDATED)

In a proper ordering of the thoughts conveyed in this piece, it is important to stress that being the worst All-Ivy First Team member is akin to being the dumbest member of Mensa.

Any criticisms of either need to be placed within the context that the achievement in question is one of extremely high quality, and doubting whether a candidate cleared the necessary bar is hardly analogous to taking the negative side of a binary good-bad argument.

Noruwa Agho is a 6'3 shooting guard who just completed his junior season at Columbia. He led the Ivies in points per game, which was enough to get many, but not all, league coaches to vote him to the Ivy League's First Team.

In so doing, however, Agho became one of the worst First Teamers of the past 15 years, joining a group that includes Yale's Emerson Whitley, Cornell's Ka'Ron Barnes, Dartmouth's Shaun Gee and Harvard's Dan Clemente (twice).

While the casual Ivy observer will recognize some of those names, it's a lot to expect that all but the most fervent supporters will remember each of their individual league campaigns, and for that reason, we'll focus on Agho, who was by almost every aggregate metric the worst All-Ivy First Team member of at least the past five years.

Much like the on-base percentage vs. batting average discussion in baseball, the fight between points-per-game and effective field goal percentage or true shooting percentage in basketball serves as a fundamental dividing line in the evaluation of offensive performance of hoops players.

For many, the fact that a player can average 15 or more points per game is enough to indicate that they're an effective scorer. The implicit (and in my opinion fallacious) argument here is that scoring is a skill and that even medium-sized deviations in efficiency are fine, because there are only a certain number of folks that are "scorers" at any number of shots.

Sure enough, on a points produced per 40 ("PPD40") minute basis (points produced is an allocated measure of points based on one's own scoring as well as assists and offensive rebounds, but is not judged per-possession) Agho ranks 25th among the 76 All-Ivy First Teamers over the past 15 years.

As mentioned in the parenthetical, though, PPD40 is a counting stat, not a per-possession stat, which is to say that a player could use any number of possessions to get to their total, making the metric irrelevant to the argument of efficiency. Efficiency is important because any Division I player can score 20 points in a college basketball game. Some may need to shoot 50 times, others 25, and others just 15, but every player would wind up with the same resulting total in a "counting stat" like points per game.

Since basketball is merely a series of possessions, what matters is what a player can do with a possession, and on that basis, we can judge that the player who took 50 shots hurt his team while scoring 20 points, while the player that took just 15 probably helped his team.

That's where Agho's candidacy falls apart. His weighted offensive rating (points per 100 possessions weighted for the strength of opponents' defenses) was 98 in conference play, 72nd out of the 76 First Teamers. His effective field goal percentage of 45 percent was 75th out of 76, and his true shooting percentage of 48 percent was dead last with the next closest player at 51 percent. In fact, opening up those efficiency stats to all 222 All-Ivy players over the past 15 years, Agho was 190th in offensive rating, 210th in eFG% and 216th in TS%. Ironically, one of the few players finishing behind him in all three categories was the 2010 version of himself, who took home Second Team honors.

Thus, Agho might be a prolific scorer, but he needs far more attempts to get his points than almost every First Teamer or even the average Honorable Mention designee.

The Dean Oliver efficiency stats provide an important view of a player's contribution, especially on the offensive side of the court, but there are more angles from which to approach the issue of player performance.

Similarity scores match several different categories of player stats and compare one player to a database of players from the same league. The basis for matching is a Z-score, which treats the categories as normal distributions and measures where along the normal distribution the original player and every other player falls. Differences in Z-scores are aggregated across all the categories to arrive at how similar each player in the database is to the original player.

Obviously there are flaws in the system - ones which become readily apparent upon running hundreds of these comparisons - but the information generally points in the correct direction, at least.

Agho's top 15 matches include six All-Ivy First Team designees, four Second Teamers and one Honorable Mention. Each of the other four members of the 2011 All-Ivy First Team had all 15 of their matches receive All-Ivy honors, and most Second Team guys had higher hit rates including Ian Hummer (13/15 All-Ivy including 10 First Team selections), Brandyn Curry (14/15 All-Ivy including seven First Team selections) and Chris Wroblewski (14/15 All-Ivy including 10 First Team selections).

Even some 2011 Honorable Mention designees had higher quality matches than Agho, including Jack Eggleston (12/15 All-Ivy including seven First Teamers) and Brian Barbour and Tucker Halpern (each 12/15 with six First Teamers).

The point is not to say that Agho didn't deserve to make the All-Ivy team at all. While the Oliver stats indicate such, as an Honorable Mention candidate - where this blog had Agho placed - he would have been only below average on the offensive efficiency side, but his solid rebounding for a guard and otherwise good defense could have bridged the gap. Clearly from a similarity score perspective, Agho fits in decently well with the Honorable Mention group as well.

The final angle from which to approach the discussion is plus/minus. More specifically, we'll look at the Roland Rating (data from statsheet.com), which captures the difference between the plus/minus performance of a team when a player is on the court and when he is off the court. The Roland Rating and plus/minus in general are rough metrics with a ton of noise affecting the results (primarily residing in the lack of off-court sample size if a player plays a ton of team minutes and also stemming from a player's most common on-court pairings). That being said, using the statistic as a directional guide can be instructive.

Three Ivy First Team members (No. 3 Keith Wright, No. 4 Kareem Maddox and No. 7 Greg Mangano) finished in the top seven, while Zack Rosen checked in much lower on the list at No. 22. Agho failed to even crack the list, registering a score of basically zero, meaning that his team was as good with him as without him.

Regardless of whether you buy into the Roland Ratings (again, I think they can be useful as part of a larger set of information, but aren't always useful, especially in a vacuum), it becomes the third metric that casts serious doubt on Agho's First Team chops.

All the statistics we've considered above are conference-only. That's an important point for two reasons. First, the Ivy coaches are supposed to more heavily weight league performance versus non-conference performance (thus Harvard's Kyle Casey makes the Second Team despite missing most of the first half of the season). Second, Agho has played significantly better in each of his first three years at Columbia during the non-conference portion of the season than he has during the league slate.

For instance, looking at full year similarity scores, Agho has 13/15 All-Ivy matches instead of 11/15 and eight First Teamers instead of six. While that's still not up to par with the rest of the First Team, it does match up well with the profiles of the Second Team members. Thus, while Agho's Ivy performance might have only been worthy of Honorable Mention, his full year stats imply a distinction a level higher.

That being said, none of the stats - except for contextless counting ones like points per game - point to Agho as deserving of the league's top honor. As the Columbia faithful look to their returning First Teamer to guide the Lions to the Ivy upper division, there is some doubt as to whether Agho can carry the load efficiently enough to do just that.

Update (8/23/11, 12:00 p.m.): The incomparable Stuart Suss sent me his Ivy-only Hollinger numbers. (The core stat in the Hollinger numbers is a "Game Score," which can essentially be read on the same scale as points per game, but incorporates all of the box score information). Agho ranked 24th in Game Score per 40 minutes (11.0), while fellow First Teamers Kareem Maddox, Greg Mangano and Keith Wright were 1-2-3 (19.1, 17.7 and 17.3, respectively), while Zack Rosen was 15th at 12.3.

The players three spots above and three spots below Agho were Harvard's Oliver McNally and Christian Webster, Brown's Sean McGonagill, Yale's Reggie Willhite and Cornell's Drew Ferry and Johnathan Gray. Once again, this metric puts Agho among the Honorable Mention and just off the cusp types, rather than among First Team players.


  1. Could you publish the complete Ivy-only PERs for last season (minimum 20mpg or so)? Thanks!

  2. Those are Stu's numbers, so it's probably not my place to post the whole list, but if you ask on the Basketball-U boards, he might put them up there.

  3. Oh okay, thanks.