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Ekpe Udoh, Monta Ellis And The Dissonance Caused By Advanced Statistical Analysis

In this metaphor, Kemba Walker is adjusted +/-, which drives a serious wedge between Monta Ellis and Ekpe Udoh.
In this metaphor, Kemba Walker is adjusted +/-, which drives a serious wedge between Monta Ellis and Ekpe Udoh.

The Milwaukee Bucks made a big splash when they maneuvered to land Monta Ellis and Ekpe Udoh at the 2012 NBA Trade Deadline, but that duo presents an intriguing, yet uncomfortable tension between traditional scouting and advanced statistical analysis. Most fans have expressed a quiet confidence in Udoh that could only reasonably emanate from the insights provided by advanced statistical analysis, as much of what he does escapes the discrete and limited accounting provided in a traditional box score. However, Monta Ellis is still considered the biggest asset acquired in the trade, despite the fact that his value takes a significant hit when viewed through the same prism applied to Udoh. It's almost as if Ellis exists to test one's convictions with regards to Udoh. You couldn't design a more challenging contrast of players if you tried.

Certain aspects of the trade can't be argued. Everyone concedes that Monta Ellis is easily the most athletic and explosive backcourt player Bucks fans have seen since Ray Allen, and is a proven scorer in the traditional sense as well. I have adopted the slogan "They Just Get Buckets" for Monta Ellis and Brandon Jennings, because it has the flexibility to meet the demands of any fan on the vast NBA spectrum. It all depends on where you put the emphasis. I would venture to guess most people would say it like this: "Ellis and Jennings just get buckets!" Those who put more stock into the insights provided by advanced statistics, like myself, would utter that phrase a bit differently: "Ellis and Jennings just get buckets." Why? Most advanced stats suggest that all the points and bite-size highlights don't really do much to help the team win, because subtleties like inefficiency and sub-par defense turn both players into net-negative volume scorers.

Can you feel the tension yet? When statistics undermine clear visual impressions of talent and value, people usually dismiss them. Advanced stats such as regularized, adjusted +/-, TS% and other measures are mentioned pejoratively as a convenient outlet for the "haters" who simply can't appreciate obvious skills and ability. Evidence that Monta Ellis and Brandon Jennings don't help their team win isn't treated like evidence at all. Stats don't tell the whole story.

The interesting aspect of the Bucks trade is that it juxtaposes Monta Ellis with Ekpe Udoh, an advanced stats god who wouldn't make you look twice at his box score on most nights. Cognitive dissonance can be an amazing thing. Everyone readily accepted the insights of advanced stats when evaluating Udoh's value in the trade. There was literally nowhere else to look to see exactly how good he is at basketball, yet it's difficult to find even a stray negative comment about adding Ekpe to the mix in Milwaukee -- despite the fact that there are legitimate reasons to be concerned about him too, which I will get to in just a bit. When stats say positive things about players, they typically become a lot more appealing to everyone. Who wouldn't want to hear that players on their favorite team are better than they appear?

The same stats that prop up Udoh's value are the ones that chip away at Monta Ellis and leave nothing behind. It's the perfect storm. Let's take a deeper look.

The basic concept of adjusted +/- Knowing how a team fares with a particular player on the floor is extremely valuable information, because it cuts to the heart of the goal of basketball: outscoring your opponent. The problem is that the nine other players on the hardwood create serious "noise" that tends to obfuscate individual contributions at the +/- level. I might be able to pull off a positive rating playing with Kevin Durant, Russell Westbrook, James Harden and Serge Ibaka, but it wouldn't be because I'm particularly good. Pile on the problems associated with garbage time matchups, bench players, opponent lineups and various situational strategies, and there is a clear need for intelligent adjustments.

For the best article on the history of adjusted +/- and the theory behind those modifications, I highly recommend you read this piece by DanielM of Here is a snapshot from another article by By Steve Ilardi, Ph.D. and Aaron Barzilai, Ph.D from that confronts the issue of collinearity and explains how adjustments are made:

...where does the noise come from, and how can it be eliminated? Mostly, it results from the fact that teams tend to put the same players on the court together at the same time. That is, many players' minutes are strongly inter-correlated, so the underlying adjusted plus-minus model has a hard time disentangling individual player effects at a high level of accuracy. In addition, the number of unique observations (i.e., lineups) of a given player in a single season is surprisingly small [4], typically under 1,000.

However, there exists a straightforward solution to both of these problems: use multiple seasons' worth of data. How many seasons of data are needed? As many as possible. With only one season, the standard errors are very high - typically around 5.0 points per 100 possessions (with corresponding margins of error of roughly +/- 10.0 points). Such ratings, of course, are highly suspect. With two seasons of data, the noise level drops by about 40%, but it's still uncomfortably high. The picture, however, gets appreciably clearer with each additional season that's added to the model.

In general, more data means better results, so the most reliable +/- data incorporates multiple seasons worth of data and some even make adjustments to weight the more recent play more heavily to adjust for players entering or leaving the prime of their career. Anyhow, let's take a look at where advanced metrics like this get us with regards to Monta Ellis and Ekpe Udoh.

EvanZ's 2.5-Year Adjusted Four Factor +/- (A4PM): At his terrific NBA blog, The City, Evan Zamir set out to create a player metric based on Dean Oliver's Four Factor analysis (using effective FG%, free throw rate, turnover rate and offensive rebound rate) and the insights of adjusted +/-. His regression analysis produced the following insights regarding how each factor explains point differential in the NBA:

Factor DeanO Regression
Shooting 40% 54%
Turnovers 25% 22%
Rebounding 20% 15%
Foul Rate 15% 10%

Using two and a half years worth of play-by-play data and the information from above, he constructed a full list ranking NBA players according to the value they provide (based on his regression analysis and adjusted +/-). Inclusion of play-by-play data is what allows for a deeper analysis of individual defensive value than anywhere else you can find on the internet. As for the results, out of 434 qualifying NBA players, Ekpe Udoh ranks No. 2 (behind Lebron James), while Brandon Jennings is at No. 247 and Monta Ellis lags back at No. 319 overall. Andrew Bogut? No. 36. Hello again, Mr. Dissonance!

If you want to read the spreadsheet below, Evan reminds us that "PID is the unique basketball-value player ID. A4PM, O4PM, and D4PM are the total, offensive, and defensive adjusted four factor +/- ratings. RAPM is my 2.5-year version of ridge-regressed APM."

I have annotated a visual representation of Evan's data set created by DanielM, so if you don't like looking at a chart full of numbers, here is another prettier presentation of the same information:

All Other Major +/- Metrics Corroborate These Findings. No matter where you look, the same things always come up with regards to Ekpe Udoh and Monta Ellis. Udoh's contributions are always in green, and Ellis' contributions are always in red. Well, at least when their accomplishments are viewed through the prism of +/-. The most interesting thing is that Udoh appears in a list of top players that otherwise satisfies my basketball sensibilities. He nestles in with LeBron James, Chris Paul, Dirk Nowitzki, Kevin Garnett, Dwyane Wade, Dwight Howard, Steve Nash, Manu Ginobili, Tim Duncan, etc.

Well actually, the etc. is important, so let's not move on quite yet. The thing that scares me a bit is that other role players with a smaller sample of minutes to draw upon also make unexpected appearances at the apex. Jeremy Lin, Kyrylo Fesenko, Matt Bonner, Omer Asik, Kyle Korver and Jason Collins grace the top 25 on Evan's 2.5-Year Adjusted Four Factor +/- (A4PM) list. Likewise,'s two-year adjusted +/- top player group includes Chase Budinger at No. 9, Rodney Stuckey at No. 17, Trevor Booker at No. 24 and Omer Asik at No. 25.

Are these guys terrible players? No. Might I think about them differently after seeing this information? Sure. But the fear is that when they play more minutes and the sample size expands, their +/- rating will regress to a more modest level. In other words, it's possible that the Bucks not only sold low on Andrew Bogut, but they also bought at the peak of Udoh's value. Violation of the "buy low, sell high" principle usually doesn't work out well for the violator.

Now that advanced metrics have helped people understand where to look for Udoh's value, everyone is paying closer attention to the details that make Ekpe so good. The early returns from scouting his game are encouraging, and a live look has helped to quell my fears of any fatal regression in his value. Let's take a look at a few plays on a custom highlight reel I created from the March 20 win against the Portland Trail Blazers:

Consistent contribution of timely help defense, effective pick-and-roll hedges, strong screens, disruptive shot challenges, solid box outs and high levels of awareness are things box scores aren't equipped to record and minds aren't build to reliably cross-reference or recall accurately over time. There is no doubt these hidden skills can compound in value over the course of a game and a season. Next time you watch a Bucks game, see how many times opponents risk running a pick-and-roll involving the man Udoh is defending (hint: they don't do it often, and when they do it's not very successful). Likewise, keep an eye on whether penetrating guards and forwards get quality angles to the basket or clean looks at the rim.

With my video highlight package at your disposal, let's take another look at the other leading adjusted +/- metrics around the NBA universe to reinforce Udoh's value, and then to question Monta Ellis' effect on wins and losses.

It's hard to like the trade after digesting this information, right? Everything Ekpe Udoh has done right over the last two years through the lens of adjusted +/- (+6.83) has been undone by Monta Ellis (-6.23) in an even larger and more reliable sample size. He's the $11M/year lead guard the Bucks aimed for and then immediately plugged into the starting lineup, while Udoh is waiting behind Drew Gooden and Ersan Ilyasova.

Even if they let Ersanity leave in the offseason, is it reasonable to think Udoh can continue to walk among the basketball gods when his minutes increase? Likewise, what becomes of the whole experiment if the Bucks hold on to Ellis for the two-years (and $22M) he has left on his deal and it all works out to a net of zero under even the best circumstances?

These are questions worth asking, and the assumptions propping them up are reasonable enough to concoct a scary picture of the future. Another round of "not good enough to compete for anything meaningful, but not bad enough to gain opportunities in the draft capable of changing the long-term fortunes of the franchise" might be headed our way.

The hope lies in the possibility that Ekpe Udoh really is as good as his adjusted +/- numbers make him out to be, because that would mean the Bucks have a legitimate replacement for Andrew Bogut. It still requires a bit of hope, however, because a regression seems like the most reasonable assumption at the moment. As for Ellis, any optimism comes not from taking a closer look, but from casting a wider and more unfocused gaze on the best moments and traits he has to offer.

On the best day, these concerns go answered by an uptick in efficiency and renewed focus on the details of winning basketball by Ellis and by continued strong play from Udoh that increasingly manifests in the box scores as well. On the worst day, Udoh falls from his fascinating heights and Ellis remains the same player Golden State traded away. Things will likely fall somewhere in the middle, but that's what makes the whole exercise so perplexing. Do the Bucks trust the insights of advanced statistical analysis? If so, it's very hard to explain the inclusion of $33M worth of Monta in the deal and equally difficult to understand underlying decision to part with Andrew Bogut and build a Jennings-oriented, open-court team.

John Hammond's vision to build a team fit for meaningful NBA competition feels impenetrable to me in the wake of the blockbuster deal of the 2012 NBA trade deadline. In 1880, philosopher and psychologist William James crafted this beautiful paragraph to describe the creative process, but I want you to think about the Bucks when you read it a second time (the first should be to enjoy it as spectacular prose, of course):

"Instead of thoughts of concrete things patiently following one another in a beaten track of habitual suggestion, we have the most abrupt cross-cuts and transitions from one idea to another, the most rarefied abstractions and discriminations, the most unheard of combinations of elements, the subtlest associations of analogy; in a word, we seem suddenly introduced into a seething cauldron of ideas, where everything is fizzling and bobbing about in a state of bewildering activity where partnerships can be joined or loosened in an instant, treadmill routine is unknown, and the unexpected seems the only law ."

- Williams James, Great Men, Great Thoughts, and the Environment.

Lecture delivered before the Harvard Natural History Society.
Published in the Atlantic Monthly, October, 1880

As a description of the creative process, you'd be hard-pressed to do better than this classic line. I think it also works as the definitive poetic indictment of the Bucks franchise during the last decade. The ironic use of the word "treadmill" inspired me to stretch the quotation a bit long, but I hope you appreciate the nature of my abstract association. If you want to take a closer look at the Bucks, it's only right to see the whole picture. The view isn't great. Then, again, maybe it's best to not look too closely at the Bucks. Cognitive dissonance is a difficult thing to deal with, after all.