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Rankings are Rank (But Also Meaningful)

Variables Types and (Dis)Liking

NBA: Playoffs-Miami Heat at Milwaukee Bucks Jeff Hanisch-USA TODAY Sports

With our Ranking the Roster series officially wrapped up, I want to spend some time ruminating on the data that we produced and offer a few tentative conclusions.

Our entry point is the scintillating subject of variable types. Typologies of variable types abound, but I’ll focus on the difference between ordinal and interval variables. Ordinal variables, as the name suggests, indicate order. The outcome of our Ranking the Roster series is an ordinal variable: it consists of Bucks players ranked in an order.

We then assigned each player an integer (1, 2, 3...) based on where they fell in the ranking. This is intuitive, but it can also mislead. Although the difference between one and two (one) is the same as the difference between two and three (also one), the difference between the first and second best players (Giannis and Khris) is not necessarily the same as the difference between the second and third best players (Khris and Jrue). In other words, unlike integers, our ranking is not an interval variable; the intervals between players are not equal.

In addition to the ranking, we gauged confidence that each player would be in the playoff rotation on a one to five scale. This question may remain in the realm of ordinal variables, but hews closer to an interval variable: the interval between “Might play a few rotation minutes here and there” (2) and “Will get some minutes, depending on the series” (3) is arguably similar to the interval between “Will be part of the rotation, playing steady minutes” (4) and “Firmly in the rotation, playing heavy minutes!” (5). As a result, our Ranking the Roster series produced both an ordinal variable (the ranking) and an interval variable (the confidence data). We’ll keep that in mind going forward.

Starting with the confidence data (see Van’s post), the ordinal nature of our ranking is readily apparent: the intervals between players are not equal. In fact, we see tiers of players that are not that surprising: Giannis, Jrue, Khris, and Brook in the top tier; Bobby, Pat, Grayson, and Jae / Malik in the second tier (with bigger gaps between them); MarJon in his own tier (lol); and so on.

Both the upside and the downside of these data is that they were collected for each individual player. To delve into the ranking data beneath the final ranking, I scraped together how people voted in each round to form a more continuous ranking variable that represented their average rank.

(Peeking behind the curtains: I calculated the percentage of votes that a player received for a given rank; multiplied that percentage by that rank; repeated this procedure until they were voted off the island; added everything together; and divided by the sum of all of their percentages. For example, Lindell Wigginton received 9% of the votes for 17th and 45% of the votes for 16. His continuous ranking would be calculated as ((.09 * 17) + (.45 * 16)) / (.09 + .45).)

These data aren’t perfect. There was some missing data, which I mostly ignored (a tie for 11th place yielded no ranking data for 12th place, a technical issue yielded only the votes for the top-two vote getters for 10th place, not every player was included in every poll, and TyTy) or occasionally imputed (I gave Giannis 176 votes for first place - the average number of votes across polls - and also assumed that 176 folks voted for 10th place). The sample size (i.e., the number of y’all who participated) also fluctuated across polls, which motivated in part my focus on percentages rather than raw numbers of votes. But these imperfections should not meaningfully sway the takeaways below.

Here are the results:

Continous Rankings

Player Continuous Ranking
Player Continuous Ranking
Giannis Antetokounmpo 1.36
Khris Middleton 2.66
Jrue Holiday 3.64
Brook Lopez 4.96
Bobby Portis 5.64
Pat Connaughton 6.79
Jae Crowder 9.24
Malik Beasley 9.61
MarJon Beauchamp 10.82
Grayson Allen 10.38
A.J. Green 11.98
Robin Lopez 13.58
Andre Jackson Jr. 13.71
Chris Livingston 14.70
Thanasis Antetokounmpo 15.74
Lindell Wigginton 16.17
Omari Moore 17.00

In general, we see the same tires of players as we did with the confidence data above. However, there is one notable exception: Grayson Allen. Unlike the confidence data, but in line with the overall ranking, he finished behind Jae and Malik. Unlike the overall ranking, here he finished above MarJon, but that is simply a result of MarJon being included in the polls from the get-go - Grayson is quickly surpassed when you remove MarJon’s 11 votes for 17th. On the whole, these four players - Jae, Malik, MarJon, and Grayson - are remarkably clustered together.

Things get even more interesting when you unpack their raw data. In the polls for 10th, 9th, and 8th place, Jae took second place every time: losing to Grayson 53-52 (30%-30%), losing to MarJon 66-64 (32%-31%), and losing to Malik 94-84 (46%-41%). Indeed, in the above results, Jae’s average ranking (9.24) was further below his actual ranking (7th) than any other player, befitting of his near-misses to be ranked 10th, 9th, and 8th. People who didn’t like Grayson liked Jae more than MarJon, and people who didn’t like MarJon liked Jae more than Malik.

The question is why. I think that the answer has to do with the distinction between liking and disliking. Liking and disliking are often thought to be opposite sides of the same coin: if I like someone, I don’t dislike them, and vice-versa. However, a lot of research has shown that liking and disliking are not simply opposites. Anecdotally, I’m sure you know people whom you like and dislike at the same time - not to mention folks that you neither like nor dislike.

Ultimately, our Ranking the Roster series is geared toward disliking. In our bottom-up ranking structure - starting with 17th place and concluding with first - a player bows out of the exercise when they are the most disliked. This does not bode well for players like Grayson, who have a strong contingent of haters despite being liked by the majority of the fanbase. Indeed, based on the confidence data, he may even be more liked that Jae, Malik, and MarJon. The Grayson hatred won out in a crowded field of similar players; only about 30% of folks wanted to show him the door, but they prevailed. G may has noted that it was inexcusable for our fifth starter to be ranked 10th. I would offer the groundbreaking conclusion that people don’t like Grayson, but also suggest that under a top-down ranking structure - starting with first place and concluding with 17th - he might have finished 7th.

On the other hand, Jae found a better sweet spot between being liked and disliked. He was clearly (and, in this author’s eyes, fairly) relatively disliked based on the ranking results, but he was also relatively liked based on the confidence data. Unlike Grayson, he was not disliked enough to be voted out at any stage of the rankings, leaving him in 7th place. Under a top-down ranking structure, however, I would expect that he would be 8th instead.

Long story short, I hope these ruminations and conclusions prove at least somewhat interesting. Feel free to leave your thoughts in the comments below.