Putting Decimals In Their Place

Like many of us, I have been frustrated with the on-screen product right now. It’s not uniform. It’s changed from previous years. It just looks off.

That’s right - we’re talking about decimals.

If you have looked at the ticker during a Bucks game this season - and to be honest, as of late it has been a welcome reprieve from watching the game - you will likely share my indignation. Numbers are rounded to the integer, the tenths place, and even the hundredths place (!) with reckless abandon. In particular, I don’t recall them rounding to the hundredths in previous years. On the whole, it’s a hodgepodge of decimals that grinds my gears.

I realize that I may be alone with this umbrage. Thus, I’ll spend the first part of the article cataloging this issue, so you can at least see where I’m coming from. Then I’ll connect it to something of broader significance: the tradeoff between accuracy and clarity. Finally, rather than simply complain, I’ll crunch some numbers, put on my thinking cap, and propose a better way to treat decimals places in basketball statistics.

Let’s revisit last Friday’s game against Charlotte. (Sorry.) The Bucks were already down 15 midway through the first quarter when the ticker added insult to injury by showing the NBA Leaders across various categories. First up in points per game was one L. Doncic with 34 on the nose. That’s odd (well, even) - usually they throw us a tenths place. I guess we’re sticking with integers. Next up, though, is J. Embiid, with 33.5. What? Is Luka’s average 34.0, or did they forget the tenths place? Or is Embiid’s stat at fault? Moving on, in third place is G. Antetokounmpo - hey, that one’s ours! He clocks in at 32.7. Okay: tenths place is it.

On to assists. (Assists? Not rebounds? Okay...) Leading the charge is T. Haliburton with 10.2 - really hitting the tenths. T. Young and N. Jokic have 9.9 and 9.5 assists per game, respectively - consistency!

Next up is steals. Scarf-man and helpfully-abbreviated OG Anunoby is up first with 2.2... 1. (Giannis swishes a free throw to bring the Bucks within 14). The hundredths place departs from points and assists, but the totals are lower, so I’ll roll with it. (Props to Tyrese for taking third in steals to go with being first in assists - doing Wisconsin proud!)

Area Man B. Lopez is first up in blocks with 2.65 - again, due to the lower totals, I’ll let it slide. He’s followed by N. Claxton (2.51) (Giannis bricks the second) and Future Buck M. Turner (2.21). The ticker person was distracted by flashing (coincidentally abbreviated) P.J. Washington’s power line of 8 points and 2 fouls, so we get an encore of the block leaders. Lol, thanks Bally. Charlotte up 16. I hate Plumlees.

Now the kicker: rebounds. D. Sabonis takes the crown with... 12.44? Hundredths again? But there are so many rebounds! Anyway, Giannis has 12.06, C. Capela has 11.93, and the Bucks nearly throw it out of bounds. That’s a wrap.

Kudos for making it this far - I promise longer sentences going forward, but with just as much snark. It’s time to turn these decimal places into something bigger.

Let’s start with a basic question: Why do we have basketball statistics? I would answer that it is to get a rough sense of the value of a player. Moreover, because they are quantifiable, they are often leveraged in the service of comparing one player to another. “Player X is better than Player Y because they score Z more points per game” - that sort of stuff.

With that in mind, let’s return to the rebounding totals. Let’s say that I try to argue that Domantis “Freaking” Sabonis is a better rebounder than Giannis because he has 12.44 rebounds per game to Giannis’ 12.06. You laugh, but you may think that he doesn’t snag an extra .38 rebounds a game for nothing. Alright. What about Giannis and Clint Capela, who differ by .13 rebounds a game? Regardless of your answer, it’s a tougher call to make.

My point is that basketball statistics - and statistics period, for that matter - should not be all about accuracy. If we really wanted to be accurate, we could have millions of decimal places! But we’re not nuclear physicists. (“Oh no! The fusion reaction is ruined! I knew we shouldn’t have rounded Brook’s blocks per game to the nearest tenth!”) Instead, we want to clearly express when one player has more of something than another, and we want decimals that serve that purpose. Hundredths places DO NOT. They falsely suggest that .01 is a meaningful difference between two statistics. In almost all cases, it is not.

There is likely a more nefarious purpose for decimals too: they allow for more jockeying for position. When grabbing an extra .01 rebounds / steals / blocks per game is enough to slip by your competitor, the rankings can fluctuate more. Just like the US News has a financial incentive to garble the college rankings on an annual basis so people pony up for the “new” rankings every year, so too does the NBA have a financial incentive to keep our eyeballs on the leaderboards. (Case in point: my alma mater was ranked the sixth, ninth, and seventh best liberal arts college the last three years - I wish academic institutions changed that fast!) To end this section on (yet) another metaphor, it’s like the announcer of a horse race yelled, “IT’S JUSTIFY BY A HAIR! NO, IT’S AMERICAN PHAROAH BY A HAIR! NO, IT’S...”, but the race lasted months instead of minutes. (Not an inaccurate description of national basketball coverage, come to think of it...) A less accurate but markedly clearer announcer would simply scream, “IT’S NECK AND NECK!” on repeat.

Enough carping - how do we fix this? Let’s use decimals places that allow us to clearly distinguish meaningful differences between players.

I “downloaded” (read: copy and pasted) the top 260 scorers in the league from NBA.com. This doesn’t include everyone, but it includes P.J. Tucker’s 3.3 points per game, so it’s pretty close to rock bottom. (And we would probably exclude folks scoring 0 or 0ish a game anyway - stay tuned.)

For each statistic, I calculated the standard deviation. The standard deviation is higher when the values are more spread out and lower the the values are more bunched together. Although it’s best when you have a normal distribution - our distribution is skewed since there are more people who score not much than score a lot (which would have been further inflamed by having the 0ish per game scorers in our data) - it works well enough for our purposes. Let’s check those out:

These make sense. There’s a large spread for points; a medium spread for rebounds and assists; a small spread for steals and blocks; and a just right spread for Goldilocks.

The reason I calculated standard deviations is that they effectively create bins. You typically won’t see values more than plus or minus three standard deviations from the mean (those would be Malcolm Gladwell’s famous “outliers”). That means that using the standard deviation as our “decimal” would effectively sort players into six buckets (pun intended). That may not be enough, but that’s okay - we can divide the standard deviation as needed, depending on how fine-grained we want our statistics. A fun upshot of this approach is that these bins are “standardized,” allowing us to compare apples and oranges. For example, leaping from one bin to the next in terms of points per game could be roughly compared to one-bin leaps in other statistics.

My personal vote would be for dividing the standard deviation by 2. Fudging a bit, we would round points to the nearest divisor of 3 (which neatly aligns with three-pointers), rebounds and assists to the nearest integer, and steals and blocks to the nearest .2. That would really clean up the leaderboards, and for some reason the idea that there are 12 tiers of players seems about right to me. A case could be made for dividing it by 3, where we round points to the nearest divisor of 2 (which neatly aligns with two-pointers), rebounds and assists to the nearest .5, and steals and blocks to the nearest .1, but I’m not sure whether the gain in accuracy is worth the loss in clarity.

What would this look like? Using “most to least disruptive” logic, let’s look at the leaders in points per game:

To me, that is a breath of fresh air. Rather than tearing our hair out over decimal places, we can clearly delineate general tiers of players that, at least to my Bucks-only eyes, seem to make sense. I’ll leave the remaining categories as exercises for the enterprising reader. Please turn in your work in the comments.

A possible rejoinder to this change would be that rounding can also make things less clear. I agree that the tradeoff between clarity and accuracy only holds to a certain extent, at which point rounding would simply be unclear and inaccurate (e.g., dividing NBA scorers into two bins, where anything less than 17 is 0 and anything 17+ is Luka.) But I think rounding to this degree is still clear.

Relatedly, it may be harder to see gradual change over time if people are locked into the nearest divisor of three. But season averages aren’t even the best way to examine that change. If you say that Giannis is dropping off because his season average in points per game dropped from (say) 34.2 to 32.7, you could have said that Giannis is dropping off because his point average the last few games is a lot less than his season average. Statistics are used to tell stories; basketball is no different. I prefer my stories clear.

So, to conclude, a message to Bally Sports, NBA.com, and the broader basket-sphere: value clarity over accuracy. Your viewers - or this viewer, at least - will thank you.