Which Three Should You Shoot? The Wing, the Top of the Key, and 7,255 Attempts

When I measured the corner three last month, one question stayed open. That piece priced the corner against the above-the-break three as if everything behind the top of the arc were one shot — and it is not. The shot file splits “Above the Break 3” into three zones: left wing, top of the key, right wing. Run the split on the 7,255 above-the-break attempts in our 25,000-shot sample and the top of the key is the worst-paying three on the floor: 34.6% and 1.04 points per shot, against 36.2% and 36.9% on the wings and 38.6% in the corners. But hold that headline loosely, because this article is mostly about how it survives scrutiny — and it only half does. The corner-versus-top gap is real at 2.7 standard errors. The wing-versus-top gap is 1.5 SE of maybe, and once you match distances, most of it dissolves.

The three-way ledger

Every attempt in the bundled file carries a BASIC_ZONE and a side-of-floor ZONE_NAME. Filter to three-pointers, drop backcourt heaves as usual, and the arc splits four ways — two wings, the top, and the corner baseline already published, recomputed here from the same file as a consistency check (it matches to the decimal):

(The three zones sum to 7,251, not 7,255: four attempts launched from 41–44 feet carry the zone name “Back Court,” and they exit with the heave trim below.) Three readings. First, volume: the league does not treat these as one shot. The wings carry 55.6% of all three-point attempts between them while the top carries 18.2% — players shoot from each wing about one and a half times as often as from the top, which is roughly what the zone map would predict from the geometry of drive-and-kick offense. Second, the ordering: corner, wings, top — accuracy falls as you walk around the arc toward the longest part of the line. Third, the sizes: the corner out-shoots the top by 4.0 percentage points (SE 1.5, 2.7 standard errors) — the one within-arc gap in this file that clears the 2-SE bar. The wings out-shoot the top by 2.0 points (SE 1.3, 1.5 SE), which is a lean, not a finding. Our house rule from the symmetry audit applies: differences under 2 SE get called what they are.

Is it the zone, or is it the feet?

Before believing anything about the top of the key, check the suspect the corner piece already convicted once: distance. The arc is 23 feet 9 inches at the top and flattens toward 22 feet at the corners, so top-of-key threes should be longer — and they are, in two ways. Trim the 195 attempts from 30-plus feet (they hit 24.1%, and they spread evenly across zones: 58 left wing, 64 top, 69 right wing) and the average top-of-key three is still 25.83 feet against 25.62 on the wings. More telling is the tail: 24.2% of top attempts come from 27 feet and beyond, against 20.4% of wing attempts. The heave-trimmed gap is wings 36.79%, top 35.03% — +1.75 points at 1.3 SE.

So decompose it. Reprice the top of the key at the wings’ distance mix — take the top’s actual accuracy at each foot of distance, weight it by where wing attempts come from — and its 35.03% becomes 35.45%. Distance mix, in other words, pays back 0.4 of the 1.75-point gap and leaves a 1.3-point residual sitting at about one standard error. And the residual is not spread evenly across distances — it lives almost entirely in one band:

Walk the feet and you see it. At 24 feet: wings 39.3%, top 38.9%. At 25 feet the top is actually ahead, 38.6% to 37.0%. Then the floor tilts: 33.0% against 34.7% at 26 feet, and at 27 feet the top falls to 29.5% while the wings hold 37.0% — a 7.5-point crater that looks decisive until you notice it rests on 258 top-of-key attempts, and that it is one of six per-foot comparisons in a piece that already ran four zone comparisons. That is exactly the multiple-comparisons terrain where the symmetry audit taught us something is supposed to wander past the line by accident. A boring mechanical story would fit — a 27-footer from the top is disproportionately a late-clock pull-up over a set defense, while a deep wing three is more often a kick-out relocation shot — but this file carries no shot clock and no assist flag, so that is a hypothesis for a dataset we don’t have. What this dataset supports is narrower: the top’s deficit is a long-range phenomenon; at rhythm distances the wing and the top are the same shot.

Left wing versus right wing

The within-piece symmetry check, since the split hands it to us. Left wing 36.18% on 2,803 attempts, right wing 36.92% on 2,660 — a 0.74-point gap at 0.6 standard errors, i.e., nothing. That is the same null, on the same zones, that the left-right audit found when it mirrored the whole floor (its wing numbers were these numbers), and the corners told the identical story in the corner piece: 38.9 left, 38.2 right, 0.4 SE. Both wings also carry the same slightly heavier attempt load relative to the top. Whatever structure the arc has, it is radial, not sided — the floor still has no grain.

So which three should you shoot?

Priced per 100 attempts: corners 116 points, right wing 111, left wing 109, top of the key 104. The corner-versus-top spread — 12 points per 100 attempts — is now the widest arbitrage between three-point zones on the site’s books, and unlike the wing-top gap it is statistically solid. But the decomposition above says to read it the way the corner piece read the corner premium: as geometry collecting rent. The corner is a 22.9-foot shot, the top averages 26.0 feet, and accuracy falls about 0.8 points per foot across this range. A team’s shot-selection lesson is therefore not “avoid the top of the key” — at the distances that dominate real possessions, the top converts like a wing. The lesson is the same one the arc has been teaching for a decade, now with within-arc resolution: every foot behind the line is real money, and the extra feet players give away launching from 27-plus at the top are the most expensive feet in the file.

Limitations

One season (2023-24), and a bundled 25,000-shot sample of it rather than the league’s full attempt log — that is why the wing-top question, which needs to resolve a 1–2 point gap, ends in an honest shrug while the 4-point corner-top gap resolves cleanly. Distances are integer feet. The zone boundaries are the data provider’s, not mine; “Center” spans roughly the width of the lane extended, so “top of the key” here includes straightaway threes generally. The matched-distance comparison conditions on where players chose to shoot — if defenses concede different shots in different zones, matching distance does not fully equalize shot quality, and with no defender or shot-clock context I cannot close that door. And all of this is league-aggregate: your favorite high-volume pull-up shooter is priced into these averages, not described by them.

Reproduce it

The whole piece is two groupbys and a reweighting:

import pandas as pd
df = pd.read_csv("data_layer/nba_league_shots.csv")
df = df[df.BASIC_ZONE != "Backcourt"]
atb = df[df.BASIC_ZONE == "Above the Break 3"]
print(atb.groupby("ZONE_NAME").SHOT_MADE.agg(["size", "mean"]))

sub = atb[atb.SHOT_DISTANCE <= 29]           # heaves out
w = sub[sub.ZONE_NAME.isin(["Left Side Center", "Right Side Center"])]
t = sub[sub.ZONE_NAME == "Center"]
mix = w.SHOT_DISTANCE.value_counts(normalize=True)
ft = t.groupby("SHOT_DISTANCE").SHOT_MADE.mean()
common = mix.index.intersection(ft.index)
print((mix[common] * ft[common]).sum() / mix[common].sum())
# 0.3545 — the top, repriced at the wings' distances (raw top: 0.3503)

charts/chart_wing_vs_top.py runs the full version on every rebuild — the four-zone ledger, every difference with its SE, the heave trim, the reweighting, and the per-foot table — and prints every number quoted above.