Force Document

Interior Dominance — Shaq Factor

The score in one sentence

SHAQ FACTOR: a single number (0-100) that captures a player’s OFFENSIVE INTERIOR DOMINANCE.

Close your eyes and visualize prime Shaq. What do you imagine? Celebrating one of his dominant performances with the Lakers in the finals? A preposterously sized man carrying half the New Jersey Nets to the hoop? An anxious trip to the foul line, sweat dripping into his eyes as he lines up for another clank? A surprisingly soft touch on hooks around the paint? Gathering in offensive rebounds by the dozen?

These are all Shaq, anecdotally, and they are lenses on the most physically dominant player of the full-data (post 1997) era¹. A bull in the china shop of a player - lives at the rim, goes through (rather than around) defenders, and converts the paint into their sovereign territory. The Institute can now exclusively release the data that backs up this claim, but also casts some interesting light on it.

Note: all data is post-1997 — the shot data required for populating the formula is lacking prior to then.

author: Albert W. Pikenrohl

experiment: Index of physical interior dominance

document classification: HWRI-PLR-AQV9-FR90-63BW-CAAP-838X

approved by: The Hardwoodist

clearance: Public Release

version: v5 (2026-04-27)

supported eras: 1997 –

Section I — The Top of the Index

The Top of the Index

Top 30 player-seasons by shaq_factor. Each row is a single season. Traded players appear under their primary stint.

Giannis Antetokounmpo

Giannis Antetokounmpo

Editor’s note · the eponym

A note on the index, and the man himself.

A reader has perhaps already arrived at the obvious objection. Where is the man himself? Shaquille O’Neal’s 1999–2000 MVP season — 67 wins, an 18–2 playoff run, the first of three consecutive Larry O’Briens — sits well outside the top of this leaderboard. His best-rated season (2000–01 LAL) lands inside the top twenty but not anywhere near the head. A long bench of modern bigs sit above the literal name of the award.

This is not a bug — this is the factor telling us something new.

shaq_factor’s component structure measures the archetype of physical interior dominance. The interesting outcome of this formula is that, while Shaq himself dominates the factor vs. his contemporaries, the efficiency required by the modern game produces a more concentrated form of that archetype: pace, spacing, and the league-wide leveraging of the extremely efficient lob mean today’s pure rim-runners (Drummond, Gobert, DeAndre, Capela) take 85–90% of their shots from the restricted area. Shaq’s shot diet was wider — a working mix of dunks, hooks, turnaround jumpers, and drop steps, presumably due to the archetype he inherited as “franchise center.” Was this why his game skewed more towards Hakeem, Patrick, Robinson, and Kareem? And “should” it have been even more concentrated than it was?

The 1.25× premium this index applies to rim attempts over paint-non-restricted-area finishes is the differentiator that edges a pure rim-runner past a more varied interior diet at the very top of the leaderboard.

The point is not that Shaq does not deserve for the award to be named after him. His dominance relative to the league, year after year, speaks for itself. What is interesting is that 2000 LAL and 2016 LAC are different shapes of force, and the modern game has refined the shape into a more concentrated expression. On the matter of a physical and athletic marvel, unparalleled in power and effectiveness², he remains uncontested.

View top 200 →

Section II — The Lopez Arc

The Lopez Arc

Brook Lopez is a fascinating illustration in year-over-year shaq_factor. Across sixteen seasons he travelled most of the index — classic low-block operator into his late twenties, then a complete reformation into a Mike Budenholzer floor-spacing big. When you visualize Brook Lopez now, it isn’t a mammoth human clearing space in the post, it’s setting his feet for a trailing three.

The dashed line is the league-wide qualifying-player average. Interestingly, league-wide shaq_factor is a near-constant, year over year.

Brook Lopez, shaq_factor by season. Dots colored by team; the league-wide qualifying average sits remarkably flat, 42–45, across the entire span.

Three more arcs that travelled the same road

Marc Gasol

Memphis post-up DPOY → Toronto title 5-out floor-spacer. The arc people remember; the span people forget.

Carmelo Anthony

Three-level scorer with a healthy interior diet through Denver and New York. By the LAL/POR ride-along years he was a stationary corner shooter.

Kevin Love

Minnesota 20-and-15 → Cleveland stretch-4 → Heat & Jazz spot-up specialist. The basketball case for shaq_factor in one career.

And three counter-trends — non-shaq → shaq

Giannis Antetokounmpo

Skinny project to full-bull MVP. Twelve consecutive seasons of upward pressure on the index — the cleanest non-shaq → shaq line on file.

Nikola Jokić

The soft-touch big who quietly grew into one of the heaviest interior diets in the league. Each MVP year another tick north.

Shai Gilgeous-Alexander

A guard. The index does not, as a rule, flatter guards. SGA disagreed: the foul-drawing component carries him into territory normally reserved for centers.

Section III — The Podium

Two Low Block Artists, Then Everybody

shaq_factor was, for nineteen consecutive seasons, the domain of exactly whom you would think. From 1996–97 through 2014–15, the same two men held the #1 slot — Shaquille O’Neal for the first ten, Dwight Howard for the next nine. Beginning 2015–16, however, the index broke into a roll call: DeAndre, Gobert, Drummond, Giannis, Zion. Is this the result of the decline of the singular paint-bully and the rise of the league’s deepest ever interior-finisher rotation? The league lacking a generational athletic marvel? Better overall shooting? More specialization? The data is clear, but the conclusion is not.

Top three shaq_factor entries per season, dots colored by team. The faint horizontal tick is that season’s qualifying-player mean. Hover to identify the player.

Section IV — Read the formula

Read the formula

shaq_factor is a composite of four z-scored components, blended at 0.25 / 0.20 / 0.30 / 0.25 weights and squashed through a sigmoid into a 0–100 scale. The component identities:

shot diet
When this player shoots, what shape are those shots? A weighted blend of rim and paint-non-restricted-area frequency, with rim attempts carrying a 1.25× premium over hooks and post-up jumpers. Dunks are layered on as a small additional signal.
```
weighted_interior_freq = 1.25 × rim_freq + 1.00 × paint_freq

shot_diet_z = 0.75 × (weighted_interior_freq − 0.50) / 0.20
            + 0.10 × (dunk_rate              − 0.10) / 0.10
```
interior volume
Not just rate, but absolute volume. A high-frequency rim diet on six attempts a game is one thing; the same diet on eighteen attempts is Shaq territory. Anchored to 8 weighted interior attempts/game = league mean rotation big.
```
weighted_interior_apg = weighted_interior_freq × fga_per_game

interior_volume_z = (weighted_interior_apg − 8.0) / 4.0
```
fouls drawn
Free throw drawing rate (FTA per FGA + FTA correction) and per-game free throw volume, in a 60/40 blend. Drawing fouls in the paint is the mechanical signature of physical inevitability — demonstrating when defenders have run out of legal options³.
```
ft_drawing_rate = fta / (fga + 0.44 × fta)

foul_z = 0.60 × (ft_drawing_rate − 0.30) / 0.15
       + 0.40 × (fta_per_game    − 5.0)  / 3.0
```
finishing
Field goal percentage, offensive rebounds per game, and offensive charges drawn per 36 minutes. The chaos that happens after the move: the ball goes in, the rebound comes back, the defender flops.
```
finish_z = 0.35 × (fg_pct              − 0.50) / 0.10
         + 0.45 × (oreb_per_game       − 2.5)  / 1.5
         + 0.20 × (off_charges_per_36  − 0.10) / 0.05
```

Notable absences: there is no stretch penalty. A center who shoots threes is not less Shaq-shaped on the possessions where they do go down to the block; they’re just doing fewer of those possessions. The volume signal captures that naturally. Jokić landing in the high 70s while still often spotting up on the perimeter is a feature, not a bug.

Weight is also not a signal. We are deliberately not rewarding players for being heavy. An undersized energy big who lives at the rim and draws contact (Kenneth Faried, Jonas Valančiūnas off the bench) should land high. A 7′2″, 240-pound center⁴ who plays outside-in should not.

Coverage starts at 1996–97. The composite is shot-events derived; pre-1997 player-seasons have no shot location data, so shaq_factor renders as “—” rather than a guess, per the Institute’s standing policy.

composite

Weighted blend of the four z-scores, then squashed through a sigmoid to a 0–100 scale. Weights sum to 1.0; the sigmoid steepness k = 0.8 keeps elite seasons in the 80s–90s without saturation.

shaq_z = 0.25 × shot_diet_z + 0.20 × interior_volume_z
       + 0.30 × foul_z      + 0.25 × finish_z

base = 100 / (1 + exp(−0.8 × shaq_z))

tracking bonus · 2013-14 +

When league-tracked paint and post touches are available, a smooth-gated additive bonus credits players who actually operate in those zones. This separates high-volume rim-runners from genuine low-block operators. Pre-tracking seasons skip this enhancement, and use base alone.

rim_factor = smooth ramp on weighted_interior_freq
             0  at 0.50    →    1.0  at 0.80

paint_bonus = max(0, paint_touches_per_game − 5.0) × 0.8
post_bonus  = max(0, post_touches_per_game  − 1.5) × 0.6

interior_bonus = min(8, (paint_bonus + post_bonus) × rim_factor)

shaq_factor = clamp(base + interior_bonus, 0, 100)

Footnotes

With apologies to Chris Dudley. ↩
Setting aside when he was rehabbing on company time. ↩
There is likely some noise around this stat with bigs who were catastrophically poor free throw shooters, but also — what’s more Shaq than going 0 for 2 but going back into the post on the next possession anyway? ↩
Also not factored in — whether or not the player is Latvian. ↩