EWMA in Sports Analytics: How Exponential Weighting Adapts to Change

A "last 10 games" rolling average has two problems. First, game #1 and game #10 get equal weight — but a game from three weeks ago is less relevant than last night's game. Second, when game #11 drops off the window, the average can jump discontinuously even though nothing actually changed.

EWMA solves both issues. Weights decline smoothly and continuously — there's no cliff edge where old data suddenly disappears.

EWMA_t = α × x_t + (1 - α) × EWMA_{t-1}

Where:
  x_t    = today's observed value (e.g., offensive rating in this game)
  α      = smoothing factor, between 0 and 1
  EWMA_t = the updated exponentially weighted average

α is derived from the half-life (h):
  α = 1 - exp(-ln(2) / h)

The beauty of this formula is its simplicity: you only need the previous EWMA value and today's observation. No need to store or recompute over a window of past games.

The half-life (h) is the number of games it takes for an observation's weight to drop to 50%. It's the intuitive knob that controls how "reactive" vs. "stable" your metric is:

Think of it like this: a half-life of 10 means that a game played 10 games ago contributes half as much as the most recent game, a game 20 games ago contributes one-quarter, and a game 30 games ago contributes one-eighth.

Predictium's B4 prediction model computes 28 EWMA features across three half-lives for key team statistics like offensive rating, defensive rating, pace, and scoring:

• h10 (short-term) — Captures the last ~2 weeks of play. If a team just traded for a star or lost a key player to injury, h10 adapts within a few games.
• h20 (medium-term) — Smooths over game-to-game noise while still reflecting meaningful changes. This is often the most predictive single half-life.
• h40 (long-term) — Provides a stable baseline that resists overreaction to small sample sizes. Useful for identifying true talent level vs. variance.

The combination of multiple EWMA half-lives is one reason Predictium adapts to mid-season changes faster than models that rely on flat season averages. When a team makes a major trade, the h10 features update within days while traditional "season average" stats take weeks to shift meaningfully.