Why Repeated Ticks Are Not Repeated Evidence

A probability path can be recorded many times during one game. That creates a useful sequence for describing how the published forecast moved, but it does not create the same number of independent games. The observation-dependence page makes this visible with lag-1 residual autocorrelation: a comparison between each signed residual and the residual immediately before it within the same eligible game-side series. The residual is defined in the artifact as probability at time t minus the terminal outcome. The series are ordered by timestamp.

Lag-1 autocorrelation ranges from -1 to 1. A value near 1 means that consecutive residuals tend to move together. A value near 0 would indicate little linear relationship between adjacent residuals in that series. A negative value would indicate alternating movement. The page does not turn a high autocorrelation into a claim about forecast quality by itself. It describes dependence: how much one recorded residual resembles its neighbor in the same path.

The MLB model distribution provides a worked example. The artifact has 78,986 records across 227 candidate series. After its eligibility rules, 222 model series remain. Their median lag-1 residual autocorrelation is 0.9809, and 95.5% of eligible model series are above 0.9. In plain language, a 0.9809 median says adjacent residuals are extremely similar on the published linear autocorrelation measure. It does not say that 98.09% of predictions were correct, that the terminal outcome had a 98.09% frequency, or that one tick supplies 0.9809 of another tick's sample size. It is a property of the within-game residual sequence.

The structure of the data explains why this is plausible. The terminal outcome remains fixed for all ticks of a completed game, while a probability path often changes gradually from one timestamp to the next. Subtracting the same terminal value from a smooth path produces a smooth residual path. Many adjacent rows can therefore describe almost the same game state with only a small update between them. Treating every row as a fresh game would overstate how much distinct game-level evidence sits behind a calibration summary.

The page reports ticks and games separately because they answer different questions. The tick count tells the reader the size of the displayed recorded population. The eligible-series count tells the reader how many within-game series contributed to the autocorrelation distribution. The artifact applies a minimum of 10 rows per game and a minimum residual variance of 1e-9 before a series is eligible. In the MLB model population, two series were skipped for too few rows and three for flat residuals. Those exclusions are published rather than hidden inside the median.

It would be tempting to take the 0.9809 value, insert it into a formula, and declare a single effective sample size for every page. This site does not do that. An effective sample size depends on the estimand, the dependence structure beyond one lag, the weighting scheme, and the procedure that aggregates observations. One lag-1 summary is evidence of strong dependence, not a universal conversion from ticks to games. Publishing a precise-looking conversion without those ingredients would add an unsupported calculation.

The page keeps model and market arrays separate for the same reason. For MLB, the market series have median autocorrelation 0.9799 and 96.44% above 0.9 across 225 eligible series. Those are close published summaries, but they are still different populations with different skipped counts and paths. The dots are not paired observations. A comparison should preserve the side, sport, and eligibility context attached to the original value.

Use this page alongside the reliability diagram rather than in place of it. The reliability page reports bins, tick totals, game totals, and clustered bootstrap intervals. This page supplies the descriptive reason that repeated ticks deserve caution: the observed residual paths are highly serially related. Together, the pages make the counting rule visible without pretending that a single transformed count solves every inferential question.

Inspect the worked example

Where to go next

• Observation dependence
• Calibration
• Effective sample size finding

Sources