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The Owlcroft Baseball-Analysis Site
Baseball team and player performance examined realistically and accurately.
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Proving the TOP: Tabular
“Upon the whole you have proved to be Much as you said you were.”
This page displays the full results in tabular form; those wanting to see the individual data points laid out in graphical form can do so on this main formula-proof page.
Seventy-One Years of Baseball Data
The Table below shows the results of applying the full Owlcroft formula for runs scored and runs allowed (that’s two separate datasets per team per year) to 73 years of actual major-league data: all teams in all years from 1954 through the last completed season, inclusive.
As to why that start-year limit: there was a scoring-rule change (Sacrifice Flies were added back in as a scoring category) between 1953 and 1954; prior years’ data would be incommensurable (granted, the difference would be small, but we are here refining error size down to hundredths of a percent).
The team data used in that formula include: at-bats, walks, hit batsmen, sacrifice hits (bunts), sacrifice flies, singles, doubles, triples, home runs, catcher’s interference calls, stolen bases, caught stealing, double plays, and opponents’ errors allowing an otherwise-out man to reach base safely. All but that last are widely published, and the other can be found by looking (the Baseball Reference site, for one, has it). The methodology of the TOP (projected-runs) calculation is explained elsewhere on this site.
In our opinion, the graphical representation available elsewhere on this site more clearly shows the accuracy and quality of the measure. But for those who insist on seeing a long, detailed tabulation in numbers, here it is.
The formula was applied individually to every major-league team’s batting and pitching stats for every year from 1954 through 2024 inclusive (3,656 team-seasons). The average per-team-per-season percentage error size for the formula is 2.39% (more precisely, 2.3898731037913%). If you know what RMSE (Root Mean Squared Error) signifies, it is 20.578344718047 runs (roughly 20.58).
(The Wikipedia page linked just above contains the following note: “Some researchers have recommended the use of the mean absolute error (MAE) instead of the root mean square deviation. MAE possesses advantages in interpretability over RMSD. MAE is the average of the absolute values of the errors. MAE is fundamentally easier to understand than the square root of the average of squared errors. Furthermore, each error influences MAE in direct proportion to the absolute value of the error, which is not the case for RMSD.”
We cannot use the actual MAE because the data are disparate: in some years there were 162 games in a season, in others 154 games, and in a few years (1981, 1994, 1995, and 2020) considerably fewer. An error size of, say, 20 runs means one thing when the runs average is 300 and quite another when it’s 725; so, when quoting error rates we use the percentage size of error. That is strongly analogous to the MAE error-size measurement, and we agree that it is a more meaningful measure than RMSE; but we include RMSE because some analysts fancy it.
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