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Defensive Regression Analysis (DRA)


DRA was created by Michael Humphreys and its method is described in the book Wizardry. He has provided the data for seasons from 1893-2009. The remaining years (1871-1892 & 2010-present) have been calculated by The Baseball Gauge.

Mult-Year Statistics

For most players, this is a 3-year average. These three seasons are the current year, the year before, and the year after. If over the course of those three years a player has not reached the required minimum innings at that position (1458), the span is increased to five years by adding the year before and the after the original three. If the total innings from the 5 years is still under the minimum (1458), the span is increased to seven years.


A player only accumulated 1000 innings in the original three year span. Since it does not meet the required 1458, the span is increased to 5 years. But let's say the total number of innings from the two new seasons is 700. To give more weight to the seasons in the three year span, we prorate the number of runs saved from years 1 and 5 into 458 innings.
5 = Total runs saved in three year span
1000 = Total innings from three year span
-1 = Total runs saved from years 1 & 5 of the 5 year span
700 = Total innings from years 1 & 5 of the 5 year span
5 + (-1) * (458 / 700) = 4.3 runs saved above average (in 1458 innings)

Players With Limited Playing Time

If even after the span has been increased to seven years a player still has not accumulated 1458 innings at that position, we will regress their runs saved to zero. The amount of how much we regress is based on their total number of innings from the seven year span.


*This is a different player than the example above
After the span was increased to seven years, a player only has accumulated 500 innings at that position. During those 500 innings, they have saved 20 runs above average. We will figure how many innings (at zero runs saved above average) to add to this players total with this formula: ((Min / Inn) ^ 0.55 - 1) * Inn

RAA = 20
Inn = 500
Min = 1458

Regressed Innings = ((1458 / 500) ^ 0.55 - 1) * 500 = 400 2/3 Innings

So instead of saving 20 runs in 500 innings, this player has saved 20 runs in 900 2/3 innings

Final Proration

Once we have finished this process of figuring totals from 3, 5, or 7 year spans, we will prorate the runs saved above average totals to the original year's innings.


*This is a different player than the examples above
1200 = Innings from original season
3500 = Total innings from three year span
44 = Total runs saved above average from three year span

Final Multi-Year Runs Saved Above Average = (1200 / 3500) * 40 = 13.7 runs saved (in 1200 innings)

DRA Categories


Total runs saved from all categories below.


Runs Saved from a fielder's range. Catchers are not included.


Total runs saved per 1000 innings.


Runs Saved from catcher's assists in the field. Does not include caught stealings.


Runs Saved from catcher's caught stealings and stolen bases allowed.


(GO2 + CS)
Runs Saved from catcher's assists in the field, caught stealings, and stolen bases allowed.


Runs Saved from catchers avoiding passed balls.


Runs saved from outfield assists