The Total Defense Tool (TDT) estimates AL and NL standings based purely on different aspects of team defense. For example, it can be used to estimate what the league standings would look like if every team was league average, in every respect, except for the total fielding performance of its position players (range + errors).
The TDT uses a modified version of the wOBA formula to measure team defense. In its pristine form, the wOBA is arguably the very best measure of offensive production. It was developed by Tom Tango, and you should read more about it here. I have modified the formula to make it a measure of pitching and fielding. The modifications are:
1. Use of opponents’ offensive statistics
2. Removing SB and CS
3. Adding team specific, park adjusted, run-value coefficients for batted ball types (BBT). (The coefficients for the BBTs are derived by calculating each team’s wOBA for ground balls, fly balls and line drives. Home runs and runners reaching on errors are excluded from these calculations so that defensive range is isolated. Park adjustments are applied to each BBT – http://www.statcorner.com.)
Here is the TDT equation: = (2.08 * # of park adjusted HR allowed) + (.72 * #HBP) + (.92 * #ROE) + (.69* #NIBB) + (Park adjusted wOBAgb * #GB) + (Park adjusted wOBAfb * #FB) + (Park adjusted wOBAld * #LD).
Once the TDT coefficient is calculated for each team, it is turned into an estimate of runs allowed, then a Pythagorean win percentage, then estimated wins.
When the actual team totals for the 2011 season are plugged into the TDT formula, it churns out very accurate results. For the 2011 season, the TDT estimates an average of 694.4 runs allowed per team. The actual average runs allowed was 693.6. On a team-by-team basis the correlation between predicted and actual runs scored was .96. The Root Mean Square Error is 21.9 and the R-squared is 92.2.
While the TDT is not necessarily the most sophisticated of run estimators (though it is pretty good), its greatest strength is its flexibility. By simply changing the combination of variables that are set to league average, the impact of different skill sets can be isolated and compared. For example, if you think a team has below average range, and you want to see how many wins that could cost them over a season, all you have to do is set every variable to league average except for batted balls types- BBTs. The resulting coefficient is then transformed into that team’s expected wins based purely on its defensive range.
Now to the results:
2011 League Standings
I have measured six aspects of team defense. I will describe each of them in turn, as well as provide a table that identifies the variables that are being held to league average (L), and those that are allowed to vary based on actual team performance (V). The abbreviations are as follows:
V=Varies based on team’s fielders/pitchers performance;
L= Set to league average rate
PaHR=Park adjusted HRs allowed
HBP = Hit by Pitch
ROE=Reached on error
rGB / FB / LD = number (or rate) of ground balls / fly balls / line drives
cGB / FB / LD = coefficient for ground balls / fly balls / line drives
Total Team Defense (TTD)
The TTD estimates the number of wins for each team based on its total defensive performance. All variables are allowed to vary with actual team performance.
Interpretation: These are the estimated aggregate league standings for 2011, if only thing that distinguished teams were their pitching staffs and fielding ability.
In other words, all teams are exactly league average in terms of offense and the ball park they play in.
Pitcher Responsibility (PR)
PR isolates runs that are clearly the responsibility of pitchers. All variables are normalized to league average except walks, park adjusted home runs allowed, and hit batsmen. It is called Pitcher Responsibility because pitchers have total control over PaHR, HBP, NIPP. In other words, there is nothing a team’s fielders can do about these events.
Interpretation: These are the estimated aggregate league standings for 2011 if the only thing that distinguished teams was the ability of their pitching staffs to prevent events that they had total control over.
Pitcher Responsibility + Batted Ball Types (PR+BBT)
PR+BBT is the same as PR, except it assumes pitchers have some responsibility for the kinds of batted balls hit against them. In other words, it assumes pitcher have some responsibility for the rate of GB, FB, LD they allow. (Pitchers that give up more LDs put more pressure on their defense and hurt their team.)
Interpretation: These are the estimated aggregate league standings for 2011 if the only thing that distinguished teams was the ability of their pitching staffs on events that they have total control over (NiBB, HBP and HR) and those that they may have some control over (batted ball types).
Team Range/Team BBT Rate (TR)
TR isolates team defensive range and includes the team’s actual BBT rate.
I define range like Tom Tippett, programmer Diamond Mind Baseball, does, “range implies the ability to cover ground. And while that’s part of the story, it’s not the whole story…(range) actually measures each fielder’s overall playmaking ability (minus throwing and his tendency to commit errors, as we have separate ratings for those things). And playmaking ability is not just about range, it’s about the ability to turn all sorts of batted balls into outs.”
Interpretation: These are the estimated aggregate league standings for 2011 if only thing that distinguished teams was their team defensive range, and the rate at which their pitchers gave up GB, FB and LDs.
Team Range with League Average BBT Rate (TRL)
TRL looks at range again. However this time the rate of BBT is held to league average.
Interpretation: These are the estimated aggregate league standings for 2011, if the only thing that distinguished teams was their defensive range.
Total Position Player (TPP)
TPP examines all the aspects of team fielding included in TDT. It factors in both range and errors. The rate of batted ball types is allowed to vary with the team’s pitchers.
Interpretation: These are the estimated aggregate league standings for 2011 if only thing that distinguished teams was their team fielding, and the rate of BBTs given up by their pitchers.
I will be updating the TDT at the All-Star break of the 2012 season.
I, and everyone else who uses wOBA, owes a huge debt of gratitude to Tom Tango for his fine work in the field of baseball research. Do yourself a favor and check out his webpage and buy his book. You will be happy you did.
I will work on publishing a calculator for the TDT if you would like to use it. Just let me know if there is any interest.
For lots of baseball tweets and talk (especially during Pirates and Tigers games), consider following me on twitter @highoutsidebaseball
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