The formula for DIPS is, unfortunately, a little complicated. See the sample code that follows for an explanation of DIPS calculations. I’ll just launch into the code to explain how to calculate this measurement. (I used Voros McCracken’s own explanation for DIPS 2.0 numbers to make the following calculations.)

The process proceeds in two phases. First, a set of defense-independent measurements are calculated: DIPS intentional walks allowed (dIBB), DIPS hit batsmen (dHP), DIPS total walks (dBB), DIPS home runs (dHR), DIPS hits (dH), and DIPS innings pitched (dIP). A couple of other numbers are calculated that are used in later calculations. A few more variables are calculated based on a mix of actual values and DIPS values: strikeouts per ball in play (sSO), home runs per ball in play (sHR), and hits per ball in play (sH). These also are used in some later calculations. Finally, DIPS earned runs (dER) and DIPS ERA (dERA) are calculated.

Here is some sample code for calculating DIPS in R:

	# 4
	dIBB <- BFP * .0074
	# 5
	sHP <- HBP / (BFP - IBB)
	dHP <- sHP * (BFP - dIBB)
	# 6
	sBB <- (BB - IBB) / (BFP - IBB - HBP)
	dBB <- sBB * (BFP - dIBB - dHP) + dIBB
	# 7
	sSO <- SO / (BFP - HBP - BB)
	dSO <- sSO * (BFP - dBB - dHP)
	# 8
	sHR <- HR / (BFP - HBP - BB - SO)
	dHR <- sHR * (BFP - dBB - dHP - dSO)
	# 9
	sH <- .304396 + .002321 * (throws == "L") - .04782 * sSO - .08095 * sHR
	# 10
	dH <- sH * (BFP - dHR - dBB - dSO - dHP) + dHR
	# 11
	dIP <- (1.048 * (BFP - dBB - dHP - dSO - dH) + dSO) / 3
	# 12
	dER <- (dH-dHR)*.49674 + dHR*1.294375 + (dBB-dIBB)*.3325 + dIBB*.0864336 + dSO*(-
	.084691) + dHP*.3077 + (BFP-dHP-dBB-dSO-dH)*(-.082927)
	# 13
	dERA <- dER * 9  / dIP Summary Statistics
	# calculate summary stats for 2003
	> summary(subset(dERA, yearID == 2003 & BFP > 249))

To compute this in SQL, you can use the following code. This code creates a temporary table called dipsERAs from which you can query DIPS ERA results. Notice the nine subqueries in this statement; I calculated each formula in sequence, just as I did in the R code.

	CREATE TEMPORARY TABLE dipsERAs AS
	SELECT nameFirst, nameLast, idxTeams,
	   lgID, ERA, dERA, IPOuts
	FROM ( -- p_w_d
	 SELECT *, dER * 9  / dIP AS dERA
	 FROM ( -- p9
	 SELECT *,
	   (dH-dHR)*.49674 + dHR*1.294375
	    + (dBB-dIBB)*.3325 + dIBB*.0864336
	    + dSO*(-.084691) + dHP*.3077
	    + (BFP-dHP-dBB-dSO-dH)*(-.082927) AS dER
	FROM ( -- p8
	 SELECT *,
	    (1.048 * (BFP - dBB - dHP - dSO - dH)
	   + dSO) / 3 AS dIP
	 FROM ( -- p7
	 SELECT *,
	   sH * (BFP - dHR - dBB - dSO - dHP)
	   + dHR AS dH
	 FROM ( -- p6
	  SELECT *,
	    .304396
	     + .002321 * (CASE WHEN throws='L' THEN 1 ELSE 0 END)
	     - .04782 * sSO - .08095 * sHR AS sH
	  FROM ( -- p5
	  SELECT *,
	     sHR *(BFP - dBB - dHP - dSO) AS dHR
	  FROM ( -- p4
	  SELECT *,
	    sSO * (BFP - dBB - dHP) AS dSO,
	  HR / (BFP - HBP - BB - SO) AS sHR
	 FROM ( -- p3
	  SELECT *,
	   sBB * (BFP - dIBB - dHP)
	   + dIBB AS dBB,
	   SO / (BFP - HBP - BB) AS sSO
	   FROM ( -- p2
	   SELECT *,
	   sHP * (BFP - dIBB) AS dHP,
	   (BB - IBB) / (BFP - IBB - HBP) as sBB
	   FROM  ( -- p1
	   SELECT p.*, m.nameFirst, m.nameLast, m.throws,
	    BFP * .0074 AS diBB,
	   HBP / (BFP - IBB) AS sHP
	   FROM pitching p inner join master m
	   ON p.idxLahman=m.idxLahman
	         ) p1
	          ) p2
	          ) p3
	         ) p4
	        ) p5
	       ) p6
	      ) p7
	     ) p8
	    ) p9
	   ) p_w_d
	;

To better understand DIPS ERA, let’s look at the distribution of DIPS ERA, as shown in Figure 5-12. Notice that the range and shape of the distribution is similar to ERA.

Figure 5-12. DIPS ERA distribution and box plot

	  Min.  1st Qu.   Median    Mean  3rd Qu.    Max.
	 1.048    3.821    4.339   4.360    4.946   6.652

	 Min.    1st Qu.    Median    Mean  3rd Qu.    Max.
	1.048      3.895     4.419   4.409    4.943   7.676

	 Min.   1st Qu.   Median     Mean   3rd Qu.    Max.    NA's
	1.048     3.816    4.276    4.291    4.747   7.676  141.000

As I noted earlier, when a ball is put into play, it’s the defense’s responsibility to convert it into an out. If a pitcher is lucky, the defense will convert a lot of balls in play into outs, and a pitcher will have very few earned runs. If a pitcher is unlucky, the defense will miss a lot of balls, and a pitcher will have many earned runs. DIPS is designed to estimate a pitcher’s ERA independent of defense. So, we can use DIPS to determine which pitchers were lucky and which were unlucky.

We’ll just calculate the difference between actual ERA and dERA to measure how lucky or unlucky each pitcher has been. Interestingly, the five luckiest and five unluckiest players had similar DIPS ERAs. The lucky players had great ERAs (all under 3) and the unlucky players had poor ERAs (all over 7).

Here’s the SQL code I used. It’s almost identical to the earlier code, except I added a luck variable to measure the difference between DIPS ERA and ERA.

	select nameFirst, nameLast, yearID, teamID, lgID, round(ER / IPOuts * 27,3) ERA, dERA,
	    round(dERA - ERA, 3) AS luck, IPOuts
	FROM (select *, round(dER * 9  / dIP, 3) AS dERA
	FROM (select *,
	(dH-dHR)*.49674 + dHR*1.294375 + (dBB-dIBB)*.3325 + dIBB*.0864336 +
	dSO*(-.084691) + dHP*.3077 + (BFP-dHP-dBB-dSO-dH)*(-.082927) AS dER
	FROM (select *,
	(1.048 * (BFP - dBB - dHP - dSO - dH) + dSO) / 3 AS dIP
	FROM (select *,
	sH * (BFP - dHR - dBB - dSO - dHP) + dHR AS dH
	FROM (SELECT *,
	.304396 + .002321 * (CASE WHEN throws='L' THEN 1 ELSE 0 END) - .04782 * sSO - .08095 
* sHR AS sH
	FROM (SELECT *,
	sHR * (BFP - dBB - dHP - dSO) AS dHR
	FROM (SELECT *,
	sSO * (BFP - dBB - dHP) AS dSO,
	HR / (BFP - HBP - BB - SO) AS sHR
	FROM (select *,
	sBB * (BFP - dIBB - dHP) + dIBB AS dBB,
	SO / (BFP - HBP - BB) AS sSO
	FROM (select *,
	sHP * (BFP - dIBB) AS dHP,
	(BB - IBB) / (BFP - IBB - HBP) as sBB
	FROM  (select p.*, m.nameFirst, m.nameLast, m.throws,
	BFP * .0074 AS diBB,
	HBP / (BFP - IBB) AS sHP
	FROM pitching p inner join master m
	ON p.playerID=m.playerID
	where yearID>1954 AND IPOuts > 161
	) p1) p2) p3) p4) p5) p6) p7) p8) p9) p_w_d
	ORDER BY luck DESC
	LIMIT 5
	;

Table 5-5 shows the luckiest pitcher seasons; Table 5-6 shows the unluckiest pitcher seasons. Interestingly, Roy Halladay made the list in 2000. He’s now Toronto’s ace pitcher, and he won the Cy Young Award in 2003.