Note: The following was retrieved from the Internet Archive Wayback Machine after it disappeared from its previous home at It's Voros McCracken's work, not mine, but he has granted me permission to display it here to keep it in circulation. — Jay Jaffe

James Fraser's Note: The following is an article by Voros McCracken. He introduces his new method for evaluating pitchers. I think its some of the more original and interesting sabermetrical work I've seen in a while. Enjoy and Happy Holidays!

Defense Independent Pitching Stats

By Voros McCracken

Consider the following two pitchers:

Pitcher         W  L   ERA     IP    H  HR TBB  IB   SO  HP  BFP
Aaron Sele     18  9  4.79  205.0  244  21  70   3  186  12  920
Jose Rosado    10 14  3.85  208.0  197  24  72   1  141   5  882

Alright, who pitched better?

I bet you think you know what's coming, don't you? It's "anti-Won/Loss record argument number 3,178." You know the one. It goes like this:

"The sportswriters and Cy Young award voters place WAY too much emphasis on Won/Loss records. So they vote for Aaron Sele when it's obvious Jose Rosado was the better pitcher. Rosado's ERA is almost a full point lower than Sele's. Rosado gave up 52 less baserunners in three less innings. The sportswriters have yet to understand how meaningless Won/Loss records are for a single season and that they rely too heavily on run support. Plus the things it supposedly measures is measured better by ERA. Nevertheless Sele will get more Cy Young votes anyway ."

I'm sure you've heard it before and I agree with a lot of the above. So if you ask me who the better pitcher was, I would answer confidently...

...Aaron Sele. That's right, as far as I'm concerned, Sele was not only better than Rosado but one of the top three pitchers in the American League. And believe it or not, this assessment gives ZERO weight to his Won/Loss record.

I reach this conclusion by using something I call Defense Independent Pitching Stats ("DIPS"). DIPS use the same categories as regular stats, but adjust them to a neutral context for park, league and defense. What the method does is use only those elements of the pitcher's record that can not be affected by the defense behind him. Those stats would be BFP (as the playing time standard), HR, HB, TBB, IB and SO (I realize an outfielder can occassionally save a home run, but the rarity of that event makes it virtually meaningless for our purposes). That's it, we'll only use those stats. Stats which will have NO effect on our final analysis will be W, L, ERA, IP, ER and, most controversially, H. That's right, we will not use the pitcher's hits allowed total AT ALL.

I suppose I'll pause here in my explanation of DIPS because I've probably got quite a few disbelievers by now. Since this is essentially a "one-way" discussion I'll go ahead and make your arguments for you (as I'm pretty sure I'll hit on at least one of your objections.) One argument is, "I think you over-estimate the amount of control the defense has over balls in the field of play. A majority of such plays are routine and therefore should be credited to the pitcher." There is, "Removing hits gives too much credit to strikeout pitchers and not enough credit to the guys who get lots of one and two pitch outs." And also, "Don't you think you should just make a general adjustment based on the overall team defense?"

I've heard these a lot and have done a lot of work to try and explain why I don't agree with these arguments. The idea of NOT using a pitchers hit totals to evaluate his performance is not well supported in any community including the Sabermetric one. One of the more talked about recent stats is Bill James Component ERA which relies heavily on hits allowed totals. But what I'm going to detail here is why I think it's important to remove Hits Allowed from our evaluations of pitchers. I'll warn you that this will be relatively lengthy and involve some statistics, but if you're at all interested in statistical evaluations of pitchers, I think it's important to understand some things about the various pitching stats.

What I'm going to do is a comparison of pitching statistics from 1998 to 1999 for the group of pitchers who pitched 162+ innings in both seasons (there were 60 such pitchers). I'll start off by defining some rate stats. The only statistics used will be IP, H, HR, BB and SO. The raw figures I have don't include BFP but for our purposes here we don't really need it. We can simply estimate BFP by the formula ((IP*3)+BB+H). Later on, when we do Aaron Sele's and Jose Rosado's DIPS, we'll use a bit more complicated formulae, which use the actual BFP totals along with Hit Batsmen and Intentional Walks. rate stats are only for the purposes of establishing the year to year correlation of the basic elements of a pitcher's record.

$BB=BB/((IP*3)+H+BB); This rate stat is essentially measuring how often the pitcher walked the guy during the season per number of batters he faced. Obviously the second half doesn't equate accurately with the pitchers actual BFP, but I'm sure it equates pretty precisely with it, i.e. the difference between BFP and that part of the equation is most likely pretty constant in the long run from pitcher to pitcher.

$SO=SO/((IP*3)+H); This stat is designed to measure how often he struck guys out relative to how often he gave up fair batted balls. A measure of how difficult it is to make contact in other words.

$HR=HR/((IP*3)+H-SO); This stat measures how often a batted fair ball left the park against the pitcher.

$H=(H-HR)/((IP*3)+H-SO-HR); This stat measures how often a batted ball in the field of play not leaving the park falls in for a hit. This stat is the central focus of the discussion and its behavior is the basis for my decision for leaving hits allowed totals out of the evaluation method.

(these are difficult stats to write out every time, so to understand the following you might need to refer back to what the $BB, $SO, $HR and $H abbreviations mean).

What I did was compare each rate stat for each pitcher in 1998 with what that same pitcher did in 1999. For example, Andy Benes $BB in 1998 was .075 and his $BB in 1999 was .092 (note these numbers will not be park or league adjusted for simplicity's sake). These figures were used in a linear regression analysis where the correlations of the stats from 1998 to 1999 will be computed and compared to each other (a measure of the stat's consistency). The correlations when each stat is compared to it's counterpart (i.e. 1998 $BB to 1999 $BB and so on) are as follows:

$H =.153

If you know about statistics and you know about baseball, this should have your attention. The higher the figure the higher the correlation, so in three of the stats, the correlation ranges from ok ($HR) to very good ($SO). In the other stat ($H) there really is a very low level of correlation. Considering many of these pitchers had the same defenses and pitched in the same parks, one could argue that any correlation there is might be due to those factors as much as anything.

What does this mean? Essentially it means that if a pitcher posts a very low $H rate one year, you really can't expect him to repeat that with any level of certainty at all. However if a player posts a very high $SO rate, there is a level of comfort in thinking he'll have a good one the following year as well. I cannot stress how important I think this is. Think about a second. How much value would you give to a stat, if you KNEW that it meant virtually nothing towards that players future stats? IOW, we don't give Aaron Sele credit for the seven runs a game his team scored for him because we know that he had little to do with it. Those runs are very real and very valuable but there isn't a real reason to give Sele credit for them. In my opinion, Hits Allowed deserves the same treatment.

To leave the realm of linear regressions and show examples of what I'm talking about, I'll provide the following:

10 Lowest $H in 1998 and 1999 (of the 60 pitchers) (In order)
1998: Hideki Irabu, Pete Harnisch, Woody Williams, Kenny Rogers, Greg Maddux*, David Wells, Dustin Hermanson, Brian Moehler, Al Leiter, Tom Glavine.
1999: Kevin Millwood*, Omar Daal, Masato Yoshii, Curt Schilling, Pete Harnisch, Bartolo Colon, David Cone, Rick Helling, Eric Milton, Kevin Brown.

You may have noticed the asterisks next to Maddux's and Millwood's names on these lists. I want you to remember that they were on these lists.

Notice that only one pitcher, Pete Harnisch, made the top 10 both years. If this stat really had anything to do with the pitchers actual ABILITY, one would expect a few more guys to be on the list both years.

10 Highest $H in 1998 and 1999 (in order)
1998: Aaron Sele, Shane Reynolds, Brian Meadows, Scott Erickson, Pedro Astacio, Randy Johnson, Mike Sirotka, Kevin Millwood*, Brad Radke and Darryl Kile.

That's interesting. In 1999 Kevin Millwood had the lowest $H rate of any pitcher in the majors while in 1998 he had the 8th highest. If $H reflected pitching abilities, would that make sense? Does Mark mcGwire ever finish among the lowest in the league in HR%? Does Rey Ordonez ever finish among the highest? And in Back to Back years !?!? We'll move on.

1999: Aaron Sele, LaTroy Hawkins, Jon Lieber, Greg Maddux*, Pedro Martinez, Shane Reynolds, Pedro Astacio, Steve Woodard, Livan Hernandez and Charles Nagy.

And there's Millwood's teammate, Maddux, pulling the opposite trick. After posting the 5th lowest in 1998, Maddux then proceeded to post the 4th highest. In other words, there was one instance of a pitcher making the top 10 both years, and two instances of pitchers making the top 10 one year and the bottom 10 the other. There is an increase in players being on both lists here though as Aaron Sele (the star of our story), Shane Reynolds and Pedro Astacio (Coors effect mostly I assume. Kile the only other Rockies pitcher who qualified made the 1998 list too). However I bet the name Pedro Martinez jumped out at you (for 1999 no less!) Pedro was rightfully considered unhittable this year, but in fact when they did hit Pedro, a large number of balls went for hits this year. Did you expect that?

In the other categories things make more sense. In $BB, seven pitchers were on the lists for lowest $BB both years. Five Pitchers were on the lists for highest $BB both years. No pitchers were on one list one year and the other list the other.

For $SO, five pitchers were on the lists for highest $SO both years. six pitchers were on the lists for lowest $SO both years. Again, no pitcher was on one list one year and the other list the other.

For $HR, four pitchers were on the lists for lowest $HR both years. Four pitchers were on the list for highest $HR both years. There was one pitcher who was among the lowest in 1998 (10th lowest) and the highest in 1999 (5th highest). It was the enigmatic Chan Ho Park.

Again, this shows us that for at least 2 of the stats and to a certain extent the third, the guys that do well one year in a stat tend to do well the next year too. In the $H stat though, such a conclusion is not possible.

This borders on heresy, really. We thought we were finished with Strikeouts once it was shown that their direct value (relative to other outs) was very minimal. But it appears their indirect value for pitchers is large due to the instability of the hits allowed statistic (i.e. if you strike the guy out, you control your own destiny as a pitcher). Quite simply, I can't look at the above and think that a pitcher's Hit total is more important than his strikeout total. I just can't do it. I've looked at historical patterns regarding these numbers back to 1946, and the same correlations keep popping up. High and very high for $BB and $SO respectively. Mid range for $HR and low for $H. I can pass along exact figures to whomever is interested.

These correlations are the basis of my DIPS work. More accurate forms of $BB, $SO and $HR are used to compile the numbers (as will be explained in a bit), but I simply didn't see a good reason to bring $H into this. Yes the hits given up were costly and can lead to runs, but I've yet to see much information that suggests the pitcher has a whole lot of control in giving up the hits or preventing the hits, OTHER THAN PREVENTING BATTERS FROM HITTING THE BASEBALL. Getting hits off Randy Johnson or Pedro Martinez is tough, not because their pitches are tough to center (remember both pitchers made highest $H lists) but because they strike you out so often.

So lets get back to the DIPS methods and Aaron Sele and Jose Rosado. To get our DIPS we do the following (The rate stats defined here will be similar to the ones above, but these will be a little more complex and use more data) :

We add BFP and HP to the pitcher's records, unchanged. (If we were comparing pitchers across leagues, we'd make an adjustment so that their leagues would be "equal." Obviously a pitcher in the AL is at a disadvantage having to face a DH instead of other pitchers. We would adjust for this normally, but since both pitcher's are American Leaguers, we don't have to.)

Pitcher  BFP  HP
Sele     920  12
Rosado   882   5

Now we start off by adjusting the Walk totals. First off we subtract the Intentional Walk total from his total walks and divide that figure by the pitcher's (BFP-HP-IBB) total:

Sele: (70-3)/(920-12-3)=.07403 Rosado: (72-1)/(882-5-1)=.08105

Now we take that figure and adjust for the park's influence on walks:

Sele: .07403*.995=.07366 Rosado: .08105*1.007=.08162

Now we can argue over Park Factors from here until doomsday. I'm using Park Factors provided by Tom Fontaine at, but whatever you come up with for factors will work here. Anyway the figures above are then multiplied by (BFP-HP-IBB) (remember we would also adjust for leagues if necessary) and then multiplied by a league average (TBB/(TBB-IBB)) rate (1.0544):

Sele: .07366*(920-12-3)*1.0544= 70 = TBB Rosado: .08105*(882-5-1)*1.0544= 75 = TBB

Which so far gives us DIPS of:

Pitcher  BFP  HP TBB
Sele     920  12  70
Rosado   882   5  75

Now we move on to strikeouts. You'll notice as we move on, our denominators will shrink slightly each time as figures we've already computed are siphoned off. The idea is to keep each rate as close to a real percentage as possible. It is necessary to do this to maintain the interdependence of all of these stats (i.e. a pitcher that walks half of the guys he faces won't be able to post very high numbers in the other areas once adjusted).

For strikeouts we simply take the pitcher's strikeout total and divide it from BFP-HP-TBB:

Sele: 186/(920-12-70)=.22196 Rosado: 141/(882-5-72)=.17516

Adjust for park:

Sele: .22196*1.0384=.23048 Rosado: .17516*1.0466=.18332

And now we multiply by the DIPS (BFP-HP-TBB) total (remember interdependency is the key. If DIPS adjust something to a large extent upward or downward, it will affect the later adjustments):

Sele: .23048*(920-12-70)= 193 = SO Rosado: .18332*(882-5-75)= 147 = SO

And our DIPS are now:

Pitcher  BFP  HP TBB   SO
Sele     920  12  70  193
Rosado   882   5  75  147

Next we move on to Home Runs. We take the pitcher's HR total and divide by (BFP-HP-TBB-SO):

Sele: 21/(920-12-70-186)=.03221 Rosado: 24/(882-5-72-141)=.03614

The park factors:

Sele: .03221*.9867=.03178 Rosado: .03614*1.0384=.03753

And then we multiply those by our DIPS (BFP-HP-TBB-SO):

Sele: .03178*(920-12-70-193)= 20 = HR Rosado: .03753*(882-5-75-147)= 25 = HR

And now we have our DIPS:

Pitcher  BFP  HP TBB   SO  HR
Sele     920  12  70  193  20
Rosado   882   5  75  147  25

Okay we are now done with Sele's and Rosado's raw stats. The rest will be done using a series of "league averages." The stats above represent all the stats from a pitchers record that are not affected by defense (Balks aren't counted but they are rare events, e.g. neither Sele nor Rosado had one called against him).

We now use the same denominator for much of the rest of what we do. It will be the new DIPS version of (BFP-HP-TBB-SO-HR). These represent all the BFPs where the defense had some hand in the outcome. Let's recreate the Hits statistic and we'll see where the system dissents from the Raw stats. We take the AL average of (H-HR)/(BFP-HP-TBB-SO-HR), which is .3008. We then multiply that number by the above denominator (at this point both our park and league factors no longer apply since every pitcher will now be assigned the same "league average" for each rate):

Sele: (920-12-70-193-20)*.3008=188 Rosado: (882-5-75-147-25)*.3008=190

And then we add our DIPS HR stat to get our much anticipated DIPS H stat:

Sele: 188+20=208 Rosado: 190+25=215

And our DIPS are now:

Pitcher  BFP  HP TBB   SO  HR    H
Sele     920  12  70  193  20  208
Rosado   882   5  75  147  25  215

Okay. Now we'll stop and notice the MAJOR change we have now. Rosado has now gained 18 hits by this method and Sele has lost 36! What's going on is simple. Aaron Sele pitched in a hitters park for a team who played Todd Zeile at 3B, Mark McLemore at 2B, Tom Goodwin in CF and Juan Gonzalez in RF, all substandard defensive players most at relatively important defensive positions. Rosado on the other hand played for a team with three CFs in the outfield, Rey Sanchez (who is ALL glove) at SS and good defenders at 2B and 3B. This was a team that left Jeremy Giambi in AAA for a month over concerns about his defense at 1B. The Royals decided the key to their team was defense and they played very good defense (side note: those convinced that defense wins championships might want to check out the Royals 1999 record). Add in the fact that there's always a lot of random noise involving hits allowed stats anyway and Rosado's large advantage in the hits allowed department doesn't seem to have much to do with his pitching abilities to me.

Let's move on. Now we'll nail down our IP numbers (remember, now that Sele's given up less hits, he has gotten more outs so his IP will increase). We use our denominator above again (BFP-HP-TBB-SO-HR). We'll multiply that by the following AL "league average" (for non SO outs):

((IP*3)-SO)/(BFP-HP-TBB-SO-HR), which yields for 1999 in the AL, .7363. This brings us:

Sele: (920-12-70-193-20)*.7363=460 Rosado: (882-5-75-147-25)*.7363=464

Which is a non-SO out total for the pitcher. We add the DIPS SO total and divide by three to get our DIPS IP total.

Sele: (460+193)/3= 217.2 = IP Rosado: (464+147)/3= 203.2 = IP

Our DIPS are starting to round out:

Pitcher  BFP  HP TBB   SO  HR    H     IP
Sele     920  12  70  193  20  207  217.2
Rosado   882   5  75  147  25  215  203.2
We're moving now. Now we need to derive the all important ER stat. I've decided to use Jim Furtado's Extrapolated Runs formula ("XR") as the basis for determining this. First thing we'll do is figure out how to "league average" what we need. First we determine the league's XR (we'll leave off SB and CS totals here, as they are negligible and one could argue that they're not really "pitching"). To figure XR we do the following:


Which we get for the 1999 AL of: 11689.73

Now we divide the leagues ER total by that figure and we can now multiply that factor by the XR total we get for the pitcher. That total will be our DIPS ER figure:


ER=.9297*(Whatever we come up with for the pitcher's XR)

I'm sure you noticed the 2B and 3B totals above for XR. Getting those for our pitchers will be easy. We'll simply multiply the league average of:

(2B/(H-HR))=.21743 (3B/(H-HR))=.02225

to our DIPS (H-HR) totals:

Sele: (207-19)*.21743= 41 = 2B Rosado: (215-25)*.21743= 41 = 2B


Sele: (207-19)*.02225= 4 = 3B Rosado: (215-25)*.02225= 4 = 3B

We now have enough to come up with our XR figures for each pitcher:

Sele: ((208-41-4-20)*.5)+(41*.72)+(4*1.04)+(20*1.44)+((70+12)*.33) -((920-208-70-12)*.098)= 99.3 = XR

Rosado: ((215-41-4-25)*.5)+(41*.72)+(4*1.04)+(25*1.44)+((75+5)*.33) -((882-215-75-5)*.098)= 111.054 = XR

And now we get our DIPS ER totals:

Sele: 97.762*.9297 = 92 = ER Rosado: 111.054*.9297 = 103 = ER

Pitcher  BFP  HP TBB   SO  HR    H     IP  ER
Sele     920  12  70  193  19  207  217.2  92
Rosado   882   5  75  147  25  215  203.2 103

Let's make an ERA!

Pitcher  BFP  HP TBB   SO  HR    H     IP  ER   ERA
Sele     920  12  70  193  19  207  217.2  92  3.80
Rosado   882   5  75  147  25  215  203.2 103  4.55

And while we're at it, let's exhume Pythagoras. We'll use the theory of:


Substituting the league ERA (4.86) for R and the Pitcher's new DIPS ERA for OR, we get:

Sele: (4.86^1.83)/((4.86^1.83)+(3.80^1.83))= .611 = WIN% Rosado: (4.86^1.83)/((4.86^1.83)+(4.55^1.83))= .530 = WIN%

In the AL there were 2263 decisions and 20076.2 IP so:



Decisions = .11272 * IP

Sele = 217.2*.11272 = 25 = Decisions Rosado = 203.2*.11272 = 23 = Decisions


Sele = 25 * .611 = 15 = wins and (25-15)=10=losses Rosado = 23 * .530 = 12 = wins and (23-12)=11=losses

Now we add our final touches and rearrange:

Pitcher  W   L   ERA     IP    H  HR TBB  SO  
Sele    15  10  3.80  217.2  208  20  70 193
Rosado  12  11  4.55  203.2  215  25  75 147

And there we have it. Those are Defense Independent Pitching Stats and their results say that Aaron Sele was a far better pitcher than Jose Rosado in 1999.

Easy, wasn't it? :)

So what have we done? We've taken individual pitcher stats and we've used only the ones that are not affected by defense and have a definite relationship to pitching ability. Hits allowed is not one of these statistics and so we don't use it. ERA is another and so we don't use it either (as our new method with a few minor adjustments will correlate with ERA the following year much better than ERA itself as you'll see in a future article). Instead we use stats like BB, HR and SO (the most important of the pitching stats) and league averages for the others. The method can affect our evaluations of pitchers by a LARGE MARGIN (as you saw above). The method adjusts for park and league and most importantly, THE QUALITY OF DEFENSE THAT WAS PLAYED BEHIND HIM IS COMPLETELY REMOVED FROM THE EQUATION.

A listing of all the 1999 DIPS for every pitcher can be found at:

(note: the DIPS on the page for Rosado and Sele will be slightly different as the method should maintain it's decimals, but for simplicity's sake, I rounded my numbers in the examples above.)

The possibilities for application of this method are pretty huge. Armed with DIPS, we might now be able to obtain the long sought after Minor League Equivalencies for pitchers that we now have for hitters. We could apply them on a team by team basis to see, for example, what the maximum effects the team's fielding could have had on run scoring. We can see how DIPS are a better indicator of future ERA (and as such pitching ability) than ERA and even Bill James' Component ERA. We'll also see that as our pitcher's sample sizes reduce, DIPS advantage over the other stats grows to a very large margin (The last two sentences will be addressed in a future article).

Finally and most importantly, we'll be armed with the knowledge that pitchers don't have as much control over certain things as we've previously given them credit for. We'll be able to recognize true exceptional pitching performances and other more deceptive performances, just by knowing what's important and what isn't. In short, we will come to the understanding that a HUGE amount of what we used to think was "Pitching" is actually "Defense."

Comments to Voros McCracken at

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