Is there a better measure of team defense in pro football?
After hearing every week during the NFL season how Bill Belichick, often described as a defensive mastermind, was terrorizing opposing offenses with his innovative schemes, I got to thinking, "Is New England really the best defense in the AFC?" At first glance I wasn't convinced. Their roster is filled with players taken from teams that didn't think twice about letting them leave. And while Ty Law, Richard Seymour and Willie McGinest are all impact players, other teams weren't clamoring for the Teddy Bruschis, Mike Vrabels, and Asante Samuels--despite their importance to the success of the Patriots.

Was the Patriots defense that much better than other teams? That's what I aimed to find out.

When thinking about what makes a defense successful, for me four things come to mind. First, how many yards do they give up; second, how long are they on the field; third, how many turnovers do they create; and finally, how many points do they allow?

Currently, the NFL ranks team defense by looking at total yards allowed per game (YPG) and total points allowed per game (PPG). While this lets you to compare one team to another, it doesn't offer any insight into why some defenses are successful and others struggle. I hope to shed some light on this problem.

Every week during football season, most newspapers publish NFL team defensive rankings by both YPG and PPG. Without much thought, it certainly seems reasonable that defensive rankings should probably entail more than these two statistics. So what statistics provide a good measure of a defense's success?

Yards allowed per Game
First, let's start with YPG. This is pretty simple--the more yards a defense allows, the more likely it is the offense will score. In 2003 for example, for every seven points allowed, AFC defenses gave up 100 yards, on average.

But what if it was the case that a defense known for giving up huge chunks of yards routinely stopped the offense from scoring (maybe through turnovers, missed field goals or loss of downs)? For example, the New York Jets allowed 323 YPG (seventh highest in the AFC), but only gave up 18.7 PPG (fifth lowest in the AFC). Is there one statistic that gives us an idea of how many yards a defense allowed that resulted directly in points for the opposition?

If we take the yards allowed per scoring drive and divide it by the total yards allowed per game, we have an idea of the percentage of yards directly resulting in points (I'll call it Yards Given Up Resulting in Points--YGURP). For example, in week one, the Pittsburgh Steelers defense allowed 228 total yards against the Baltimore Ravens offense. However, only 82 yards contributed directly to Baltimore points (the Steelers won 34-15).

The Steelers YGURP = 82/228 = 0.36

Stated differently, 36 percent of all the yards allowed by the Steelers resulted in points for the Ravens. Now, instead of just having the raw number of yards a defense allows, we can see what percentage of yards contributed to points being scored. YGURP has its shortcomings, however. What if a team has an YGURP of 0.90--that means 90 percent of all yards allowed contributed to points being scored. On the surface that sounds horrible. But let's say a defense gives up one 90-yard drive and then plays stifling defense the rest of the game and only gives up ten more yards. You have an YGURP of 0.90 (90/100), but any defense that only gives up one score and 100 yards has put forth a pretty solid performance.

One way around this problem is to also consider the defense's average starting field position. Including field position in the YGURP calculation helps account for situations cited in the example above. Revisiting that example, let's assume that the defense's Average starting Field Position (AFP) was 68 yards from their own goal line (which was the AFC's average starting field position in 2003); we will still assume that they gave up 100 total yards, only one 90-yard scoring drive and have a YGURP of 0.90 (I divided AFP by 100, to get a number between 0 and 1).

If we recalculate YGURP when now considering AFP we get the following:

YGURP*AFP = 0.90*0.68 = 0.63

This new number now represents the yards given up that result in points when accounting for the average starting field position. 0.63 seems much more reasonable (and probably more reliable) than the 0.90 estimated above. I'll discuss this in more detail later.

Time on the Field
The total time a defense spends on the field is very highly correlated with the number of points they allow, but it is seldom mentioned when discussing good defenses. We can take an approach similar to the one used to estimate YGURP when talking about getting a meaningful metric for time on the field.

If we take the ratio of the time on the field during scoring drives to the total time on the field, we have an idea of the percentage of time on the field directly resulting in points (call this Time on Field Resulting in Points--TOFRP). Revisiting the week one game between the Steelers and the Ravens, the Steelers defense was on the field a total of 27:20. Of that time, only 3:00 were on scoring drives.

The Steelers TOFRP = 3:00/27:20 = 0.11

That means that 11 percent of the time spent on the field was directly related to scoring drives. Just like YGURP, TOFRP also has some drawbacks. One can create a scenario where a defense is consistently starting at its own 10-yard line and as a result the offense scores quickly. This will lead to very high values of TOFRP, but would not necessarily be indicative of defensive performance--especially as it related to time on the field. I will come back to ways around this limitation of TOFRP.

Turnovers Created
Surprisingly, turnovers do not correlate that highly with PPG. You would expect that the more turnovers a defense created, the fewer points they would allow. San Diego's defense allowed almost 28 points per game in 2003 (highest in the AFC), but were third in the AFC in turnovers created (30). The New York Jets's defense was fifth in the conference in fewest points allowed (18.7), but was 12th in the league in turnovers created (18). Why this might be the case raises some interesting questions, but I'll save that discussion for another time.

(I should note that even though turnovers were not highly correlated with PPG, team winning percentage was pretty highly correlated with turnovers. This indicates that turnovers do contribute team wins, but it doesn't necessarily reduce the number of points the opposition scores.)

Points Allowed per Game
The statistic that most obviously portrays how well a defense is performing is PPG. San Diego gave up an AFC worst 28 PPG and finished at 4-12. New England gave up an AFC best 15 PPG and won the Super Bowl. So it's probably safe to say that the fewer points a team allows, the better their chances of winning. But is PPG the best measure to compare defensive effectiveness?

What if the San Diego defense had an average starting position on their own twenty yard-line and the New England defense had an average starting position on their opponents twenty yard-line? That would mean that offenses would in all probability score more often on San Diego's defense than on New England's defense. So part of the blame for San Diego's high PPG should fall on San Diego's offense and special teams (since they are responsible for the lousy field position).

Is there a way to account for field position when determining PPG? If we weight the points allowed per game by where on the field the defense starts, we will have a much more accurate portrayal of PPG. The formula I used to obtain the Weighted Pointe Per Game (WPPG) is as follows:

(Points scored per Drive*Yards Allowed per Drive)/100

Returning to our ubiquitous week one example, the Ravens had thirteen offensive drives. Of those drives, they scored on two of them. Their first scoring drive was 80 yards and resulted in a touchdown. There final scoring drive was two yards and also resulted in a touchdown. To estimate the Steelers WPPG using the formula above, we get:

Drive 1: (7*80)/100 = 5.60

Drive 2: (7*02)/100 = 0.14

Because drive 1 went 80 yards and resulted in a TD (and an extra point) we multiply the yards allowed by the defense by the points scored by the offense. This number divided by 100 gives us a weighted score of 5.60. Drive 2, on the other hand started at the Steelers two yard line but also resulted in a TD. Doing the arithmetic shows that the weighted score is only 0.14.

The benefit of WPPG is that the score is now dependent on where the defense starts. The Ravens second scoring drive was a result of a Pittsburgh turnover deep in their own territory. Weighting the ensuing touchdown by field position prevents the Pittsburgh defense from being 'penalized' by the Pittsburgh offense's miscue (as would be the case with the traditional measure of PPG).

Creating an Overall Measure of Team Defense
We now have three statistics that give us some insight into yards allowed, time on the field and points allowed. But how can we aggregate these numbers into one meaningful statistic of team defense? I took several steps to arrive at one measure, so let's go through them, one-by-one:

First, by multiplying YGURP by TOTYDS we get the total yards given up resulting in points (let's call this TYGURP). For example, New England gave up 290.9 total yards per game (6th fewest in the AFC), but their TYGURP (this is simply 0.46*290.9) is 135.0 (which was a league best). TYGURP gives us a better sense of how many yards, of the total yards allowed, resulted in points. Next, we multiply TYGURP by AFP (call it T_TYGURP). Remember, AFP accounts for the defense's average starting field position. This metric will alleviate the problems detailed earlier concerning spurious values of YGURP.

We can also use the same methods for TOFRP. Multiplying TOFRP by TOT_TOF gives the total time on the field that resulted in points being scored (call it T_TOFRP). For example, New England's defense averaged 29:10 minutes on the field per game (this ranked fifth lowest in the AFC). However, New England's T_TOFRP was 9:49 minutes per game (ranking them second lowest in the AFC). The calculation, as above, is straightforward (0.34*29:10).

With these new statistics, we're almost there. We still need to account for the weighted score. We can do this by multiplying T_TYGURP*T_TOFRP*WPPG (call it ADM--Aggregated Defensive Metric). ADM now gives us a way to look at several important variables that contribute to team defensive success with one number. These numbers, by themselves aren't very intuitive, but we can rescale them and make them more meaningful. Using a 0.0-100.0 scale where 100.0 is a defense that gives up 0 PPG, 0 YPG and 0 TOFRP (the most dominant defense possible) and 0.0 is a defense that gives up 10 percent over the: maximum PPG, maximum YPG and maximum TOFRP (a sufficiently bad defense that allows for variation with the worst 'real' defense in the AFC. Also specifying the scale this way allows for comparison of team defenses across years). Here are the results:

team	adm	nflavg	ypg	ppg	wppg
BUF	84.3(4)	2.5(1)	276.6(2)	17.4(3)	9.3(4)
BAL	89.1(2)	2.5(1)	271.6(1)	17.6(4)	7.9(2)
NE	91.0(1)	3.5(3)	290.9(6)	14.9(1)	7.3(1)
DEN	81.8(5)	4.5(4)	277.6(3)	18.8(6)	9.9(5)
MIA	86.3(3)	5.5(5)	304.1(9)	16.3(2)	8.8(3)
CLE	78.2(7)	7.5(6)	299.1(8)	20.1(7)	10.1(6)
JAC	75.9(8)	7.5(6)	282.6(5)	20.7(10)	11.0(9)
NYJ	72.1(11)	8.0(8)	322.9(11)	18.7(5)	11.0(8)
PIT	81.4(6)	8.0(8)	295.6(7)	20.4(9)	10.7(7)
IND	75.3(9)	8.0(8)	279.1(4)	21.0(12)	11.9(11)
TEN	74.8(10)	9.0(11)	304.3(10)	20.3(8)	11.3(10)
KAN	69.0(12)	11.5(12)	339.5(12)	20.8(11)	12.7(12)
CIN	52.2(14)	14.0(13)	340.9(13)	24.0(15)	14.2(14)
OAK	53.3(13)	14.5(14)	364.8(16)	23.7(13)	13.8(13)
HOU	43.7(16)	14.5(14)	362.9(15)	23.8(14)	14.4(15)
SD	50.1(15)	15.0(16)	342.4(14)	27.6(16)	14.9(16)

The table above lists ADM, NFL AVG, YPG, PPG and WPPG, with each team's ranking in parentheses (notice that the teams are ranked in ascending order by NFL AVG and all other categories are compared to this one). For example, in the PPG column, Tennessee ranks 8th (20.3 PPG), but in the WPPG column, Tennessee ranks 10th (11.3 WPPG). Additionally, I took the average of the rankings for PPG and YPG as kind of an ad hoc measure of defensive success (Note: the NFL has a total team defense statistic--I've called it YPG here, but I'll use the NFL AVG for the sake of comparison).

A couple of things stand out as you look at the table. First, PPG and WPPG are for the most part very similar. In fact, their correlation coefficient is 0.95 (where 1.0 means two variables are perfectly correlated). The largest difference in rankings when looking at PPG compared to WPPG is with the New York Jets; they go from fifth in PPG (18.7) to eighth in WPPG (11.0). The fact that PPG and WPPG are very similar implies that field position across teams was relatively similar. Houston's defense had the best AFP (their opponent's 29-yard line) while Jacksonville's defense had the worst AFP (their opponent's 35-yard line). Six yards separates the best team from the worst team when comparing AFP and because of the similarities, PPG and WPPG turn out to not be that different. Nonetheless, WPPG is a more precise measure of points allowed, because it also accounts for field position.

ADM also correlates highly with NFL AVG. But what is important when considering ADM is how each team obtained its ADM ranking. For example, the NFL AVG ranks Buffalo and Baltimore as the two best defensive teams (based on YPG and PPG), with New England ranked third. ADM however, has New England ranked first and Buffalo ranked fourth. Why? Well remember that ADM is made up of several variables (YGURP, AFP, TOFRP, TOTYDS and WPPG) that account for defensive success. One reason the ADM ranked New England ahead of Buffalo was that New England led Buffalo in all the categories that comprise the ADM. In fact, when looking at the NFL AVG, Buffalo only faired better than New England in YPG (see the table above). To be more specific, out of all the AFC teams, New England ranked first in TYGURP and WPPG, second in T_TOFRP and third in AFP, while Buffalo ranked fourth, fourth, seventh and fourteenth, respectively.

Another team that dropped in the rankings when using ADM was the New York Jets. Their NFL AVG was eighth and the ADM rank was eleventh. This was primarily the result of the Jets being eleventh in the AFC in YPG, tenth in TYGURP, twelfth in T_TOFRP, eighth in WPPG and ninth in AFP. Despite the Jets being fifth in the conference in PPG, all of the factors contributing to the ADM resulted in their defense being no better than eleventh overall.

So after going through all this, what's the big deal about ADM? Well, on the surface there doesn't seem to be much difference between the ADM and the NFL AVG. But it's important to consider a couple of things:

First, ADM offers a more precise estimate of team defense because it considers variables that determine how successful a team performs. Yards given up that result in points, time on the field, average starting field position and weighted points per game are all important factors that affect how a defense will perform. Finding a way to incorporate all of these factors into one measure is a good thing (although it can certainly be argued that there are better measures than ADM).

Next, it's important to remember that the ADM estimated above looks only at AFC teams for the 2003 season. Perhaps looking at both conferences, or looking at data from previous years might yield more variation between the ADM and the NFL AVG (I'll put this on my to-do list). But as I stated above, the ADM does consider many variables when constructing a measure of team defense. Additionally, it more precisely portrays the overall effectiveness of team defense when compared to the statistical measures used before.

So to finally answer the question I posed at the beginning of this post: "Is New England really the best defense in the AFC?" Well, based on the ADM, New England gets a score of 91.0 with the Baltimore Ravens close behind with a score of 89.1. So as an unbiased observer (in reality I'm a Steelers fan so I don't even like the Patriots) I guess New England can claim the crown as the best defense in 2003. While the Patriots ranked near the top in most defensive categories, they also did the little things that translated into wins on the field. For example, they were sixth in the AFC in YPG, but were first in the conference in TGURP. They ranked fifth best in time on the field, but ranked second best in TOFRP. They ranked ninth in turnovers created, but ranked first in WPPG. Maybe Belichick new all of this years ago and fashions teams that emphasize these parts of the game. Whatever the case, the Patriots have proven over the last few years that a defense can be great without a surplus of great players--apparently what's more important is great strategy.

[A quick note: Hopefully this exercise had shed some light on new ways to measure team defensive success and has offered some insight into why some defenses succeed while others continue to struggle. Please send me an email about any questions or comments you might have because this is version 1.0 (like why did I include 'X' or exclude 'Y' in the estimates). I'm sure there are a lot of ways this metric can be improved.]

Garciaparra has a problem with steroid testing
Nomar Garciaparra says that if MLB decides to test him for steroids he's also going to get his doctor to test him as well because he 'does not trust tests.'

"I don't trust testing...I don't know where [the sample] is going or who's doing [the testing], or what they are looking for. Testing is just not the answer."

So then the question becomes, 'if testing is not the answer, what is?' How does one go about finding out if a player is using steroids? The NFL tests its players and there hasn't been much in the way of complaints (or even cries of false-positive test results). Any time a player offers resistance when it comes to testing, it immediately raises questions (whether that's right or wrong is another discussion--although prejudging people is usually a bad idea). I don't think there is anything wrong with Garciaparra insisting on being tested twice--in fact, it's probably a smart move. But if he doesn't have a solution to the current testing situation he might be better off not saying anything--especially when two of his teammates are more than willing to be tested to prove they're not on the juice.

Terrell Owens impact may be overstated
The Baltimore Ravens landed one of the best wide receivers in the NFL yesterday when they traded their 2nd round draft pick to San Francisco for the services of Terrell Owens. On the surface this looks to change the dynamic in the AFC North that now proclaims the Ravens as favorites. But before everyone gets too far ahead of themselves, first consider two things:

1) If Jamal Lewis can't play in 2004, the Ravens are back to square one--a one-dimensional team on offense with a great defense. But now, instead of relying on Lewis's legs, Billick must rely on Boller's ability to get TO the ball (FYI, Boller had surgery on his non-throwing shoulder yesterday). I'm sure most defensive coordinators would rather game plan against stopping TO than trying to stop Jamal Lewis.

2) If last year was any indication, Boller has a long way to go in terms of throwing the ball down the field. Granted, he really didn't have anyone to throw to other than TE Todd Heap, and Billick made it clear to anyone that would listen that he was going to run the ball. But the times that Boller did drop back he was largely ineffective. To be fair to Boller last year was his rookie year, but don't forget that TO spent a lot of time in Jeff Garcia's face for being inept (and Garcia has been to the Pro Bowl three times in the last five years) and the only reason that might not happen this season is because of Ray Lewis.

So depending on what happens to Jamal Lewis, and what kind of progress Boller makes, this could be virtually the same team as last year, but now utilizing a different weapon.

Jeff Garcia visits the Browns
In related news, Jeff Garcia is scheduled to visit the Browns as they decide what to do with Tim Couch. They also auditioned Drew Henson last week and may try to acquire him via a trade or draft him April 24. Whatever happens, it looks like Kelly Holcombe is out of the picture as starting QB.

Marcus Washington opts for Redskins
As soon as free agent LB left Pittsburgh yesterday, he flew to Washington and signed on the dotted line. The Skins gave Washington a $7 million signing bonus while the Steelers were only willing to give him $5 million.

"I'd be lying to you if (I said) money wasn't an issue," Washington said after signing with the Skins (at least he's honest, but don't forget that SS Dexter Jackson spurned the Steelers last year to play with the Cardinals for a few million more and look how that turned out).

That leaves the Steelers without a free agent signee and holes to fill at CB, RB and LB (and eventually QB). This also means that Jason Gildon won't be going anywhere (at least for now) although the Steelers will visit with Carlos Emmons today.

Steelers sign Kreider, and meet with other free agents
The Steelers resigned FB Dan Kreider to a 4 year $4.04 million contract yesterday. They also met with Indy OLB Marcus Washington, who could possibly replace Jason Gildon (they're the same size, but Washington is five years younger). On a more curious note, the Steelers plan to have three cornerbacks in for visits, but all three (Reggie Howard of Carolina, Fernando Bryant of the Jacksonville and Fred Thomas of New Orleans) are considered average at best. Couple that with the fact that (at least for now) Chad Scott will again be a starter, and you begin to wonder why they cut DeWayne Washington (or at least didn't give him a chance to restructure). I can't say this enough (to be fair, free agency is only a day old) but it is imperative that the Steelers get a quality cornerback. It relieves so much pressure on the linebackers and safeties when they don't have to help with double coverage because the cornerback is ineffective. And for a position that requires this 'Me against the world attitude', I'm not sure if Scott measures up. So before this is all said and done, let's hope the Steelers make some moves in the right direction.

Here's a mini-profile of the cornerbacks scheduled to visit Pittsburgh
From the Pittsburgh Tribune Review:

"...the Steelers also have shown interest in free-agent cornerbacks Fernando Bryant of the Jacksonville Jaguars, Reggie Howard of the Carolina Panthers and David Barrett of the Arizona Cardinals.

Bryant, a No. 1 draft choice in 1999, has been a starter for the Jaguars since his rookie season, but he is not expected to return to Jacksonville.

Howard, 6-foot, 190, has a reputation as a strong tackler. He started 15 games last season for the NFC champion Panthers, recording two interceptions in the regular season. In the fourth quarter of the Super Bowl loss to the New England Patriots, he intercepted a pass in the end zone.

The Steelers have shown only lukewarm interest in Barrett, who is 5-10, 198 pounds and has been a starter for the Cardinals for the past three seasons. He might visit with team officials in Pittsburgh next week, but the Lions, Houston Texans, New York Jets and Seattle Seahawks also may bid for Barrett."

Tommy Maddox--no raise yet
In related news, Agent Vann McElroy said there has been no dialogue about restructuring the contract of Steelers quarterback Tommy Maddox, who is due to earn only $750,000 this year. "It's not a good time to go there," McElroy said.

The question then becomes, should Maddox hold out? Which should be immediately followed by the question, will he make more if one of the following happens: a) hold out (maybe, but probably not--Batch is the backup), b) gets cut and signs with another team (maybe, but that may be risky), c) complains but doesn't hold out (that will probably lead to b)).

Should Maddox be paid more? Probably. But remember, when he signed this deal, he was fresh off of his MVP season in the XFL and was looking for any opportunity in the NFL--no matter how small the contract. Now if Cowher or Rooney promised him a raise, that's another story, but I'm not sure that conversation ever took place.

Did steroids really help Randy Velarde?
Poor Randy Velarde. Known primarily as a utility infielder who spent the majority of his career with the Yankees, Velarde was yesterday identified as one of six major leaguers who received steroids. His last year in the majors was 2002, when in 133 at-bats he hit .226 (his best year was 1999 when he hit .317-16-76). Many have since questioned how beneficial steroids may have been for Velarde, who was probably best described as a mediocre player (Let me state up front, that these players were accused of 'receiving' steroids, not using them--and in fact some of them are denying it. This post will work under the assumption that Velarde did in fact use steroids--even though that has not yet been proven).

Upon first glance, Velarde's name certainly seemed out of place among the likes of Bonds, Giambi and Sheffield (I won't even mention Marvin Benard). This raises the question, "Did steroids keep Velarde in the league longer than he would have been otherwise?" I decided to see if in fact, Velarde was out of place on this list. I looked at five players (Bonds, Sheffield, Santiago, Giambi and Velarde and the overall MLB average) using four statistical categories (AVG, HR, RBI & R) for the years 1987 to 2003. My first task was to see how many standard deviations each player, in each category differed from the MLB average. I then converted the standard deviations to percentiles (I included actual player averages in parentheses) which is what you see below:

Batting average
MLB avg: .263
Bonds: 87th percentile (.303)
Sheffield: 80th percentile (.293)
Santiago: 50th percentile (.262)
Giambi: 85th percentile (.299)
Velarde: 61st percentile (.272)

(A quick note about interpreting percentiles: For batting average, Bonds had a percentile rank of 87;this can also be stated as, "Bonds's batting average over his career was better than 87% of all major leaguers).

Home runs per game
MLB avg: .090
Bonds: 99th percentile (.265)
Sheffield: 92nd percentile (.189)
Santiago: 61st percentile (.110)
Giambi: 95th percentile (.204)
Velarde: 44th percentile (.079)

RBI per game
MLB avg: .406
Bonds: 95th percentile (.693)
Sheffield: 91st percentile (.640)
Santiago: 64th percentile (.469)
Giambi: 95th percentile (.694)
Velarde: 38th percentile (.349)

Runs per game
MLB avg: .429
Bonds: 98th percentile (.765)
Sheffield: 87th percentile (.611)
Santiago: 38th percentile (.382)
Giambi: 90th percentile (.634)
Velarde: 65th percentile (.491)

These numbers don't paint a very convincing picture in terms of steroids benefiting Velarde. In fact, he finished below the MLB average in two of the four categories. So this again raises the question I posed earlier. Namely, did steroids keep Velarde in the league for several years longer than he would have been otherwise?

What happens if we make a few assumptions and then look at the numbers again? Let's assume that Velarde didn't use steroids until 1997 (I have no idea when he first used steroids, but we'll use 1997 for the purposes of this discussion). If we revisit the estimates above, but this time view them as a 'before and after snapshot', we can see what, if any impact steroid use may have had (this raises a whole litany of other problems--like even if his output did increase, it could have been a result of: a) him getting better, b) a new weight training regime or c) luck--not necessarily steroids. I'll try to address this below). Here are the before and after numbers:

Batting average (before 1997, after 1997)
MLB avg: (.261, .266)
Bonds: 83rd, 92nd percentiles (.295, .314)
Sheffield: 76th, 85th percentiles (.285, .301))
Santiago: 52nd, 54th percentiles (.263, .262)
Giambi: 64th, 85th percentiles (.273, .306)
Velarde: 55th, 70th percentiles (.265, .284)

Home runs per game (before 1997, after 1997)
MLB avg: (.082, .100)
Bonds: 98th, 99th percentiles (.219, .330)
Sheffield: 90th, 94th percentiles (.168, .213)
Santiago: 71st, 53rd percentiles (.119, .094)
Giambi: 75th, 96th percentiles (.127, .226)
Velarde: 44th, 45th percentiles (.073, .090)

RBI per game (before 1997, after 1997)
MLB avg: (.391, .425)
Bonds: 93rd, 97th percentiles (.645, .761)
Sheffield: 89th, 92nd percentiles (.601, .684)
Santiago: 69th, 56th percentiles (.479, .452)
Giambi: 76th, 96th percentiles (.514, .746)
Velarde: 34th, 43rd percentiles (.321, .392)

Runs per game (before 1997, after 1997)
MLB avg: (.415, .447)
Bonds: 97th, 99th percentiles (.716, .836)
Sheffield: 83rd, 90th percentiles (.568, .658))
Santiago: 48th, 26th percentiles (.406, .342)
Giambi: 80th, 90th percentiles (.550, .658)
Velarde: 50th, 83rd percentiles (.417, .602)

I next used t-tests to see if Velarde's before-and-after numbers were statistically different (we can think of statistical significance this way: each hitter's batting average varies from year to year. By comparing before-and-after averages, we can see if the 'after' averages are so different from 'before' averages that it seems like an anomaly. For example, if Wade Boggs hit .200 his last year in the league, we'd be pretty certain that was an anomaly, because his lifetime average was well over .300. On the other hand, if he hit .315, we'd think nothing of it because that is pretty much in line with his past performances).

Velarde increased his batting average from the 55th to the 70th percentile, but statistically, the two averages were not very different (even though his average increased by 20 points, it was not a 'significant' increase).

He increased his home run production from the 44th to the 45th percentile. And while this increase seems minimal, it is statistically different. This is because prior to 1997, Velarde hit an average of 0.07 HRs per game--but with a range of 0.04 to 0.10. After 1997, Velarde hit an average of .092 HRs per game--but this time with a range of 0.07 to 0.12. Because his average after 1997 is very close to the upper range before 1997 (the upper range was 0.10), statistically, his HR production is notable.

For RBI and Rs, Velarde also improved significantly when comparing before and after statistics (His RBI production increased from the 34th to the 43rd percentile and his R production increased from the 50th to the 83rd percentile).

So all things being equal, it would seem that Velarde might have benefited from using steroids (please realize that when I say 'benefited', I'm referring to his output on the field, not any health-related side-effects). So maybe an argument can be made that Velarde extended his career by using steroids, because after 1997 (assuming that is when he started using) all of his numbers except batting average increased significantly.

Now I wouldn't be honest if I didn't admit that this analysis doesn't consider many variables. For starters, I don't account for other things that increase player output--like practice, maturity, experience, legitimate weight training and some good bounces. Furthermore, a better method for comparing before and after numbers might be to take Velarde's statistics for his first ten years in the league and then project what his numbers would have been for 1997 to 2003; then compare these numbers to his actual numbers (and this is something I'll pursue in the coming weeks--and in case you're curious, one way to predict his statistics from 1997-2003 is to find players with similar numbers across offensive categories, run a regression, and then predict his output based on the regression model).

So while this analysis certainly isn't the last word, it's a good place to start, and it gives some idea how steroids may have affected Velarde's numbers. And even though we often associate steroids with high profile, all-star power-hitters, Velarde's case may be one of a mediocre player looking to get enough of an edge to hang around a few more years--and maybe it worked.

Quotes from yesterday's action

"He was talking about how he has a tape on all the hitters...I asked him if he had my big blast against him. It went about 330 feet and barely cleared the fence."

-Kevin Millar, talking about Curt Schilling. Schilling answered Millar's question a little later. When Millar stepped in against him for batting practice, Schilling whistled his first pitch of the day just behind Millar's neck. "My heart dropped," said catcher Jason Varitek. "It scared the crap out me."

"Rashad is the big story of the game...he continues to play like one of the best players in the league, and I think he's one of the best players in college basketball. He's made some big time shots for us all year."

-Roy Williams, on Rashad McCants' 30-point performance last night against Clemson.

"Get out of my locker."

-Barry Bonds, when asked about a report that he had received steroids and human growth hormone from a nutritional supplements lab implicated in a drug-distribution ring.

April 1, 1996, Riverfront Stadium, umpire John McSherry calls time from behind the plate and collapses on the field with a massive heart attack and dies. The popular McSherry, a veteran of 21 seasons, had been suffering from a series of medical problems, aggravated by his weight of 328 pounds. The game, just seven pitches old between the Reds and Expos, was called.

"Snow this morning and now this. I don't believe it. I feel cheated. This isn't supposed to happen to us, not in Cincinnati. This is our history, our tradition, our team. Nobody feels worse than me."

-Marge Schott, owner of the Cincinnati Reds, who died yesterday. Schott, who later apologized, said it with flowers instead. But the Dayton Daily News reported that the flowers she sent were given to her by a television station covering the Reds.

Start the clock, free agency begins today
Pro Football Weekly lists some of the top free agents available and where they might end up. On that list are five cornerbacks (Antoine Winfield, Ahmed Plummer, Troy Vincent, Bobby Taylor and Shawn Springs), and the Steelers are not mentioned once as having interest in any of them. Of course that doesn't mean the Steelers don't have interest in them; but if they don't land a CB in free agency and then take a QB and RB in the first two rounds, they are headed down the same road they've traveled the last three seasons (this road is at the intersection of defensive pass interference and missed tackles).

But their is good news. The Post-Gazette reports that the Steelers have signed backup fullback Matt Cushing. Maybe he can play cornerback too.

This can't be a good idea
The Steelers are announcing their 2nd annual 'Men's Fantasy Football Camp Weekend' set for this summer. Here's the sales pitch, straight off the website:

"Guys, you have been drafted! It is time to get off the couch and on to the playing field for an experience of a lifetime"

Before you rush to sign up, be sure to first read the following disclaimer (it's at the top of the page):

"Be sure to print and complete the registration form at the bottom of this page and also print and complete the MEDICAL WAIVER."

Right. Now I remember why I enjoy sitting on my couch watching football on television. This is one of those situations that sounds great at one in the morning over a few too many beers, but once you're on the field in your new 'uniform' you start to get second thoughts. Your fears are confirmed when you're doing blocking drills across from Butterbean. Actually, I'm sure it's not that bad, and in fact, there are some photos posted from last years camp--and their pretty funny.

How many bad decisions can one team make?
Maybe Joe Gibbs and Daniel Snyder know something the rest of us don't. Is it just me or are the Redskins seemingly the most impulsive team in football. They've just signed Clinton Portis to a $50.5 million contract (including a $17m signing bonus) making him the highest paid back in the league. They gave up Champ Bailey, one of the best cornerbacks in the league, and a second round draft pick. Since when does a team give up a top five cornerback and a 2nd round pick, for arguably one of the top five running backs in the league when the upcoming draft is full of quality runners?

I guess the answer to that question is, right after the new ol' ball coach comes out of retirement, promptly demotes the 2nd year, star quarterback-in-the-making, to trade for an over-the-hill, oft-injured Mark Brunell--just to say he now has a veteran quarterback. Note to Joe Gibbs: There could be more good news--Vinny Testaverde is retiring and will soon be availabe to replace Brunell as the veteran, veteran quarterback.

Here's an idea if you're in the Washington front office--keep Champ Bailey, trade down in the first round (they currently have the 5th pick), draft either RBs Kevin Jones or Steven Jackson and the second round pick is still yours. Don't get Brunell and start Patrick Ramsey, and the third round pick is still yours. As it stands, the Redskins now have two picks in the upcoming draft. That's a great way to rebuild a team that won five games last season.

Buy hey, what do I know--maybe Gibbs has a few more tricks up his sleeve--I hear Mark Rypien might be available by minicamp.

McCants has a Big Game against NC State

"Yeah, I heard all that. I love it. Stare at me, try to psyche me out. I'm too strong mentally for that. And they didn't have much to say at the end."

-Rashad McCants,who scored 22 points, commenting on how he was unaffected by both Julius Hodge's trash-talking and the raucous fans at the RBC Center.

Adam Lucus writes in more vivid detail about how intenese this rivalry really is.

David Ortiz accomplishes Goal before the Season even Starts
I guess it's important to aim high. This is from today's Boston Herald:

"It always helps to set a goal, and David Ortiz reached one during batting practice. After days of egging each other on, Ortiz impressed himself and batting-practice mates Millar, Manny Ramirez and Jason Varitek by launching a missile that landed approximately 100 feet beyond the right field fence. The ball shattered the right tail light of a green Oldsmobile Intrigue, one of about 20 cars at which the players had taken aim.

'I told them I was feeling strong today,' Ortiz said.

One ball hit and shattered the windshield of media relations savant Peter Chase's car."

Bettis is Back
The Steelers will probably announce today that Jerome Bettis will be back for one more season at a restructured salary of $1 million.