Heels, Sox & Steelers

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.