The below post continues a debate I had in another forum over whether Matt Cain throws a "straight" fastball or a "moving" fastball relative to his peers. However, that particular point is of less interest, in my mind, than the findings on lefties vs. righties, starting vs. relief, and sinkers vs. 'normal' fastballs once the data is analyzed.

Having conceded XXXXX's point that my initial Pitch F/X sample--which showed that Cain's fastball was slightly above average in lateral movement--may be unrepresentative (especially given that it had an n = 20), I have since gone back to the Fogg Pitch F/X Player Cards and drawn a much larger sample (using the list of player cards as the sampling frame and a systematic random sampling procedure w/ skip & starting values randomly generated). This sample consists of 157 pitchers taken from the player card list (at: http://baseball.bornbybits.com/plots/players.html).

If you're unfamilliar with the Pitch F/X data (a primer):

http://mvn.com/mlb-stats/2008/01/14/a-pitchfx-primer/

For the distinction b/w break & movement:

http://www.hardballtimes.com/main/ar...of-the-sinker/

For the method of determining types of pitches including a definition of what movement in the x & z dimensions means:

http://www.hardballtimes.com/main/ar...tion-tutorial/

OK, so now that you've familliarzed yourself with the method and details, let's consider the data. In examining the x-dimension data, I employ the absolute value of that dimension (as the left vs. right direction of the pitch is irrelevant for the purposes of assessing how much the pitch moves). For the z-dimension, I subtract the z scores from a constant (20 inches)...so that the data analyzed is distance from that constant (and thus can be compared). For example, if pitcher X's z-score is 10, then their z_abs = 10. If their z-score is 6, then their z_abs will be 14. If their z-score is -5, then their z_abs will be 25 and so forth. The sink variable is whether or not the pitcher throws a sinker (it's import will be discussed later).

ALL PITCHERS

Code:
Variable      N            Mean         Std Dev         Minimum         Maximum
-------------------------------------------------------------------------------
x           157      -1.5543949       6.0245805     -10.4200000      12.3000000
z           157       9.3687261       2.5669379      -3.3400000      15.3900000
sink        157       0.1464968       0.3547351               0       1.0000000
x_ab        157       5.7012739       2.4524100       0.6400000      12.3000000
z_ab        157      10.6312739       2.5669379       4.6100000      23.3400000
-------------------------------------------------------------------------------

So from this table, the average horizontal movement (left or right) for a pitcher is 5.7 inches. Recall, Matt Cain's x-score was -5.01, hence it would appear initally that Sonic was right (my previous sample was biased). As that would put Matt Cain's movement south of the average movement for a pitcher, right around the 45th percentile.

Yet it should be noted that still means that a good bulk of the pitchers in the league have less movement than Matt Cain on their fastball. And furthermore, we should recall that the mean is influenced by higher values, and these dimensional scores are censored at zero. The median (middle score) for the x_ab variable is 5.03, hence Cain's x-dimension movement is almost squarely in the center of the distribution. And note, this is the worst case for Cain, as we've compared him to every pitcher in the sample, making no allowances for potential confounding factors. I consider those in the following analysis.

STARTING VS. RELIEF PITCHERS
It is the conventional wisdom that relief pitching is a different animal than starting pitching. Starters have to "pace" themselves, as they are likely to deliver 90-140 pitches in a start. Whereas relievers may only throw 10-40 in an appearance. Thus we expect starters to have to "dial it back" on their pitches...giving considerably less than maximal effort whereas relief pitchers are not so constrained. Furthermore, starting pitchers may deliver many more pitchers in a "tired" state, and hence are more likely to throw more pitches to the plate that are less than their best stuff. It stands to reason that this may not merely effect velocity. It could also effect movement as well. A starting pitcher may not give full effort throughout his start, resulting in less movement on his pitches. A starting pitcher may tire in latter innings, causing his stuff to "straighten out."

Code:
                            MEANS: STARTING PITCHERS

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           64      -1.7575000       5.6690426      -9.5800000      10.9100000
 z           64       9.3792188       2.5907726       0.1700000      15.3900000
 sink        64       0.1718750       0.3802542               0       1.0000000
 x_ab        64       5.3731250       2.4386770       0.6400000      10.9100000
 z_ab        64      10.6207813       2.5907726       4.6100000      19.8300000
 ------------------------------------------------------------------------------Code:
                           MEANS: RELIEF PITCHERS

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           93      -1.4146237       6.2839989     -10.4200000      12.3000000
 z           93       9.3615054       2.5644649      -3.3400000      14.3200000
 sink        93       0.1290323       0.3370526               0       1.0000000
 x_ab        93       5.9270968       2.4493316       1.1400000      12.3000000
 z_ab        93      10.6384946       2.5644649       5.6800000      23.3400000
 ------------------------------------------------------------------------------

As is apparent from this data, it looks like there is evidence to support the above intuition. Relief pitchers have about a half-inch more movement on their fastballs than do the starting pitchers on average. Taking a look once again at Cain among starting pitchers, his z-score, while still below the mean, is much closer (probably in the 48th-49th percentile [2.99 25th, 6.33 75th ]).

LEFTIES VS. RIGHTIES

There's an artifact in the Pitch F/X data that we've yet to account for that should be accounted for. For whatever reason (and I'm open to speculation on this), Lefties demonstrate much more lateral movement in their pitches than do Righties. Whether it's because there are much fewer Lefties in the league (you have to be 'better' to slot in as a Lefty), whether it is a function of their delivery...whether it is a function of them pitching to off-handed batters more...whatever. It's apparent and it is consistent, as you can see below:

Code:
                               MEANS: RIGHTIES

                              The MEANS Procedure

Variable      N            Mean         Std Dev         Minimum         Maximum
-------------------------------------------------------------------------------
x           113      -5.0404425       2.0764033     -10.4200000      -0.6400000
z           113       9.5243363       2.2673092       0.7900000      13.0200000
sink        113       0.1504425       0.3590971               0       1.0000000
x_ab        113       5.0404425       2.0764033       0.6400000      10.4200000
z_ab        113      10.4756637       2.2673092       6.9800000      19.2100000
-------------------------------------------------------------------------------Code:
                             MEANS: LEFTIES

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           44       7.3984091       2.5484696       2.6300000      12.3000000
 z           44       8.9690909       3.2075121      -3.3400000      15.3900000
 sink        44       0.1363636       0.3471418               0       1.0000000
 x_ab        44       7.3984091       2.5484696       2.6300000      12.3000000
 z_ab        44      11.0309091       3.2075121       4.6100000      23.3400000
 ------------------------------------------------------------------------------

This is the most significant difference found in the sub groups. There is a more than two-inch differential between the fastball of lefties and the fastball of righties on the X dimension. Once we take this in to account, Cain's movement is dead-on the average movement for Righties.

SINKERS

Finally, the last sub-group I want to identify is the sinker-ballers. These are pitchers whose only fastball is a sinker. What's interesting is that, not only do sinkerballers have more downward movement on their pitches...they also tend to have more lateral movement on their pitches. Most likely a consequence of how they grip the pitch (thus giving it a different spin). Let's continue looking at righties, and examine the difference b/w sinkerballers and those pitchers who feature a normal fastball:

Code:
     MEANS: RIGHTIES W/ SINK

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           17      -7.7823529       1.4706356     -10.4200000      -4.3400000
 z           17       5.4111765       1.8157673       0.7900000       8.2100000
 sink        17       1.0000000               0       1.0000000       1.0000000
 x_ab        17       7.7823529       1.4706356       4.3400000      10.4200000
 z_ab        17      14.5888235       1.8157673      11.7900000      19.2100000
 ------------------------------------------------------------------------------Code:
      MEANS: RIGHTIES NO SINK

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           96      -4.5548958       1.7706329      -8.6000000      -0.6400000
 z           96      10.2527083       1.3934708       5.0600000      13.0200000
 sink        96               0               0               0               0
 x_ab        96       4.5548958       1.7706329       0.6400000       8.6000000
 z_ab        96       9.7472917       1.3934708       6.9800000      14.9400000
 ------------------------------------------------------------------------------

Again, the difference between the two subsets is striking. Not so much on the vertical plane, as expected sinkerballers throw fastballs that "fall off the table" much more than regular fastballs (14.6 inches to 9.7 inches). What's interesting is that sinkerballers also have much more horizontal movement on their pitches. Again, it is an over two inch difference (4.55 for our 96 fastballers and 7.78 inches of lateral movement for our 17 sinkerballers). Note, once we factor out the pitchers that feature sinkers as opposed to normal fastballs, Cain's fastball now rates as above average in movement. His 5.01 slots in somewhere around the 60th to 65th percentile (75th 5.7).

CONCLUSION

Finally, let's take into account all these factors and truly compare apples to apples: Cain's fastball vs. the fastball of Righty starting pitchers sans sinkerballers:

Code:
               MEANS: RIGHTY STARTING PITCHERS N/S

                              The MEANS Procedure

 Variable     N            Mean         Std Dev         Minimum         Maximum
 ------------------------------------------------------------------------------
 x           38      -4.3907895       1.9775201      -7.8300000      -0.6400000
 z           38      10.2652632       1.3632012       7.1000000      13.0200000
 sink        38               0               0               0               0
 x_ab        38       4.3907895       1.9775201       0.6400000       7.8300000
 z_ab        38       9.7347368       1.3632012       6.9800000      12.9000000
 ------------------------------------------------------------------------------

In this group, Cain's fastball is well above average in lateral movement. His fastball is more than a half-inch better in "busting in on the hands" of right-handed hitters than his fellow right-handed starting pitchers (sans sinkers). He slots in somewhere around the 70th percentile here. Certainly no Jake Peavy or Sergio Mitre, but no where close to a Yovanni Gallardo or Chris Young. D.GOOCH