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“The scientist is not a person who gives the right answers, he is one who asks the right questions.”
Claude Levi-Strauss

One of the aspects of writing a weekly column that I enjoy most is the reader feedback; sometimes it starts to arrive just minutes after the column is posted. Although I may not get to every email, rest assured that they’re all read and many of them populate my “future columns” queue. So in that vein–and as a thank you for asking the right questions–today we’ll answer two specific questions prompted by previous columns: one related to baserunning and, and another taking a look at plate discipline.

One of the most frequently asked questions after last week’s column concerned the repeatability of all the baserunning metrics, including Equivalent Other Advancement Runs (EqOAR). Reader Aaron voiced it this way:

How much correlation is there year to year in the baserunning metrics? Is there significant year-to-year consistency in the individual metrics? Or in the combined sum of the various baserunning metrics?

I ask because given the relatively modest range in values on a year-to-year basis, I’m wondering how much predictive value these metrics have in estimating a player’s future worth.

That’s a question that can be answered definitively, so the following table records the correlation coefficient for all consecutive seasons by any runner who meets or exceeds the opportunity thresholds noted for the given metric:

```
Metric   Opps     r
EqHAR      30   0.36
EqSBR      10   0.19
EqGAR      10   0.18
EqOAR     100   0.03
EqAAR      10   0.02
---------------------
Total      25   0.26
```

Advancing on hits is the clear leader, followed by stolen base runs and advancing on ground outs, with other advancement and advancing on fly outs bringing up the rear. The reason the latter two lag behind is the combination of their scarcity and the disparate impact that individual events can have on seasonal totals. That is, runners simply don’t get very many opportunities to advance on fly outs, wild pitches, and passed balls; when they get thrown out (which is rare) the impact can significantly drag down their total for an entire season.

To answer Aaron’s question, we can say that none of the metrics is that strongly correlated from season to season, and so outside of the top runners like Chone Figgins (who you could reasonably assume will contribute between five and 10 runs) and those at the bottom like Paul Konerko or Jorge Posada (who cost their teams around 4.5 runs), I wouldn’t bet a great deal on repeatability in runs contributed through baserunning.

With that said, when grouping seasons into even and odd years and then performing correlations on the totals, the numbers–as you would expect–go up:

```
Metric       r
EqHAR      0.60
EqSBR      0.55
EqGAR      0.30
EqOAR      0.07
EqAAR      0.07
----------------
Total      0.37
```

Finally, this discussion also provides the opportunity to update a graph that I created last summer that puts each metric into perspective in terms of its overall contribution to the running game, as measured in runs:

So, not only is EqHAR the most repeatable–because it allows good baserunners to differentiate themselves from their peers and is therefore less susceptible to randomness–but it also has the highest aggregate impact because of the greater number of opportunities. On the flip side, EqAAR has a relatively high impact since it primarily deals with scoring on sacrifice flies but encompasses relatively few opportunities and has a low skill component.

But Fish Aren’t Square?

After our discussion two weeks ago on plate discipline for hitters, several readers wondered if a similar version could be created for pitchers. Typical was this question from Bryce:

Your Fish/Eye charts for hitters were very interesting and makes me wonder how the pitchers would stack up? Which pitchers encourage chasing more than others?

Using the same metrics as with hitters, we can get a pretty good sense of a pitcher’s stuff. But before taking a look at the pitching leaders and trailers in the four metrics, it should be noted that I’ve tweaked the calculations a bit this time around. Previously, the area of the strike zone was defined by the regulation width (17″) and the height as recorded in the PITCHf/x data. Now I’m accounting for any part of the baseball touching the zone, and so have expanded the area an inch and a half (the radius of a baseball) in all directions.

Without further ado, here are the leaders and trailers for the 204 hurlers who’ve recorded 350 or more pitches:

```
Pitchers Sorted by Fish
Name                 Pitches    Fish  Square BadBall     Eye
------------------------------------------------------------
Cole Hamels              445   0.423   0.788   0.738   0.252
Scott Baker             1140   0.384   0.878   0.699   0.189
Cla Meredith             757   0.383   0.857   0.567   0.202
John Smoltz             1893   0.376   0.829   0.576   0.261
Takashi Saito            682   0.357   0.757   0.594   0.216
Johan Santana            729   0.354   0.713   0.558   0.204
Jonathan Broxton         926   0.350   0.799   0.562   0.220
Bobby Howry              640   0.348   0.826   0.791   0.185
Jeremy Bonderman         980   0.348   0.899   0.649   0.240
Aaron Harang            1236   0.347   0.857   0.623   0.234
------------------------------------------------------------
Matt Chico               375   0.227   0.846   0.841   0.267
Jorge de la Rosa         492   0.222   0.903   0.653   0.243
Brian Bannister         1258   0.221   0.933   0.762   0.267
Ryan Feierabend          529   0.220   0.894   0.784   0.220
Jo-Jo Reyes              619   0.216   0.907   0.848   0.248
Jamey Wright             848   0.214   0.929   0.707   0.246
Steve Trachsel           598   0.210   0.920   0.754   0.275
J.D. Durbin              539   0.206   0.920   0.704   0.283
Cliff Lee                371   0.201   0.906   0.759   0.249
Mike MacDougal           359   0.178   0.815   0.639   0.271
```

When used to evaluate pitchers, Fish can be seen as a measure of how often the pitcher enticed the batter to swing at a pitch out of the strike zone and so is a direct answer to Bryce’s question. Cole Hamels is separated a bit from the pack at over 42 percent, although the sample size is a bit smaller than it is for the other pitchers. Unlike with hitters, although I didn’t actually run the numbers, it’s clearly the case that the performance of the pitchers at the top of the list far exceeds those at the bottom, indicating that their stuff is more deceptive. The average value for this metric is 29 percent; attentive readers will note that this average will be lower since the strike zone is expanded.

```Pitchers Sorted by Square
Name                 Pitches    Fish  Square BadBall     Eye
------------------------------------------------------------
Franklin Morales         378   0.239   0.955   0.681   0.282
Jon Lester               428   0.320   0.941   0.648   0.264
Aaron Laffey             354   0.280   0.938   0.815   0.284
Kenny Rogers             461   0.315   0.934   0.725   0.238
Odalis Perez             388   0.287   0.934   0.650   0.333
Livan Hernandez         1060   0.228   0.934   0.788   0.260
Brian Bannister         1258   0.221   0.933   0.762   0.267
Mike Mussina             526   0.322   0.932   0.886   0.319
Jamey Wright             848   0.214   0.929   0.707   0.246
Tom Glavine              626   0.265   0.924   0.825   0.245
------------------------------------------------------------
Cole Hamels              445   0.423   0.788   0.738   0.252
Ron Mahay                403   0.236   0.785   0.509   0.248
Brandon Morrow           820   0.269   0.782   0.641   0.252
Ryan Rowland-Smith       376   0.257   0.774   0.773   0.279
Scott Kazmir             704   0.272   0.774   0.582   0.232
Takashi Saito            682   0.357   0.757   0.594   0.216
Joaquin Benoit           862   0.330   0.751   0.591   0.187
Michael Wuertz           365   0.310   0.750   0.397   0.256
Johan Santana            729   0.354   0.713   0.558   0.204
Santiago Casilla         389   0.320   0.707   0.452   0.268
```

Square records how frequently hitters make contact with pitches that they swing at that are in the strike zone. An average value is 86.5 percent, and Rockies rookie Franklin Morales–who has had mixed success thus far–leads at over 95 percent. He’s somewhat atypical of the group, since many of the rest are soft-tossers who don’t induce many swinging strikes. On the other end of the spectrum, Santiago Casilla (the suddenly aged A’s reliever formerly known as Jairo Garcia) is down around 71 percent. Although the performance difference between those at the top and at the bottom is not as obvious as in the above table, we could reasonably interpret low Square values for pitchers as an indication of pitchers with exceptionally good stuff, since hitters are having difficulty in getting a bat on the ball, even when the pitches are in the strike zone.

```Pitchers Sorted by BadBall
Name                 Pitches    Fish  Square BadBall     Eye
------------------------------------------------------------
Mike Mussina             526   0.322   0.932   0.886   0.319
Paul Byrd                887   0.309   0.918   0.870   0.291
Kyle Kendrick            654   0.347   0.906   0.851   0.276
Jo-Jo Reyes              619   0.216   0.907   0.848   0.248
Carlos Silva            1394   0.326   0.902   0.846   0.243
Woody Williams          1088   0.304   0.914   0.844   0.263
Curt Schilling           699   0.305   0.869   0.843   0.277
Matt Chico               375   0.227   0.846   0.841   0.267
Horacio Ramirez         1270   0.276   0.912   0.836   0.282
Vicente Padilla         1570   0.283   0.913   0.836   0.250
------------------------------------------------------------
A.J. Burnett            1495   0.299   0.866   0.556   0.268
Tyler Yates              640   0.290   0.800   0.556   0.203
Sean Green               512   0.301   0.842   0.545   0.266
Erik Bedard              564   0.293   0.873   0.525   0.281
Ian Snell                775   0.274   0.862   0.514   0.243
Ron Mahay                403   0.236   0.785   0.509   0.248
Carlos Marmol            748   0.296   0.801   0.496   0.368
Francisco Rodriguez      689   0.282   0.802   0.462   0.332
Santiago Casilla         389   0.320   0.707   0.452   0.268
Michael Wuertz           365   0.310   0.750   0.397   0.256
```

As you might expect, the top of the list is populated primarily by pitchers who don’t throw all that hard, and it should come as no surprise that Square and BadBall are pretty strongly correlated (r=.52). The bottom of the list contains pitchers like Michael Wuertz, Casilla, K-Rod, and Carlos Marmol, all of whom sport nasty sliders that make it difficult for hitters to make contact on balls out of the strike zone. The average for everybody is 70 percent.

```Pitchers Sorted by Eye
Name                 Pitches    Fish  Square BadBall     Eye
------------------------------------------------------------
Scot Shields             839   0.263   0.895   0.663   0.379
Carlos Marmol            748   0.296   0.801   0.496   0.368
Dustin Moseley           890   0.321   0.923   0.789   0.347
Odalis Perez             388   0.287   0.934   0.650   0.333
Francisco Rodriguez      689   0.282   0.802   0.462   0.332
Justin Germano          1596   0.253   0.906   0.745   0.328
Heath Bell               892   0.326   0.855   0.592   0.327
Mike Mussina             526   0.322   0.932   0.886   0.319
Darren Oliver            432   0.303   0.819   0.775   0.318
Byung-Hyun Kim           687   0.245   0.835   0.679   0.317
------------------------------------------------------------
Tyler Yates              640   0.290   0.800   0.556   0.203
Cla Meredith             757   0.383   0.857   0.567   0.202
Chien-Ming Wang          608   0.275   0.913   0.667   0.199
Chris Young             2072   0.336   0.816   0.660   0.196
Eric Stults              371   0.274   0.822   0.722   0.195
Rafael Soriano           610   0.298   0.805   0.631   0.190
Scott Baker             1140   0.384   0.878   0.699   0.189
Joaquin Benoit           862   0.330   0.751   0.591   0.187
Bobby Howry              640   0.348   0.826   0.791   0.185
Alan Embree              535   0.310   0.819   0.610   0.183
```

In this metric, the link to performance as a clear indicator of stuff is probably even a little more mixed than with the others. For example, although Marmol and Rodriguez once again make appearances at the top, so do pitchers with lesser stuff, guys like Darren Oliver and Odalis Perez. The average here is 26 percent.

Using this information, we can now create a similar chart to the one we created for hitters. However, instead of plotting Fish versus Eye, in our desire to get a feel for which pitchers have the best stuff or are the nastiest to stand in against, we’ll instead plot Fish versus Square. Using Fish, we see how frequently the pitcher enticed the hitter to chase, while with Square we can capture how difficult it is for hitters to make contact, even with pitches in the strike zone. Since Fish-Square has no catchy ring to it, we’ll call our resulting plot simply “Stuff”.

One of the things you’re likely to notice here is that the pitchers are bunched up much more than the hitters were in the previous article. Indeed, there is less variability among pitchers, a result I chalk up to both the larger samples involved with pitchers, and the fact that hitters’ actions are what is being recorded, so you might expect more differentiation in approaches at the plate to show themselves.

Even so, from the plot we can see that Cole Hamels, Johan Santana, Takashi Saito, Jonathan Broxton, and John Smoltz appear in the upper right-hand quadrant, and are among those pitchers who we can crown with the title of “Nastiest Stuff”.

You’ve Got Mail

As this is the final Schrodinger’s Bat during the 2007 regular season, I’d like to also take this opportunity to thank all those who have written me to offer their opinions and ideas. Please keep them coming throughout the offseason, as they are greatly appreciated.

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