What to pack for Denver

Pedro Cerrano: Bats, they are sick. I cannot hit curveball. Straightball I hit it very much. Curveball, bats are afraid. I ask Jobu to come, take fear from bats. I offer him cigar, rum. He will come. (from the movie Major League)

Rick Honeycutt and Russell Martin discuss the finer points of pitching at Coors Field with pitcher Derek Lowe. Dodgers vs. Rockies May 4th (Icon/SMI)


Since the Rockies came into existence in 1993, people have been talking about the effects of altitude on baseball. Although the humidor has been effective at reducing Coors Field to just a good place to hit, it doesn’t solve the problem of the ball not breaking as it would at sea level. This phenomenon is caused by the thin air at elevation. This is pretty well known, but there still is some mystery what this means and how large an effect it has. Thanks to PITCHf/x, we can shed some light on what exactly happens to a pitch at Coors, thereby updating previous work on the topic.

Physics of the ball in flight

After a pitcher releases the ball, the only forces acting on it are gravity, air resistance and the magnus force (spin). (For a detailed description, you can read Dr. Alan Nathan’s paper on the subject here.) Although gravity is unaffected by the lack of air, both the air resistance and the magnus force are proportional to the air density. Nearly a mile above sea level, Coors Field reduces the air density by about 20 percent depending on the temperature. This means that both the air resistance and the magnus force will be reduced by about 20 percent. If you have read other articles using the PITCHf/x data, you have probably seen the phrase “movement of the ball compared to a ball thrown without spin.” Movement plots that you see on the web are showing exactly this, and it’s this movement that is being reduced by the lowered air density. This happens to every pitch, not just curveballs, and the effect isn’t just keeping the ball from dropping, it’s also straightening out the pitch.

Let’s look at an example. Here is a movement plot for Derek Lowe separated into Coors and non-Coors parks:

Lowe’s sinker and changeup are the large cluster on the left, and his slider is the cluster on the right. You can see that, after applying park corrections, the pitches thrown at Coors sink more and move less horizontally than do the pitches thrown in other parks. If you are wondering why Lowe’s sinker seems to rise, that is because the pitch still does have a little backspin to it; it is far less vertical movement than a four-seam fastball has, however. John Walsh has an excellent explanation of this effect.

Now that we see the effect on the movement of a pitch, we can discuss how this effects certain pitches.

The sinker: solution to all your woes?

For a while now, there has been a theory that a pitcher who throws a lot of sinkers should have more success at Coors. The theory goes that sinkerballers keep the ball down, which produces grounders, which are unlikely to leave the park. In fact, as we have just seen with Lowe, the rare air at Coors should help sinkers as it actually decreases the vertical movement (unless your sinker normally has negative vertical movement).

Well, the Rockies tried this, with mixed results at best. Sadly, there is a fly in the ointment. Although the thin air is decreasing the movement of the ball due to spin, it also is having another somewhat surprising result. Because the air resistance is also lowered, it takes less time for the ball to reach home plate at Coors than it does at sea level. Because the ball is in the air for a shorter time, gravity has less time to work its magic. Remember when we were looking at the movement plots, we were simply comparing the pitch to a ball thrown without spin, so the effect of gravity was removed. When we add gravity back in, we see that, if you throw the same pitch at Coors and at sea level, the pitch actually is going to cross home plate a little higher at Coors.

Here is a side view of Derek Lowe’s sinker at Coors and at other parks:

Notice that the tick mark representing the ball at 0.075 seconds is farther along at Coors than at other parks. Also, although Lowe does appear to have raised his release point some, the increase is greatly magnified by the time the ball crosses home plate. If the balls reach home plate higher, they are going to end up in the air more often. Now, this effect isn’t limited to sinkers, but I’m mentioning it here to say that sinkers aren’t the panacea to pitching at Coors. Let me say that again is a slightly different way: You can throw sinkers at Coors and be effective, but just because you throw sinkers at Coors doesn’t mean you are going to be effective.

The curveball: close your eyes and pray

Obviously, curveballs suffer from all the problems that Coors has to offer: They don’t move as much, due to the thin air, and they are going to be in the air for less time, so gravity will be pulling on them less. The result often is a hanging curve over the plate that is smashed into the seats; in fact, it has gotten to the point that pitchers rarely will throw their curve at Coors, even those pitchers who are known for a good curve.

I had to do some digging to find a pitcher who threw enough curves to show you the results. Ironically, that pitcher is the now demoted Rich Hill:

You can see the effect here, keeping the curveball up and making it more 12-to-6. In this game, Hill actually resorted to throwing some sliders, which are the points in the middle—something he didn’t do in any other start this year. You can also see the straightening out of his four-seam fastball. Thus, clearly curves (especially big breaking curves) are not the answer. I won’t break down sliders here but I think you can guess the results anyway.

The fastball: cooking with gas

Four-seam fastballs, especially when thrown over the top, tend to be rather straight pitches anyway and so don’t suffer much from the straightening out as do other pitches. After all, losing 20 percent of 4 is a lot less harsh then losing 20 percent of 10. Fastballs do lose a good chunk of their vertical movement, but this is replenished by the shorter time they are in the air. Also, the decreased time means the ball is going to get to the batter quicker, and if you are throwing fast anyway this is just amplified. This is a real weapon for a pitcher who can finally use the thin air at Coors to his advantage.

Specifically, I think the pitch that is underutilized the most at Coors is the high heat. Strikeouts continue to be way down at Coors because pitchers often lose their strikeout pitch if their slider or curve isn’t moving, so pitchers need something else to rely on to get swings and misses. That pitch should be the shoulder-high fastball. High fastballs tend to get the most swings and misses, and that will be amplified at Coors. There’s always a concern when a pitcher is at 0-2 that missing with a high fastball will result in a cookie down the middle, but would you rather throw a fastball down the middle or hang a curve in the middle?

The changeup: the off-speed pitch of choice

Change ups, and specifically straight changes, really should be the off-speed pitch of choice at Coors. Because they move like fastballs, they will continue to move like fastballs even after the thin-air effect. The key to a good changeup is a good speed differential between the changeup and the fastball, and because of the lower air resistance, the resulting time differential for the ball to reach home plate will be slightly increased (this is because, although the relative difference will still be the same, the absolute difference will increase because of the speed difference). This is a small effect, but the main point is that the thin air isn’t going to hurt, and if anything, it’s going to help the pitcher slightly.

Because many pitchers like to use their changeup more to opposite-handed batters, left-handed pitchers with a good changeup should do well as most hitters are right-handed. So guys like Jeff Francis and Aaron Cook should pitch pretty well, which is exactly what we have seen the past few years.

What do pitchers actually throw at Coors

Okay, so now we have some idea as to what pitchers should be throwing. But what are they actually throwing? My handy pitch classification algorithm sees things like this:

Pitch types at Coors and at all other stadiums in percent
         Coors Other
Fastball 45.0  48.1
Sinker   18.6   9.2
Curve     5.6   7.9
Slider   13.4  17.1
Change   13.5  12.0
Splitter  0.4   1.6
Cutter    3.5   4.1

Obviously, this picture is going to be heavily affected by the Rockies’ pitching staff, and right now they have more than their share of sinkerballers. So sinkers are up more than double the average, and the only other pitch that shows an increase is changeups. Everything else is being thrown less at Coors, with curveballs and sliders predictably being reduced greatly. Actually, I am a bit surprised that more changeups aren’t being thrown at Coors, but besides that it appears that pitchers have mostly caught on to how to best alter their pitch types when traveling to the mile-high city.


Although it will never easy to pitch at altitude, some pitches are affected worse than others. Although sinkers can be an effective pitch, they aren’t the complete answer to the problem. Pitchers should be warned that all of their pitches will tend to stay up in the zone at Coors, and the pitchers should “aim low” when they’re on the mound. They can take advantage of the thin air by throwing more high fastballs and changeups, but they should avoid curves and sliders in general.

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