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)
Pedro Cerrano: 球棒生病了。我打不到曲球。直球我打了很多。曲球，球棒會害怕。我請求Jobu來幫我趕走球棒的恐懼。我會請他抽雪茄，喝萊姆酒。他會來的。(出自電影"大聯盟")
Introduction
簡介
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.
自從落磯隊於1993年搬到目前所在地之後，人們一直討論海拔對棒球的影響。雖然保濕器已經有效降低了Coors Field成為打者天堂，但是卻沒有解決球的變化度不如在海平面時的問題。這個現象是高海拔的稀薄空氣所造成的。雖然這已經眾所皆知，但是仍然有一些難以理解之處與影響有多大的疑問。感謝PITCHf/x，我們可以藉此獲知各球種在Coors Field所受到的影響。我們在此更新之前同樣主題的文章。
Physics of the ball in flight
球飛行時的物理學
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.
在投手將球投出後，唯一作用於球上的力量是地心引力，空氣阻力與馬格納斯力(旋轉)。(你可以閱讀Dr. Alan Nathan的論文以獲得詳細敘述)雖然地心引力不受缺乏空氣所影響，但是空氣摩擦力與馬格納斯力卻與空氣密度成比例。由於Coors Field幾乎高於海平面一英里，所以隨著氣溫的變化，空氣密度大約會降低20%。這代表空氣摩擦力與馬格納斯力將降低20%。如果你讀過其他使用PITCHf/x資料的文章，你應該看過"一般球的變化量對照沒有旋轉的球"這個句子。你在網頁上所看到的變化量圖就是在顯示球的變化量受到較低空氣密度影響而下降。這個現象發生在任何球種上，不只是曲球，它所影響的不只是下墜，而是徹底的影響。
Let's look at an example. Here is a movement plot for Derek Lowe separated into Coors and non-Coors parks:
我們來看一個例子。這裡是Derek Lowe的變化量圖，區分為在Coors Field與其他非Coors Field的球場:
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.
Lowe的伸卡球與變速球是左邊的那一大群，滑球則是右邊的那一群。你可以注意到在經過球場校正後，在Coors Field所投的球跟其他球場比較起來會下沉的更多，水平位移則較少。如果你正在納悶為何Lowe的伸卡球似乎會上飄，這是因為球仍然有一些反向旋轉所造成的;但是垂直位移仍遠小於四逢線快速球。John Walsh對這個結果有非常出色的解釋。
Now that we see the effect on the movement of a pitch, we can discuss how this effects certain pitches.
現在我們看到對球的位移量所造成的影響，我們可以討論各種球種所受到的影響。
The Sinker: solution to all your woes?
伸卡球: 是解決問題的王道嘛?
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).
投手在Coors Field投大量的伸卡球應該可以獲得較佳的成績，這個推論已經出現了好一段時間。這個推測基於伸卡球投手讓球下沉而製造滾地球，如此被擊出全壘打的機會將較少。事實上，像我們剛剛看到的Lowe，稀薄的空氣應該會對伸卡球有幫助，事實上會減少垂直位移(除非你的伸卡球擁有反向的垂直位移)。
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.
好吧!落磯隊嘗試過了，得到了憂喜參半的結果。不幸的是有美中不足的地方。雖然稀薄的空氣降低了球因旋轉而造成的位移，但是還有其他驚人的結果。由於空氣阻力也同樣的降低了，這使得球在Coors Field到達本壘板的時間比在海平面短。由於球停留在空中的時間比較短，所以地心引力施展魔力的時間也相對縮短。還記得我們查看移動量圖的時候，我們簡單的和沒有旋轉的球相比較，所以地心引力的影響被排除了。當我們將地心引力加進來時，可以發現到如果你在Coors Field與海平面上投出同樣的球，在Coors Field球經過本壘板時事實上會比較高一點點。
Here is a side view of Derek Lowe's sinker at Coors and at other parks:
這裡是Derek Lowe的伸卡球在Coors Field與其他球場的側視圖:
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.
注 意到記號的地方顯示出在0.075秒時，球在Coors Field比在其他球場跑的更遠。同時Lowe似乎些微的提高出手點，當球經過本壘版時，這個差距隨著時間被明顯的放大了。如果球到達本壘版時的高度較 高，最後形成飛球的機率也較高。這個影響不只侷限於伸卡球，但是在這裡我必須說伸卡球不是在Coors Field投球時的萬靈藥。讓我以稍微不同的方式再說一次: 你可以在Coors Field投出具有威力的伸卡球，但是在Coors Field投伸卡球不代表你就具有壓制力。
The Curveball: colse your eyes and pray
曲球: 閉上你的眼睛祈禱吧
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.
很 明顯地，曲球將遭受Coors Field造成的所有麻煩: 由於稀薄的空氣與停留空中的時間較短，使得地心引力的拉力也較少的緣故，曲球的移動不像平常那麼多。結果通常是一顆偏高的曲球被轟到觀眾席上;事實上投手 很少在Coors Field投曲球，就算是以曲球聞名的投手也一樣。
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:
我作了一些深入的研究以找出一位曲球投的夠多，能顯示出這個結果的投手。諷刺的是，這名投手是現在被降級到小聯盟的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.
你 可以在此看到結果，保持曲球的高度，以增加它下墜的幅度。事實上在比賽中，Hill也投了一些本季其他先發場次中不曾投過的滑球，就是圖片中中間的那些小 點。同樣的你可以將他的四縫線快速球排除不看。如此很清楚的曲球(特別是大幅度曲球)不會是個好選擇。滑球我就不在此討論了，但是我相信你們應該可以猜得 到結果。
The Fastball: cooking with gas
快速球: 極具威力
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.
四縫線快速球，特別是高壓投法時，球將變得更直並且不會像其他球路受到如此大的影響。畢竟失去4的20%總比失去10的20%要來的好。快速球失去了大量的 垂直位移，但是取而代之的是停留在空中的時間較短。時間減少代表球將更快接近打者，如果你能將球投的更快，效果將更明顯。四逢線快速球是投手在Coors Field能利用稀薄空氣取得優勢的真正武器。
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?
我認為很明顯的在Coors Field，快速球是最沒有被善加運用的球種。在Coors Field的三振減少是由於滑球與曲球變化幅度小，使得投手失去了三振打者的球路，所以投手需要一些能讓打者揮棒落空的球路。這種球應該是肩膀高度的快速 球。高角度的快速球最容易使打者揮空棒，這在Coors Field將會很有用。當投手取得2好球沒有壞球時，永遠會擔心一個失投的高角度速球會跑到紅中的位置，但是你寧願將快速球投到紅中位置還是曲球呢?
The Changeup: the off-speed pitch of choice
變速球: 慢速球種的最佳選擇
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.
變速球，特別是垂直變化的變速球，在Coors Field應該是慢速球種的最佳選擇。因為他的移動像快速球，就算受到稀薄空氣的影響也相同。好的變速球的關鍵在於變速球與快速球之間的速差，由於稀薄空 氣的關係，球到達本壘版的時間差將些微增加(這是因為雖然相對差距仍然相同，但是絕對差距會因為速差而增加)。這是細微的影響，主要的關鍵是稀薄空氣不會 對變速球造成傷害，這將帶給投手些微的幫助。
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.
由於許多投手喜歡使用較多的變速球來面對慣用手相對的打者，當大多數的打者是右打時，擁有不錯變速球的左投手應該能獲得較佳的成績。所以過去幾年我們所見到的，如Jeff Francis與Aaron Cook這些傢伙都有不錯的表現。
What do pitchers actually throw at Coors
投手在Coors Field實際上都投什麼球
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:
好的，現在我們對投手該投哪些球種有些概念了。但是投手實際上都投哪些球種呢?我手邊的球種分類如下:
Pitch types at Coors and at all other stadiums in percent
在Coors Field與其他所有球場的球種百分比
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.
這個圖表很明顯的深受落磯隊的投手陣容所影響，目前他們擁有更多的伸卡球投手。伸卡球的比例增加到平均值的兩倍，而變速球是另一種比例增加的球 種。其它球種在Coors Field出現的比例皆下降，其中曲球與滑球如預期地都大幅減少。事實上在Coors Field，變速球沒有投的更多一些讓我感到有一點驚訝，除此之外，當投手到了丹佛市時，他們大多能知道如何改變球種。
Conclusions
結論
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.
雖然在高海拔投球並不容易，有些投手受到的影響甚至更為嚴重。伸卡球也許是一個有效的球種，但是卻不是解決問題的唯一答案。投手們應該要警覺 到，他們在Coors Field所投的球經過好球帶時都會有偏高的傾向，所以在投手丘上應該要瞄準較低的位置。投手可以利用稀薄的空氣投高角度的快速球與變速球，但是一般而言 應該要避免投曲球與滑球。