Target Field, with its apparently closer fences and limited foul territory, would project to have a higher run environment than the Dome, if all things were the same. But, we have weather to deal with now.
Now, I cannot project how the infield will play, or how bouncy outfield walls are, or Gardy asking for the dirt in front of the plate packed down to resurrect the Baltimore Chop. However, I can make reasonable estimates for the fence distances and heights. And oh what fun that was.
So, how does it really compare? The field dimensions listed for Target Field: 339 feet LF, 377 LCF, 404 CF, 367 RCF, and 328 RF, do not compare well to the Metrodome's dimensions: 343, 385, 408, 367, and 327 respectively. However, that is just five points in a 90 degree arc. Plus, the listed dimensions for the Metrodome are wrong. 343, 408, and 327 are right (probably). 385 and 367 though? Hah! I think a picture tells the story best:
Not quite the obvious hitter's park now. Also, all graphs and measurements use the above coordinate system. That is, -45 degrees down the left field line, 0 degrees to straightaway center, and 45 degrees down the right field line.
The main reason for the confusion are the angles used for measuring LCF and RCF are not the same between the two parks. For instance, the 367 occurs at 18 degrees in the Metrodome but 24 degrees in Target Field.
Are my measurements correct though? I have no idea. Lots of careful measuring of Target Field's seating chart, looking at the 3D seat finder, and comparing to Andrew Clem's Metrodome diagram lead me to think that my measurements are at least close.
But wait! I have more!
From the beginning of April through May 8 and from September 26 through October, the average high is less than 68 degrees1. That is approximately the lowest temperature I have seen posted for games at the Dome. This is important because colder air is denser and thus fly balls do not travel as far. Also, since the majority of games are played at night, there should be many games with a starting temp below 68 degrees (the average low in Minneapolis tops out at 64).
Starting with a windless 70 degree day, since that is environment the Metrodome always has, we get a home run percentage like so:
Quick, guess what those two drops in the 0 to 20 degree area indicate! I can wait. Meanwhile, I will give you my procedure.
After mapping out the fence distances and heights, I analyze the fence at every half a degree (-45, -44.5, ...). To do this, I generate a large number of potential home runs. Every direction gets the same set of trajectories. The set consists of balls with an initial velocity between 90 and 108 mph, in increments of 0.2 mph, and an angle above the horizontal between 22 and 38 degrees, in increments of 0.5 degrees, for a set size of 3003. Then I just map out the trajectories for every ball in each direction and compare them to the fence distance and height. And now that I think about it, because I ignore wind this could have been much quicker if I just stored the trajectories for each ball in the set and reused them for each direction. Oh well.
Anyway, back to the original question:
They are caused by the wall growing to 23 feet. Right now I think I have the baggie a bit smaller than it should be, but I lack appropriate pictures to determine where it ends. Something to do for part 2.
Eyeballing it I would guess that Target Field, on a calm, 70 degree day, will have fewer home runs on average than the Metrodome. Now, there is the problem of less foul territory (hm, part 3 maybe!), meaning fewer chances at a free out and longer at bats will even the difference.
But, sadly, we cannot have six months worth of beautiful 70 degree baseball days. I know, I wish too. Here is a graphsplosion of game time potential temperatures:
The same caveat of the first graph applies here as well: these all assume no wind. I need something for next week after all.
This could/will be quite the pitcher's park when it gets cold. Also, if you have an itch to watch some Rangers or Rockies-style baseball, those humid 80+ degree days could be promising.
Finally, some numbers. This is the total number of balls that I estimated would be home runs for each temperature. The total number of trajectories considered was 543,543.
| Temperature | Metrodome | Metrodome Percentage | Target Field | Target Field Percentage |
|---|---|---|---|---|
| 80 | 278926 | 51.3% | 276738 | 50.9% |
| 70 | 278926 | 51.3% | 262673 | 48.3% |
| 60 | 278926 | 51.3% | 247862 | 45.6% |
| 50 | 278926 | 51.3% | 232317 | 42.7% |
| 40 | 278926 | 51.3% | 216279 | 39.8% |
| 30 | 278926 | 51.3% | 199763 | 36.8% |
How do you feel about Target Field now?
1: According to wunderground.com. All weather data from this site.
The Metrodome model was based entirely on the diagram created by Andrew Clem.
The Baseball Trajectory Calculator from Alan Nathan's page was invaluable for the drag and Magnus force equations.
I hope DSPAN2 is doing his wind sprints over the winter.
This is cool! Looking forward to parts 2 thru X.
Great work sean. Let me riddle you this now? With the smaller amount of foul ground territory does it makes sense that a player like elm'n who swings at everything, will have more of his attempts go foul thus increasing his value? Or does it seem better for a player like Punto whose value lies in drawing out at bats and raking up pitch counts?
Ah, who am I kidding? they are both going to be below average bats, no need to get my hopes up.
below what? Cause I apparently at the bar Wednesday night predicted a .300+ average and 25 HR for Delmon this year. Good thing I didn't put money down.
At that point, the bartender probably should have cut you off.
At that point,
the bartender probably should have cut you offyou were probably taking to the cabbie. Fixed that for you CT.I think what we need to look at FTLT is who had the most foul pops. Actually, those counts might be interesting to see for opponents vs. Twins at the Dome.
So does this mean that Scott Baker's tediously long at bats will require even more pitches for him to retire the batters?
Possibly. But his other weakness is the long ball...and if he can avoid giving up 50 home runs in April, it might offset that.
More importantly, will the bullpen be located where Baker can see it?
Thankfully, it seems he still can. Even better, it's now closer to CF. Now he can look to the bullpen and the runner on 2B at the same time!
This could/will be quite the pitcher's park when it gets cold. Also, if you have an itch to watch some Rangers or Rockies-style baseball, those humid 80+ degree days could be promising.
I confess to a dearth of knowledge when it comes to physics, but I wonder if the humidity frequent in Minnesota summers might help reign in some of the deep flies, similar to the effect of the denser air in San Diego (though not to that extreme). I would wager that Denver and Dallas have drier heat than Minneapolis does in the summer months, though the Coors humidor will make up for some of that difference.
This is an awesome post, sean. When I saw your LTE in the CoC mentioning a desire to do this project, I really hoped we'd see something come of that urge. This post alone exceeds my wildest expectations, and there is at least another one coming. Can't wait for it.
FYI, Andrew Clem just posted his preliminary Target Field diagram this weekend. I don't know if you feel more or less confident with that compared to your measurements of the seating diagram, etc., but I thought you'd be interested all the same.
I confess to a dearth of knowledge when it comes to physics, but I wonder if the humidity frequent in Minnesota summers might help reign in some of the deep flies, similar to the effect of the denser air in San Diego (though not to that extreme). I would wager that Denver and Dallas have drier heat than Minneapolis does in the summer months, though the Coors humidor will make up for some of that difference.
It's actually the reverse that is true. More humid air is less dense than drier air. Cribbing from Wikipedia:
The Coors effect (and San Diego's) derives more from elevation and temperature. Coors is just so high that even cool weather can't counteract the elevation. Petco though, being so close to the ocean stays cooler to go with its low elevation. I'm not sure how it compares exactly to, say, AT&T park. Orientation and prevailing winds might be another factor.
FYI, Andrew Clem just posted his preliminary Target Field diagram this weekend. I don't know if you feel more or less confident with that compared to your measurements of the seating diagram, etc., but I thought you'd be interested all the same.
Excellent. I spent 30 minutes in the 3D seat finger trying to figure out how much the overhang hung. I eventually made the wildish guess that it was orthogonal to the foul line and it appears that Clem made the same decision. I feel better about that. It seems he also concluded that it's straightaway center that is 404 and not the corner to the left that is. Good good.
Finally, thanks!
One of the things I found interesting about the humidor's success in Colorado is that apparently the moisture content of the ball makes a significant difference on how the game is played. I wouldn't be that surprised if part of the reason that, say, Seattle plays as such a pitcher's park has to do with playing with a pretty wet ball.
Given the use of the humidor in Denver, it would be interesting if balls were required to be stored in humidors at all parks, sort of the way that they keep pucks in a cooler for NHL games.
Given the use of the humidor in Denver, it would be interesting if balls were required to be stored in humidors at all parks, sort of the way that they keep pucks in a cooler for NHL games.
that's entirely to rational and reasonable for MLB. It sounds like something the NFL would require.
but we really need some experimental data to show the effects on how balls with differing moisture contents carry, all else constant. Anybody got that?
I wouldn't be that surprised if part of the reason that, say, Seattle plays as such a pitcher's park has to do with playing with a pretty wet ball.
When Safeco Field opened, A-Rod once complained that a groundball felt like it had gone through a pool by the time it got to him at SS. Playing below sea level, next to the Elliott Bay, will do that, I guess. It also doesn't help hitters to have that bay wind blowing in from LF; and then there are the glare problems as well.
One interesting experiment would be to have the ball boys measure the mass of a ball or two with a precision balance before each game in the league to see if the ball changes appreciably given the varying weather conditions around the league over the course of the season.
Thanks for clearing that up, sean. Due to the baseball connection I'll probably remember this tidbit of knowledge longer than anything I learned in my lone physics course on color theory or sound propagation. As a Humanities guy I've steered as clear from physics as possible, but if I could take a course on physics applied to baseball, I'd jump at the opportunity.
Should've gone to UIUC! DeLorean not included.
Indeed. That's what I get for picking a university in Bud Selig's home state.
I wonder if the humidity frequent in Minnesota summers might help reign in some of the deep flies
Twin Cities has nothin' on StL's humidity, and Albert has no problems hitting them out here in the mid summer.
Given sean's lesson above, I'd submit that Pujols has a vested interest in remaining in St. Louis beyond his current contract, lest he wind up signing San Francisco/Oakland, Seattle, or San Diego.
Shouldn't Sean's point about air density be caveated by how much moisture the balls absorb on humid days (making them heavier, per ubelmann's comment above)??
As for Pujols specifically, his career splits are at:
34.1 HR/500AB -- Home, Pujols
37.0 HR/500AB -- Away, Pujols
I'm not sure that this is a significant result, but looking at the general population, hitters tend to hit more home runs at home than on the road:
16.1 HR/500AB -- Home, MLB 2009
14.3 HR/500AB -- Away, MLB 2009
Doing the roughest possible adjustment, you'd figure that Pujols is coming up about 5 HR/500AB short at home compared to on the road. That would boost his career total by 25 HR (~7%.) Not a huge deal, but if the humidity in St. Louis is helping him hit home runs, either his "home cooking" is really bad or he's been an unlucky hitter in St. Louis.
great point about home/away splits in general.
I think that a perhaps better test than Poo-holes would be to compare HRs hit by a selection of visitors to STL to the HRs hit by the same selection as visitors in a low-humidity city. That still leaves as a problem how to control for park effects per se.
or, even better, get some fool to provide temperature and humidity data for each game and model HRs as functions thereof.
get some fool to provide temperature and humidity data for each game and model HRs as functions thereof.
If only I had the money to hire a grad student for this project!
Maybe some bureaucrat will be kind enough to put in a grant request..!
Hmmm. Well, Albert still has no problems hitting them out here in mid summer. He did a number on Slowey et. al. during one of our hottest days this past season.
Personally, I would think the oppressive heat on the batter would be more of a hindrance than the humidity on the ball. At least my experience playing softball here would make me think that way.
I think that the oppressive heat on the pitcher would be more of a hindrance than the oppressive heat on the batter.
Now that is a good point. And the oppressive heat on the manager might even inhibit him from removing said pitcher when he should be removed, even adding to the issue.
I was aiming for facetious with the above comment, but it's cool to see an interesting discussion come of it.
Nice work, sean. One question - in your final totals table, what is that as a percentage? What's the total number of HR vs. total balls hit?
Thanks. Good point, I updated the table to include percentages. Total number of balls hit was 543,543.
Nothing to add, just wanted to chime in with an "Awesome job, Sean."
At first I thought this was an Ubelmann project, but it seemed a bit out of character for him (I don't think he's used this many graphs).
I haven't done much graphing since I stopped using Excel (because I stopped having a legit copy of Excel.) I'm not terribly fond of OpenOffice calc's graphing capabilities. One of these days I will learn a capable substitute. Graphs can be a really useful way to communicate information, though, so I wish I did more of it. Sean definitely did a bang-up job with this post.
I <3 R. Reminds me of when I started using LaTeX for any paper I did in college. Instantly gave everything a professional look.
And I agree. OO.o's graphing abilities are terrible. Plus it's hard to use. I'm gaining experience with R now and it's so much nicer. There's a wiki with a list of many different graphing options with example code to replicate it. That's how I did the radial plot, with some help from GIMP.
I've been too lazy/busy to learn R. But STATA has a very, very nice graphics engine.
Nice job, Sean.
Any thoughts to naming the anomaly/protuberance in right field in the new park?
"Stupid"
"Worked-for-the-Mets Ville"
"Top Jimmy Playground"
"This convinced Mauer to sign!"