A bit more math: Park Factors

Some good response on my bit trying to explain why Trout leads Cabrera in WAR (it’s 7.8 to 7.0 according to Baseball Reference this morning; 8.8 to 7.6 on Fangraphs) but I have to say that quite a lot of what I’ve seen shows a fundamental misunderstanding of Park Factors. I think the Twitter exchange I had with Brilliant Reader Joe more or less captures it:BR Joe: Don’t you find it a bit odd that Comerica “became” a hitter’s park at the exact time that Miggy went from great to otherworldly.Me: Fair question. Now ask it in reverse.Fair to say BR Joe didn’t buy my counter-question. He wasn’t alone. I got lots of people wondering if the sole reason that Detroit is NOW rated as a hitter’s park by Park Factors is because Miguel Cabrera is so awesome. I also got lots of people saying that the dimensions of Detroit’s park have not changed so it cannot just suddenly have become a hitters park. I also got lots of people who say they KNOW Detroit is a pitcher’s park because, well, they’ve seen it.Like I say, all of these seem to fundamentally miss how Park Factors are calculated.I can’t explain all of it because, honestly, I don’t understand all of it. There are a lot of adjustments made to equalize the innings pitched and to adjust for various quirks (such as the fact that hitters do not face the pitchers on their own team). If you want to get into all that, you can work your way through the millions of calculations here … and have fun.But the BASICS of Park Factors are the easiest thing imaginable.All you do is this:Step one: You take the average runs scored in a ballpark (both teams).Step two: You take the average runs scored in that team’s road games (both teams).Step three: You divide the first total by the second.And that’s all. Park Factors. There is so much contentiousness about Comerica Park but it’s all simple math. This year, the Tigers have scored 355 runs at Comerica and allowed 275 runs. That’s a total of 630 runs in 67 games -- 9.4 runs per game.This year, the Tiger have scored 320 runs on the road and allowed 242. That’s a total of 562 runs in 66 games -- 8.5 runs per game.You take 9.4 runs, divide it by 8.5 runs -- that’s 1.10 -- or a Raw Park Factor of 110. That’s raw so you still have to make all those adjustments I mentioned above. But it’s a good starting point. At 110, you have a Park Factor that shows Detroit to be a fairly extreme hitters park.So, you see how that works? Cabrera’s awesomeness has nothing to do with it -- we’re comparing Miggy (at home) to Miggy (on the road). Changing dimensions have nothing to do with it. How tough the ballpark LOOKS to hit in has nothing to do with it. All these various little things people keep bringing up have nothing to do with it. You are simply comparing how many runs are scored in the ballpark against how many runs are scored in other ballparks. That’s all.Now, it should be said that a single season is a very small sample size -- and we’re not even through this season yet. That Raw Park Factor for Detroit this year is not reliable at all. You need more than five months of data to feel good about what you have. This is why Baseball Reference tends to go with multi-year sample sizes.Let’s look at Comerica since the start of the decade. In 2010, Comerica Park was more or less neutral -- a slight lean to pitchers. Average runs per game in 2010:Comerica Park: 9.13Road: 9.30Raw Park Factor: 98But it shifted in 2011:Comerica Park: 9.51Road: 8.98RPF: 106Still a hitters park in 2012:Comerica Park: 8.91Road: 8.32RPF: 107And you know it’s a fairly dramatic hitters park this year. Now, look at a place like Texas. Every year, it’s a great hitters park -- but it’s been weird this year.Average runs per game 2010:Rangers Ballpark: 9.49Road: 8.70Raw Park Factor: 109And then the crazy 2011 season:Rangers Ballpark: 11.06Road: 7.85Raw Park Factor: 140!A little bit more settled in 2012:Rangers Ballpark: 10.13Road: 8.56Raw Park Factor: 118So how do you explain more runs on the road this year?Rangers Ballpark: 8.46Road: 8,.59Raw Park Factor: 99I don’t know how you explain it. Could be a fluke. Could be a weather issue. Could be a shift in the wind. But the point is Park Factors don’t TRY to explain. They just count up the numbers.Everybody knows San Diego is a great pitchers park. But what do the numbers say? This time I’ll use the overall numbers.Since 2010, at PetCo Park, there have 2,268 runs scored. Both teams, remember.Since 2010, away from Petco, there have been 2,660 runs scored in Padres games. That’s about 400 more -- about 100 more runs per year on the road.The Padres offense has scored more on the road. Since 2010, the Padres offense has scored about 13% more runs on the road. The Padres pitching staff has allowed about 16% more runs on the road. Every single year, the Padres offense has scored fewer runs at home than on the road. Every single year, the Padres pitching staff has allowed fewer runs at home than on the road.THAT is a pitcher’s park.Now, you should know that this is just a Park Factor for runs scored. Every year, Bill James in his Handbook does an involved Park Factors (he calls it Park Indices) where he calculates the best parks for home runs, for triples, for strikeouts, for all these other things. That’s very interesting. Kaufman Stadium in Kansas City, for instance, is usually the toughest home run park in the American League. But it is also a neutral to to slight hitters park overall because strikeouts tend to be low, walks tend to be up (both teams, so it’s not just Royals pitching), the outfield is so big that hits tend to drop. I think it’s a comfortable place to hit. The Park Factor there is 101.