In his excellent Ten Things I didn’t Know Last Week column, Dave Studeman speculates on the odds of two fans sitting next to each other catching a foul ball. I was asked about the LA Times article (where two fans sitting next to each other caught back-to-back foul balls) in an e-mail last week and the math to solve this problem became a huge topic of conversation over my weekend.

We previously calculated the odds of catching a foul ball/home run at about 1 in 1000, assuming that everyone in the stadium had access to all foul balls and home runs (which isn’t exactly true).

So let’s say that each foul ball hit into the stands is an independent event and they’re randomly distributed. And let’s say that where you’re sitting you have the ability to catch a foul ball. And let’s say there are 10,000 fans sitting in an area where you can catch a foul ball.

Your odds of catching any one foul ball hit into the stands is 1/10000. Now if there are 30 balls hit into the stands each game, your odds of catching a foul ball have increased to 1-((9999/10000)^30). Which is about 1 in 333.

Now your odds of catching 2 consecutive foul balls in a game is considerably worse and we’re going to assume that both these foul balls are catchable. (Dave Studeman in his evaulation does not assume that and that’s a major difference). Catching two consecutive foul balls would be (1/10000)^2, which is 1 in 100,000,000. But you have 30 chances, so the odds are 1-((99999999/100000000)^30), which is about 1 in 3,333,333.

Those are your odds of catching two foul balls in a row at any one particular game if all things were completely random.

Update: The Numbers Guy over at the Wall Street Journal did a piece on this earlier in the week and Carl Bialik (The Numbers Guy) is who sent me the initial e-mail.

The site has been updated with Win Probability stats for 1981 – 1988.

Please make note of Dwight Gooden’s 1985 season when he had a WPA of 9.94. The only player to have a higher WPA in the years that WPA has been run for is Barry Bonds. Bonds bested him in 2002 and 2004, but that’s it. His BRAA that season was 75, which is 10 runs better than any other pitcher in a single season for all WPA years calculated so far.

The next best player that season in terms of WPA was Eddie Murray who had 6.75 wins, more than 3 wins less than Gooden. And while Gooden unanimously won the Cy Young award that year, he was without a doubt the MVP that season too.

Can I Get A Hitter? (Dave Cameron)
– Middle infielders beware: 2008 wrote you a letter and it’s not nice.

Zito…Pitches…Well? (Eric Seidman)
– In a drastic turn of events, it appears Zito did something right.

The Little Red Machine (Marc Hulet)
– Marc thinks the Reds might have found some hidden gems in the 2007 draft.

Designated What? (Dave Cameron)
– Things aren’t good when some team’s pitchers are hitting better than your team’s DH.

Should I Trade Roy Oswalt? (Eric Seidman)
– I’d trade 1 Roy Oswalt for 1 Chase Utley in a heartbeat.

Jon Lieber did something today that not a whole lot of pitchers can claim to have done. He gave up 4 home runs in a single inning. He started off the fateful second inning with back-to-back home runs by Adam Dunn and Joey Votto, but eventually settled in and got Edwin Encarnacion to pop-out.

Lieber surely breathed a sigh of relief, only to have Paul Bako hit a home run on the very next pitch. Three batters later Jerry Hairston Jr. hit the final home run of the inning, tying what I believe is a record for most home runs allowed by one pitcher in a single inning.

The last pitcher to do it was Chase Wright of the Yankees, who gave up four home runs in a row on April 22nd last season. Luckily for Wright, it was a nationally televised game against the Red Sox.

Win Probability: 1974-1980
– All your favorite players from the latter half of the 70’s now have WPA stats!

Angels Big Two (David Cameron)
– No, it’s not Lackey and Escobar. It’s those other guys: Saunders and Santana.

Furcal En Fuego (Eric Seidman)
– Does batting .366 with 5 home runs count as “en feugo”? Si.

Kerry Wood 20K: 10 Year Anniversary
– Look inside for the video. You have to see it to believe it.

Are the Reds Ready to Get a Little Greener? (Marc Hulet)
– Marc kicks of Reds week with a look at Homer Baily and Jay Bruce.

Try Another Pitch, Fausto (Dave Cameron)
– We know you love your trusty old fastball, but….

Have No Fear, Church is Here (Eric Seidman)
– That trade isn’t looking so bad right now, is it?

The New York Daily News recaps Kerry Wood’s incredible 20 strikeout performance all the way back on May 6th, 1998. The SportsCenter highlights are a must watch: (hat tip: Baseball Think Factory)

All win probability stats, game graphs, and play-by-play are now available for the years 1974 through 1980.

The most productive batter in terms of WPA over those 7 years was Rod Carew with 28.9 wins, closely followed by Mike Schmidt with 28.6 wins. Jim Palmer led all pitchers with 23.2 wins, with closer Goose Gossage not far behind with 22.1 wins.

I’m hoping to have 1981 – 2001 available soon.

On a side note: FIP is now correclty adjusted by year and FIP career totals are also weighted appropriately.

All the stats made available yesterday in the player pages are now on the leaderboards.

Interesting to see the afore mentioned Nick Johnson with the second best O-Swing% (percent of pitches swung at outside the strike zone) this season. He truly does have great plate discipline.

Cust Cussing (Dave Cameron)
– Dave takes a look at Jack Cust’s off the charts performance.

Is Willingham Ready to Bust Out? (Eric Seidman)
– Will Willingham continue his terrific season for the first place Marlins?

Keeping a Rookie Pitcher Grounded (Marc Hulet)
– What’s so special about top Red Sox prospect Justin Masterson?

Maximizing Potential (Dave Cameron)
– It looks like Chien-Ming Wang has a new trick up his sleeve.

Plate Discipline Stats
– Go look at them in the player pages!

Pitching Trio of the Month (Eric Seidman)
– It’s probably not any three pitchers on the Pirates’ staff.

About two years ago I attempted to delve further into plate discipline with two articles: Dissecting Plate Discipline Part 1, Part 2.

And then a year later I took an additional look at plate discipline: More on Plate Discipline

All batters now have plate discipline stats available dating back to 2005. Here’s what they are:

• O-Swing%: The percentage of pitches a batter swings at outside the strike zone.
• Z-Swing%: The percentage of pitches a batter swings at inside the strike zone.
• Swing%: The overall percentage of pitches a batter swings at.
• O-Contact%: The percentage of pitches a batter makes contact with outside the strike zone when swinging the bat.
• Z-Contact%: The percentage of pitches a batter makes contact with inside the strike zone when swinging the bat.
• Contact%: The overall percentage of a batter makes contact with when swinging the bat.
• Zone%: The overall percentage of pitches a batter sees inside the strike zone.

What you’ll want to know is the major league averages for each stat:

Season O-Swing Z-Swing  Swing  O-Contact Z-Contact Contact   Zone
2005     20.3%   68.0%  46.0%      51.8%     88.3%   80.8%  53.8%
2006     23.5%   66.6%  46.1%      57.4%     88.5%   81.0%  52.6%
2007     25.0%   66.6%  45.9%      60.8%     88.2%   80.8%  50.3%

All the location data is from Baseball Info Solutions and you can find all these stats in the player pages at the very bottom: Vladimir Guerrero