I went to a baseball game last night in Detroit with a coworker, and like all grown men went with the intention of catching a foul ball no matter the cost. Before heading out I wondered how likely it would be that I’d actually catch one this time. This is what I wrote:

Because I love Pre-Algebra, let’s do some math.

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This basic equation is pretty much the limit of my mathematical skills:** Number of Foul Balls per Game/Number of People at Game**

I did the math in my head on the ride to my hotel. I guessed somewhere in the neighborhood of 20,000 fans per game and 60 foul balls into the seats a game. Part of the reason I used these numbers was because I knew I could do the math easier while driving a stick shift, smoking a cigarette, and singing John Denver. I should have gotten 1 foul ball for every 333 fans. What I got was 300. Considering I received all my formal education in West Virginia I count that one as a victory.

I was wrong. The numbers below are right.

**Foul Balls/Game: 48.2 (excluding foul tips and bunts)**

**Home Runs/Game: 1.03**

**Average Attendance/Game (2009): **30,338

By those numbers, if you were to sit in a random seat at a random game at a random ballpark the odds of you catching a foul ball are 0.12 percent, or 1 for every 839 fans. I just counted the number of MLB games I’ve been to in my life, and sadly came to an estimate of 25 (I grew up four hours from the closest city over 50,000 people). By that reckoning there is a 2.9% chance that I would have a caught a foul ball in my life to this point.

Of course that last paragraph isn’t at all right. To accurately reflect the odds one needs to figure out the chance of a ball being hit to each individual seat. You’d also need a working knowledge of math, which I do not have (again, West Virginia).

Usually when I go to a game I don’t have the best seats (especially when I was in my teens and 20’s). My guess is at least 15% of the people who attend games are not reachable by a foul ball or home run at all. That drops the number of people who have *any *chance of catching a foul ball to 25788. If we take the odds for the entire stadium (minus those seats that have no chance of catching one) we get 0.14% or 1 in 694 fans.

Of course the only accurate way to project the odds of you catching a foul ball at any given time is to know which seat you have in what ballpark. I’m sure the odds of catching a ball increase exponentially as you get closer to the field and either first or third base (I’m counting foul ground balls you grab over the rail).

Tonight I have second row box seats for a Tigers/Royals game ($9 each) down the first-base line. I would guess my odds increase significantly considering that’s where I’m sitting – closer to the field, on the first base line, and if there are open seats on the rail I’ll have a shot at grounders. Of course I have no clue by how much the odds are increased. Going from the equalized 0.14% chance, I would guess the odds increase at least two to three times based on where I’m sitting. That’s a 0.4% chance. Really though? That seems a *little* high. I dunno.

**Post-Script**:

So I went to the game. Kansas City won and, of course, I almost caught a foul ball. A guy two seats away grabbed one from Miguel “fucking perennial MVP candidate” Cabrera. I almost killed his wife trying to snag it from him. A series of apologies followed. They didn’t really care though because he probably just fulfilled a lifelong fantasy. The happiness on his face was a sight to see. It’s a feeling I hope to have one day, but know I run a significant risk of never having. That grinning son of a bitch’s face will forever be burnt in my memory.

It *did *make me feel better about the odds I calculated though. I would guess if I sat in the same seat for 250 games I would almost certainly get a foul ball or kill somebody’s wife trying.

A few more thoughts from the game:

- We ended up sitting on the rail for half the game. No balls came our way, but it was freaking awesome.
- This part of the park felt like a sweet spot for foul balls – there were many, many hit to our general area.
- I tried tracking the number of balls hit to the stands versus not, but got bored after one inning. Might have been easier if I hadn’t been keeping score. One observation: foul balls hit back into the net probably make the non-reachable number higher.
- I must be a good luck charm for KC; I saw them play the Sox two weeks ago. In the two games combined they had 33 hits.
- If you ever get a chance to attend a game at Comerica Park in Detroit do so. It’s a great park and a fun place to watch a game.
- Apparently someone else already did this, and the fella had the same thought process. His estimates are just a little lower.

Some of my fondest memories when you were a charming young boy:

You used to go to Wheeler’s games and hang out deep in the 3rd baseline waiting for a deep foul. You’d also hang out next to the bullpen and beg the pitchers to give you balls (now Karen has them all).

Yea, I remember your collection of old scuffed up baseballs. I hardly ever had to buy baseballs to practice with because we always had official southeastern league baseballs to use.

I hope your dreams are fulfilled.

BTW: I’m sure you know that your calculations/statistics are flawed as there are places where you can sit that increase your odds significantly of catching a foul ball.

You would have to map those spots and calculate the odds for each area of the ball park.

Clearly you didn’t read the whole thing. “Of course the only accurate way to project the odds of you catching a foul ball at any given time is to know which seat you have in what ballpark.”

Just based off of the five games I’ve been to this season at PNC Park, I would say for sure that the box seats near first and third are the best spots, but it’s still a crapshoot.

The last game I went to (Pirates/Braves) we had box seats three rows back on the first baseline, and there were about ten foul balls into our section (a group of guys in the first row left with three foul balls between them. Bastards.).

I’ve also sat on third baseline (Reds/Pirates) in the first row box, and didn’t see squat the entire game.

I didn’t check your math, but it sounded pretty good. But since I’ve been working for an economics journal, I put a little unnecessary thought into the data set.

You could change it to “Likelihood of catching a ball at an MLB game” and increase your chances — you could factor in flyout/inning ending balls that players would catch and toss into crowd, balls from warmups, and home runs.

And discussing attendance, a terrible team (like the Buccos) with lower attendance will dramatically increase your chances of catching a fly ball. So will a team that swings a lot (like the Diamondbacks or Blue Jays).

Teams that score on base hits (Rays?) would decrease chances, as would groundball pitchers, stadiums with large attendance, or douchebag first baseman (who would most likely not toss a ball to a bearded madman in the stands shrieking out their name).

I love that baseball feeds my love of processing data.

I don’t count balls thrown to the stands by players; no skill involved. Might as well count balls caught in batting practice. It would be really easy to figure out percentage of foul balls that go to the stands. Just count at the games. Problem is I also keep score, and it was hard to do both of those, hold a conversation with someone, watch the game, and remember not to play with myself all at the same time. Clearly I’m gonna drop the ball somewhere.

Good analysis. In fact, best I’ve seen – most don’t acknowledge that the odds depend on where you sit. I have gone to MLB games for more than 40 years and mostly sat high up. Recently, I got to sit about 20 rows behind home plate at a Baltimore Orioles game, and I finally snagged one.

I caught the ball on the second hop, reaching over several people [I’m tall], including a kid who was maybe nine, in the process. But I have to make it clear I didn’t lean on anyone or push anyone to get it. The kid’s father on the other side actually fell onto the empty seats in front of us reaching for the ball.

For some reason, some fans around me who didn’t have a good view apparently thought I grabbed the ball from the kid’s hands or something, and they yelled at me to give it to the kid. I looked at the black bruise made by the bat on the ball and wondered if I was going to become like the Packers fan who snatched a shoe thrown by Donald Driver from a kid’s grasp. So I succumbed to the yells and gave it to the kid. It turned out to be the kid’s birthday. But my 12-year-old son was mad at me when I told him I gave it away.

I think I did a nice thing, but still, every time I watch a game, I wonder if I will ever get another chance to grab a foul ball.

Well I know now where not to sit at Kauffman Stadium. Section 120, 2 foul balls landed in sections 119 and 121 respectively, about 8 feet to my right and left, what a bummer.

can your source the numbers you give about # of foul balls per game?

how about this for the odds. I’ve been to two baseball games in my life. both games I set in behind 3rd base up about 12 rows. the first game about 18 years ago a ball came right at my head. I threw my popcorn up into the air and put my hand in front of my face and the ball hit my hand and dropped out. someone else got the ball. I’m 65. I now live in Lancaster and I want to my second baseball game. it’s a minor league city baseball game called the Lancaster Barnstormers. when I bought my ticket I asked for upper Roe ticket. they again gave me a seat above third base. in the second inning a foul ball came at me, it hit the side the lady said in front of me, bounced off and hit the guys hand behind me sitting behind me. the ball ended up dropping between my legs in the seat. so my only two ball games I got to touch a foul ball. one came right to my face the other dropped into my lap. go figure those odds. it was nice reading your story.

OK. First the facts: I’m guessing the Mountaineers DO teach physics, because it is the only mathematics used to properly calculate this particular subject. Especially the law of total probability, including but not limited to discrete random variables, continuous random variables, marginal distribution and multivariate and bivariate distributions. So, almost the furthest thing mathematically from “Pre Algebra” and not math one can simply “do in their head”.

Next, we’re figuring the odds of catching FOUL BALLS! Not home runs. To include catching dingers changes the entire mathematical equation(s). Next, your “15%” of seats out of foul ball territory is grossly inaccurate. Remove all seats in home run territory, foul pole to foul pole, outfield wall to the last rows of the upper decks. Remove all field level covered seats, seats under/behind foul ball netting on the field level, the entire press level except for the rows in the front 1/3 of press level and finally all of the obvious nose bleed seats. That leaves about 15-20% of the seating in foul ball country. A CRUCIAL part of the equation(s) you forgot about is left handed versus right handed hitting and pitching. For example, if Justin Verlander is bringing his 94 mph heaters to say, the heavy right handed hitting Orioles, 90+% of foul balls hit OUT OF PLAY will settle on the first base side. Roughly, 85% of THOSE will land in the field level. As opposed to R.A. Dickey, who’s low velocity knuckleballs consistently land on both sides of the field for both left and right handed hitters (which is ironic because that’s about the ONLY thing consistent about the knuckleball). Of the 48 foul balls hit per game, only about 30 reach the seats. About 15 per team. I always sit third base side, field level. This is because baseball moves counter-clockwise, therefore, the game is always moving towards you (use this advice, from a collegiate starting center fielder and seasoned veteran fan of the game. Every scholar of the game and fan in-the-know sit on the third base side. And each one of them would take an upper deck seat over a field level seat on the first base side, any day that ends in “Y”. Don’t ever sit on the first base side again!). So, for we third base side dwellers, the Justin Verlander/Orioles game example used above is also a perfect example of where the law of total probability factors in enormously, while Verlander is pitching. Because in this example, of those 15 or so foul balls reaching the seats off of Orioles bats maybe five reach the third base side and only three maybe four of those five land in the field level. You’d have a better chance of getting to beat the crap out of a filthy Dodgers fan or one of those irritating, elitist Red Sox fans who, for reasons unknown, THINK that the BoSox are relevant and better than they actually are than snagging a foul ball.

One person has about a 1:3,632 chance of catching a foul ball per game. And THAT’S only IF that person is seated in the 15-20% area mentioned above.

Truth is, there isn’t and never will be an accurate solution to this mathematical equation. Hell, there really isn’t even an dependable equation! This is due to the plethora of unpredictables involved. It’s more theory than math, actually. But 1:3,632 odds is a solid figure. If you don’t care for those numbers ask yourself this, “How many people do I know, or people who know people that have two legitimate foul balls from MLB games??” MAYBE one. Two if you’re the example, not the rule. I don’t know anyone and I’m fortunate to know many people in and around the game since childhood.

The reason why I’m sharing my knowledge with anyone who cares to read this is because just yesterday in Arlington, Tx., home to the Texas Rangers, ONE person caught FIVE foul balls in ONE game! One person catching TWO foul balls in a LIFETIME is mathematically outrageous, but ONE person catching FIVE foul balls in ONE game is anomalous. I’m not sure if that’s even quantifiable, to be honest. I’ve read about people winning the lottery twice in a lifetime, sure, but ONE person catching FIVE foul balls in ONE game is simply unexplainable. I mean, the damn ball boys down each line rarely, if ever get five foul balls in one game AND THEY’RE ON THE FIELD!

Just like someone hitting .400 again or breaking Ricky Henderson’s career stolen base record or a pitcher winning 30, scratch that, 25 games in a season, we will never see one person catch five foul balls in one game again.

Remember, a baseball fan worth listening to knows three important things: First, only three things win baseball championships…pitching, pitching and pitching. Second, can explain the Infield Fly Rule perfectly without hesitation every time it comes up. Last but not least, ALWAYS sits on the third base side when in attendance of ANY baseball game.

Final thought, I think the San Francisco Giants will win the 2016 World Series.