## Calculating Foul Ball Odds: More Considerations (UPDATED)

Continuing the discussion about calculating foul ball odds, my research indicates the data reported by ESPN Stats and Info a few years ago (2013 season) was even more erroneous than originally thought. In a Distilled article from that year we learned the odds of catching a 2nd, 3rd and 4th foul ball actually decrease exponentially; in other words, the odds don’t stay the same. Thus, one doesn’t multiply 1000x1000x1000x1000 to get the odds of catching four foul balls at an MLB game. Doing so turns out to be inaccurate math.

We also discovered a foul ball forum where fans were having a discussion about the odds originally reported. Each pointed out that the odds calculated included everyone at the game, but not everyone can catch a foul ball. They rightfully noted too that there are people in fair territory. And this point, as we mentioned in our earlier post, is the crux of the argument. ESPN shouldn’t have posted those stats without double and triple checking them.

What we find interesting about this argument is that so many people base their MLB foul ball odds on averages that simply don’t do the lowly foul ball justice. Nearly every fan wants a foul or homerun ball. But not all of us get one. This is surprising since the odds aren’t all that bad in the grand scheme of things.

### ERRONEOUS COMPUTATIONS

Even with all the erroneous or incomplete computations out there a few constants do exist: Lower deck seats get more foul balls. On average there are about 25-30 foul balls HIT into the stands (there are probably another 10 or so tossed into the seats each game by players and ball boys and girls). And Pitcher/Batter matchups matter: Left-handed hitters against right-handed pitchers tend to foul off balls in one direction, while hitting them differently when facing a lefty (and so it goes for the reverse hands).

As the Distilled.com article points out, the size of the fan and their accouterments matters as well. And so does a focus on Bayesian statistics since the odds of securing a second ball, a third ball, and even a fourth ball don’t stay constant as so many assume. Surprisingly, the odds get better after each one. This is why you see so many ballhawks snagging several balls in one game. It’s about the changing odds and probabilities.

As the fans in the forum point out, there are seats which are more predisposed to foul balls than others (the main reason this site and its apps were created in fact).

Here, we return to an earlier post about calculating the odds of catching foul balls, and give a more detailed explanation of the original formula now used to offer the most accurate odds of catching a foul ball at an MLB game.

### CALCULATING THE MOST ACCURATE ODDS

The odds of catching a ball greatly improve or diminish depending on where a person is sitting. Common sense tells us that those in the upper decks won’t see as many fouls as those who sit in the front row of the lower level and who can reach over the barrier to snag a grounded foul. Regrettably, all MLB parks are not created the same, so depending on which diamond you’re at and where you bought your tickets, your odds will vary every so slightly.

In general, upper decks are mostly out of range of foul balls. So we will subtract the entire upper deck—about another 8000. That leaves us with roughly 17000 fans in seats in the lower levels who can easily be reached by a foul ball. To be consistent, we subtract five fouls from the upper deck and use 25 as the number of lower deck fouls. The odds of catching a foul ball by simply moving to the lower levels significantly drops the odds to about 1:680. Nearly HALF of the original estimate.

The odds continue to drop depending on the spectator’s distance from the field as well as the pitcher/batter match-up. Some match-ups will create more ground fouls and others result in more pop-up fouls. The nosebleeds in any stadium, such as Progressive Field, are a prime example.

Let’s not forget we fans are not static beings either. We are mobile. We move. We have a range of reach, or motion that can propel us in a myriad of directions. Thus, we need to subtract the RANGE of motion a fan has. In general, a fan can easily reach across at least five chairs near them. This means each fan actually covers at least 5 seats, thus attendance is virtually pointless to use. Regardless, we have to divide our final number (17000) by 5. Doing so gets us to 3400. Or about a 1:140 shot at catching a foul ball. None of these were considered by the ESPN report.

But let’s use the more general and generic ratio of 1:850 to finish this up. The odds of catching one when all the main, superfluous stuff is removed isn’t all that bad. Certainly a lot better, but more awkward to say than 1 trillion, is a more accurate number of 490 billion. But that’s also using “bad math”. According to the math-heads with whom I worked the odds of catching four balls always remains the same. In the case of these general calculations, the general, MLB-wide odds of snagging a foul ball is 1:835.

The probability that sitting where you are gives you a 1 in 835 shot at catching a foul ball is a relative constant, not exponential, as the ESPN article indicates. (Apparently, that assumption is a common misconception in calculating stuff like this. While averages and WHIP change based on accumulated numbers, odds don’t. They remain a constant as long as no large group leaves or enters the area.) In theory, then, you could catch every foul ball hit into the stands because you have an equal chance as all others if you go mobile. 1:835 is better than 1:1 trillion. And even when we go with the exponential stuff, the number isn’t even ½ a trillion to 1 odds.

The mobility is key too. Ballhawks like those found on MyGameBalls.com snag 5, 10, even 20 balls at MLB and MiLB games. During the season the ESPN Stats and Info piece came out, two other non-mobile fans snagged four fouls from their seats. This alone proves it is not a 1 in a trillion event as reported.

That’s the basic stuff.

### WHAT ARE THE ODDS OF SNAGGING 4 FOULS AT ONE GAME?

Now back to the lucky guy who caught four fouls at an Indians game earlier in July 2013 just before the ASG? He was at a game with an attendance of about 17000 people. Using the basic, general calculations used above, but maintaining the same number of foul balls going into those areas (30-5 = 25 into the lower decks) and other ratios (loss of about 43% of attendees), we get about 12000 within easy range of foul balls. Given the same number of fouls will be hit regardless of attendance, 12000 is divided by the 25 to get a 1:480 chance each fan has of snagging a foul ball. A far cry from the standard 1:1000 ratio typically used in predictions of the odds of catching a foul ball. That means the odds, again with just using this basic logic, drop from 1 trillion to a mere 54 billion to 1 odds, IF foul ball calculations were combined as typically believed (again, they don’t; they stay constant). Considering he was sitting in a section with few other fans and he has a minimum reach of five chairs (including his own), then the ball could have gone anywhere in that area and he stood an excellent shot of grabbing the ball. This reach cuts down the number of seats to 2400, and thereby makes the odds of catching a ball at a game with about 17000 in attendance an incredible 1 in 96! With an even longer reach, those odds can drop even more. And depending on the pitcher and the batter match ups, the ball may have been destined to travel within his reach.

In other words, it wasn’t an impressive feat. He was at a low attendance game with few obstacles, and seated in the lower decks in a foul ball “hot zone.” As noted, two other fans snagged four fouls from their seats that same season.

There is much more to calculating foul ball catching probabilities than simply saying 30000 attend and 30 balls are hit so the standard odds are 1:1000. Doing stats in this manner doesn’t do the lowly foul ball any justice whatsoever. Calculating foul ball odds is a science that should be taken seriously by sabermetrics disciples. One cannot simply plug in generic numbers and get a number. The key to accuracy, as we shown here, is to subtract the people in FAIR territory, which all current models appear to not do, and to subtract those seats which are either out of reach of fouls or highly unlikely to have one reach them.

To see the general odds in your favorite park, check out the foul ball odds calculators [currently offline]. They are the only foul ball odds calculators in existence.