podcast | short hops | trivia

Episode 10: August 6, 2010

Luck plays a huge role in baseball, more than most people realize. In fact, baseball players behave a lot like coin flips, and are subject to the same laws of probability. How much do stats actually tell about a player’s ability?

(show episode script) (hide episode script)

**Please note: this is not an exact transcription of the episode.**

In 1988, the Baltimore Orioles lost their first 6 games. They fired their manager Cal Ripken, Sr, hired HOFer Frank Robinson, and proceeded to lose their next 15 games. They lost 21 games before they finally won on April 29. They were 1-22 in April and finished the season in last place, but they did end up winning 54 games.

In 2008, rookie pitcher Brad Ziegler did not allow a run in his first 39 big league innings.

In 1952 Walt Dropo got a hit in each of 12 consecutive plate appearances, which tied the record set 50 years earlier by Johnny Kling.

On June 3 of this year, When Mariners' first baseman Casey Kotchman made an error, it was the first error he had made in almost two years and over 2000 fielding opportunities.

What do all these things have in common?

I'm Alex Reisner and you're listening to Game of Chance, a show about baseball statistics, history, culture and today more than usual the role of luck in baseball.

Baseball *is* luck. It's a game of chance just like black jack or poker. And just like in black jack and poker there are good players and bad players, but there's still a lot of luck. Now, you might be thinking about a gust of wind that blows a ball foul, or a tough bounce on a grounder, or a bad call by an umpire (like in the Marlins game last night), but I'm talking about the normal course of a normal game in a normal season. And the question I'm asking is: even under ideal conditions, how much control do the players have over the outcome of a baseball game? That's my question.

(Alright, I'm gonna start start out with a warning: this episode may piss you off. You may think I'm an idiot. You may hate me. You may cancel your subscription. Alright? Consider yourself warned.)

Here are two smaller questions for you:

1. In MLB, how often does the home team win? As you might know, the home team wins 54% of the time. So you can think of that as a 4% home field advantage.

2. In MLB, how often does the team with the better record win? How often do you think? 70%? 80%? 55.5% of the time.

55.5% of the time? Think about that. That means that 44.5%, or almost half of all baseball games are upsets. It's crazy, right?

When you flip a coin you get a random outcome. Heads or tails. A perfectly balanced coin is just as likely to come up heads as tails. It's random. If you flip a coin 100 times you'll probably get pretty close to 50 heads and 50 tails. So you could say heads "wins" 50% of the time. In baseball the better team "wins" 55.5% of the time. That's just not all that different from 50%, and yet that's how we distinguish winners from losers.

Let's look at the Cardinals and the Astros this season. The Astros lost their first 8 games and have continued to be a bad team. They were the last team to win a game, and when they finally did, they beat the Cardinals, who are one of the NL's best teams. A few weeks later they swept the Cardinals in a 3-game series. All these games were in St. Louis so the Astros did not have home field advantage. Are the Astros a better team than the Cardinals? I don't think so. And by the end of the season the Cardinals will take the lead in head-to-head matchups...or they won't. That's just how it is. We can't really tell which team is better based solely on the games they play against each other.

Just like the Orioles didn't continue to win 1 game a month in 1988, and Brad Ziegler eventually gave up some runs. These streaks happen. You can't just start drawing conclusions.

You know that when you flip a coin you're equally likely to get heads or tails, but if you've ever actually flipped a coin you've seen that sometimes you get a bunch of heads in a row, or a bunch of tails in a row. You can even get to a point, if you keep track, where heads is winning something like 10 to 4 or 20 to 5. But if you flip a coin 1000 times all of those streaks will more-or-less even out and you'll probably be pretty close to half heads and half tails. This is just how *random* events work. An event that has a 50% probability of happening in reality doesn't always happen *exactly* 50% of the time. That's just how it works.

So we know that a normal coin has a 50% chance of coming up heads, but imagine we have a coin that's weighted so it has only a 30% chance of coming up heads. It's like a batter with a .300 average: it happens 3 out of 10 times, or at least it has a 30% *probability* of happening. When you *actually* flip it, it might not come up heads at all in the first 10 flips, or it might come up heads 10 times in a row. Actually, the laws of probability state that if you flip it enough times, you *will* eventually have a 10-for-10 streak, and you'll have an 0-for-10 streak. You'll have every kind of streak you can think of: 20-for-20, 100-for-100...you might have to flip it a million times but you will eventually have a streak of 100 heads in a row. But if you flip it a million times, ignoring any mania or psychosis that may have set in at that point, the *total* will also end up very close to 30% heads. It's going to be around 35% heads sometimes and 20% heads other times, but it's always going to be revolving around 30%, for as long as you flip it.

It's the same thing with hitters in baseball. Each player has a certain skill level. They're a lot like a weighted coin. Tony Gwynn, over the course of 20 seasons hit .289, .309, .351, .317, .329, .370, .313, .336, .309, etc. We have no way of knowing his actual probability of getting a hit, which is basically what we'd call his skill. His career average was .338, and that's about the best we can do. But look, Gwynn didn't hit .338 every year. He had "good years" and "bad years" and slumps and streaks. Which shows that baseball players behave a lot like coins. Each player has a certain skill level, a certain...I guess you could call it a "true" batting average, and with enough at-bats their average would eventually come out to that theoretical level, but you need a *lot* of at-bats before you know what that level is. Way more than there are in a single season. Otherwise there's too much of what statisticians call random noise, which is fluctuations that occur in any natural phenomenon, and which are not a property of that phenomenon. These natural fluctuations obscure a player's true batting average, or true ability. Random noise is a part of everything we do. You can call it luck, chance, fluke, god, or whatever you want to call it.

Look at Robinson Cano this year. On May 4 he was hitting .376. Two weeks later he had dropped to .325. Two weeks after that he was back up in the .370s, and now he's back down in the .320s. Last year he hit .320, the year before that he hit .271, and the year before that .306. We don't know what his true batting average is, we only know what it happens to be at this moment, with all the random noise mixed in.

That's one reason you have to be very skeptical of stats in the beginning of the season. Or really almost any single-season stats. That's why you can't count out David Ortiz in May...Red Sox fans...I'm looking at you. And Mets fans, hello: you can't rely on RA Dickey to get you into September based on a 6 and 1 record at the end of June. If you manage a baseball team you have to have more information about a player's true ability, and know that they will tend towards that theoretical number, barring any significant change in physique or technique.

Now you might be thinking that players are streaky and they get hot and cold. And they might actually be better one day than another. But you don't know that. How would you know that? If a player tells you he feels like crap then that's a good indication. But if you just look at numbers you don't know. And I would bet that a lot of players don't get hits on days they feel great, and sometimes they go 3-for-4 on days they feel terrible. I mean, if a coin, which has no "skill" at all, and never feels bad, sometimes has streaks where it comes up heads 10 times in a row, and this kind of random behavior affects everything in the world, how do you know *that's* not the explanation for why a batter is in a 0 for 20 slump or on a 10 for 15 streak? You don't. There's too much random noise. You need more data.

And even if you know how a player's feeling, you don't know how he's going to perform. Again: too much random noise.

Now, this is all part of what makes baseball so interesting. If the better team won every time you'd always know what was going to happen and there'd be no point in watching. There's a reason nobody watches arm wrestling--the stronger guy always wins. I guess there are other reasons we don't watch arm wrestling too...but I think this randomness is a big reason there are so many great arguments about baseball. It's why we can talk about Mays and Aaron and Mantle for hours, and Bonds and Ruth, and who belongs in the Hall of Fame, and all these numbers are so intriguing.

(That's why trivia question answers are so surprising: ___.)

The best player in the league can be the worst player on any given day. And some bum off the bench can be the hero. We've all seen great teams collapse, and because so much of the game is random, you get the feeling that anything can happen at any moment. That when it comes down to a tie score in the 9th inning in the 7th game of the World Series, and the pitcher is getting the signs from the catcher, all the numbers in the world don't matter.

Hopefully I've given you a little insight into why this show is called Game of Chance. I'm going to continue this line of thought in a future episode, where I'll explain how we can cut through some of the random noise and figure out what a player's true skill level is, because it is possible, sort of. Until then, I'm Alex Reisner. If you have questions or complaints give me a call at 32323 00 233 or leave a comment on the web site gameofchance.alexreisner.com.

All content on this web site and in podcasts copyright © 2010-19 Alex Reisner.