In 20 games, Lucas has made 83 plate appearances. What are the chances that Lucas is hitting about where he did previously, but had a hot streak of facing pitchers who gave him what he needed?

The standard error for an n-trial sample of a binary variable with probability p is . If we assume Lucas’ ‘true’ OBP is .350, then the standard error of this 83-trial sample would be . That means about 66% of Lucas’s 83-plate-appearance streaks should be within one standard error, and about 95% should be within two. Due to the small sample size, it’s hard to be 95% sure that Lucas’ performance is due to actual improvement, but the upper bound of the 66% confidence window would be about .402. Lucas is outperforming that by about 20 basis points.

Meanwhile, backup catcher, relief pitcher, and third baseman **Anthony Recker** is on the other side – he’s made 11 plate appearances, walking four times, striking out 4, and not yet hitting the ball. Though none of those walks are intentional, that leaves Recker with a .000/.364/.000 line – quite far off from his lifetime .194/.268/.364 BA/OBP/SLG line. No wonder **Kevin Plawecki** is starting. Recker’s hitting probably isn’t that much different from last year’s .200 average – we can be 95% sure he’s not likely to hit much above .300 without some extra batting practice, but otherwise it’s not unusual for a .200 hitter to have a streak of 7 at-bats with no hits, especially since he’s working walks, too.

Filed under: Baseball Tagged: Anthony Recker, Lucas Duda ]]>

He’s having a really rough season. I mean, there’s the obvious, in that he’s suffering from a fractured forearm that’s keeping him out of the best season he’d had yet. Blevins has pitched 5.0 innings – 15 batters up and 15 batters down (although they weren’t perfect – see below). Despite a meager career .042 platoon split, including a .025 BAbip platoon split, the Mets were using Blevins as a left-handed specialist (one right-handed batter faced in 2015), and he was rising to the occasion. Then, his pitching arm was broken by a comebacker.

Blevins’ record is currently 1-0, and that one win was pretty filthy. It came on April 14, when Blevins came in to face **Dee Gordon** and **Christian Yelich** with one out and **Ichiro Suzuki** on third base. The Marlins trailed 5-4 in the top of the 7th, so this was technically a save opportunity for Blevins. Blevins pitched to Gordon, who grounded into a fielder’s choice, but Ichiro came around and scored on an error by second baseman **Daniel Murphy**. That unearned run was charged to **Rafael Montero**. Blevins then pitched to Yelich, who obligingly grounded into a double play and ended the top of the inning.

For those keeping score at home, Blevins pitched to two batters and recorded two outs; one inherited runner scored an unearned run due to an error in the field. As a result, Blevins receives a blown save. Fortunately, the Mets scored two runs in the bottom of the 7th, and the tag team of **Carlos Torres** and **Jeurys Familia** tied up the win for Blevins. As a result, Blevins has the shame of his only win being a Vulture Win, and it even came out of an inning with no hits and no walks.

At least Blevins got the win – as it happens, **Burke Badenhop** managed to blow a save on no runs, no hits, and no walks in 2014. Twice.

Filed under: Baseball Tagged: Jerry Blevins, weird lines ]]>

The whole time **Ike Davis** was a Met, I would shout at the TV every time **Terry Collins** put in a tired reliever in a laugher that Ike needed to pitch. Ike was, after all, a starter in his freshman year at Arizona State, cobbling together 47.2 innings in 12 starts and 2 relief appearances for a 7.42 ERA. He got better, though – he spent most of his sophomore year in the outfield but still managed to make one start and six relief appearances, totalling 6.2 innings and a 1.34 ERA. In his junior year, Ike pitched in 16 games and 24 innings, going 4-1 with 4 saves and a 2.25 ERA. Ike was not a bad hurler. **Buster Posey**, of course, showed him up – while playing 68 games at catcher in 2007-08, Buster also made 9 relief appearances and collected 6 saves with a 1.17 ERA.

It was only natural that the A’s turned to Ike to pitch the ninth inning of a 14-1 blowout on April 21, but Ike pitched a perfect inning on 9 pitches. No runs, no hits, no errors, no walks. (No strikeouts, either….) It’s a shame I waited through all those games and Ike finally pitched on the other side of the country.

Filed under: Baseball Tagged: Buster Posey, Ike Davis, position players pitching ]]>

Teixeira wasn’t the only player to sit out the next day – center fielders **Jacoby Ellsbury** and **Mookie Betts**, catchers **Brian McCann** and **Sandy Leon**, and most of the bullpen all sat out, among others. The Yankees called up pitcher **Matt Tracy** for a cup of coffee and sent **Chasen Shreve** down, then swapped Tracy back down to Scranton for **Kyle Davies**. Boston activated starter **Joe Kelly** from the disabled list, sending winning pitcher **Steven Wright** down to make room. Shreve and Wright each had solid outings, with Wright pitching five innings with 2 runs and Shreve pitching 3 1/3 scoreless.

All those moves provide some explanation for a surprising result. Interested in what the effect of these long games are, I dug up all of the games from 2014 that lasted 14 innings or more. In a quick and dirty data set, I traced the scores for each team in their next games along with the number of outs pitched and the length in minutes of the game.

I fitted two linear models and two log models: two each with the next game’s runs as the dependent variable and two each with the difference in runs (next game’s runs – long game’s runs) as the dependent variable. Each used the length of the game in minutes, the number of outs, the average runs scored by the team during 2014, and an indicator variable for the presence of a designated hitter in each game. For each dependent variable, I modeled all variables in a linear form once and the natural log of outs and the natural log of the length of the game once.

With runs scored as the dependent variable, nothing was significant. That is, no variable correlated strongly with an increase or decrease in the number of runs scored.

With a run difference model, the length of the game in minutes became marginally significant. For the linear model, extending the length of the game by one minute lowers the difference in runs by about .043 runs – that is, normalizing for the number of runs scored the previous day, extending the game by one minute lowered the runs the next day by about .043. In the semilog model, extending the game by about 1% lowered the run difference by about 14; this was offset by an extremely high intercept term. This is a very high semielasticity, and both coefficients had p-values between .01 and .015. Nothing else was even close.

With all of the usual caveats about statistical analysis, this shows that teams are actually pretty good at bouncing back from long games, either due to the fact that most of the time they’re playing the same team (so teams are equally fatigued) or due to smart roster moves. Either way, it’s a surprise.

Filed under: Baseball Tagged: extra innings, file drawer, linear model, linear regression, Red Sox, Yankees ]]>

Now, that’s not unusual. Last year, 2546 teams had their starter pitch 5 or more innings and allow two earned runs or fewer; 781 of those teams lost, for a winning percentage of around 69%. It’s not unusual for the Mets, either; they had 84 such games last year, including 16 from Bartolo Colon (14-1 in those games), 15 from Jon Niese (4-4), 19 from Zack Wheeler (11-2), and 13 from deGrom (9-1). The Mets were right in the middle for all of this – the median across MLB was 85 games and 61 wins in those games. Washington had the most games (101) and the most wins (79), along with the highest percentage of wins coming in 5-inning starts with 2 earned runs or fewer from the starter (82.2%).

Take note, though, of how disproportionate the wins were. Colon won all but 2 of his solid starts, with the Mets averaging 6.4 runs of support; Jon Niese only got 8 decisions, four of them losses, despite having almost as many games as Colon. Behind Niese, the Mets scored only 2.6 runs per game. deGrom had about 4.2 runs per game behind him and won 9 games; Wheeler had six more games with the same 4.2 run support average, but only got two more wins than deGrom in those games.

deGrom maintained last year’s high standards in this year’s first start, and the Mets provided very little run support; even deGrom didn’t support himself very well, shaving almost 40 batting-average points to hit only .178 in these starts compared with .217 in other starts.

Given, the Nationals are coming off a fantastic year as the best team in the National League’s regular season, so we can handle a 2-1 loss early in the season, but the offense needs to be more consistent if we’re going to take a rotation full of talent and turn it into a 90-win season.

Filed under: Baseball Tagged: 89 to go, Jacob deGrom, Mets ]]>

Unfortunately for Madison, the 2003 version of Josh Beckett did it better. He pitched a complete game to clinch the World Series for Florida and then opened the 2004 season with seven innings of one-run ball.Fortunately, Mat Latos bravely crumbled during last night’s game to provide the sports blogging community with material. Mat was knocked out of the box after only two outs, having given up a respectable seven runs before getting the hook. According to Baseball-Reference, no pitcher has lasted less than one full inning on opening day since 1982.

Latos is, however, in good company with his season-starting ERA of 94.50. Jose Contreras started on Opening Day for Chicago in 2007 and lasted only one inning, giving up 7 runs; Carl Pavano did the same in 2009 for Cleveland, giving up 9 runs in the process. Both salvaged their seasons respectably, but – and this is my Mets homer bias coming out – let’s hope Latos is remarkably consistent this year.

—

^{1} This was the right call by the official scorer, but I really wish he’d declared Jeremy Affeldt “ineffective in a brief appearance” to give Mad Bum the win. Yes, I can call 2 1/3 innings of one-hit, no-run ball during which the Giants took the lead they never relinquished both “ineffective” and “brief,” compared to Bumgarner’s five-inning save.

Filed under: Baseball Tagged: Madison Bumgarner, Mat Latos, pitching ]]>

First of all, his BAbip is off the charts. This spring, Kirk’s batting average on balls in play is .536, which is ridiculously high. Kirk won’t be able to maintain that into the season. If he’s still got a .536 OBP by the trade deadline, I’ll eat my hat and post the video. Kirk’s BAbip has been pretty streaky, though. During his rough April, Kirk had a .300 BAbip, about the league average over the season; after coming back up in late June, he had a .377 BAbip over the remainder of the season, broken up as .625 over five June games with 11 at-bats, .267 over 28 at-bats in July, .400 over 23 August at-bats, and .348 over 32 at-bats in September.

From 2012 to 2013, Kirk’s BAbip dropped from about .379 to .246, and then shot back up to .370 in 2014. Using those numbers and taking first differences, then using the ratio of differences, that means we’d expect Kirk’s BAbip to drop to about .254 this season. Nonetheless, Kirk’s platoon splits are huge – against right-handed pitchers, from 2014, he’s got a .040/.050/.283 split (although he only made 9 at-bats and 10 plate appearances against left-handed pitchers). Though Kirk’s splits aren’t readily available, it’s possible that his big spring is residual of facing mostly right-handers.

In the spring, Kirk’s BAbip denominator (AB – HR – K – SF) is 28 and the numerator (H – HR) is 15. If we take Kirk’s previous-year .377 BAbip, over 28 trials we’d expect 15 or more successes to occur about 2.86% of the time. That’s just barely within the bounds of statistical significance (which would indicate we’d expect Kirk to hit between 6 and 15 times about 95% of the time), and well outside if we assume Kirk has a true mean of .254 (which would put our confidence interval at around 3-11 successes in 28 trials).

Second, take a look at Kirk’s K/BB ratio. Kirk has typically had a strikeout-to-walk ratio above 1; in 2013, he struck out about 2.67 times for every time he walked, and in 2014 it was about 2.44 strikeouts per walk. Over this small spring sample size, Kirk’s K/BB has actually dipped below 1, at 4/6 (or .667). Assuming Kirk walked 6 times anyway, using a conservative 2:1 K/BB ratio would turn 8 of Kirk’s hits into strikeouts. That would make Kirk’s BAbip tighten up to .350. Still strong, but not the obscene .536 we’ve seen. Even if we convert one walk to a strikeout and maintain a 2 K/BB, that would leave Kirk at .409, a very respectable spring.

Kirk’s numbers have been shocking, and of course he’s out of options, so he’s extremely likely to make the team. As a left-handed bat, he’d be a strong everyday player if the outfield weren’t so crowded, but with Michael Cuddyer and Juan Lagares in the mix already along with lefties Curtis Granderson and Matt den Dekker, it’s going to be tough to find Kirk a clean platoon spot.

Filed under: Baseball, Economics Tagged: BABIP, KBB, Kirk Nieuwenhuis, Spring training ]]>

The optimal exponent turned out not to be 2 in just about any sport; in baseball, for example, the optimal exponent is around 1.82. This is found by setting up a function – in the case of the National Hockey League, that formula would be – with a variable exponent. This is equivalent to . Set up an error function – the standard is square error, because squaring is a way of turning all distances positive and penalizing bigger deviations more than smaller deviations – and minimize that function. In our case, that means we want to find the x that minimizes the sum of all teams’ . Using data from the 2009-2014 seasons, the x that minimizes that sum of squared errors is 2.2266, which is close enough to 2.23 that the sum of squared errors barely changes.

Porting that exponent into the current season, there are a few surprises. First of all, the Anaheim Ducks have been lucky – almost six full wins worth of luck. It would hardly be surprising for them to tank the last few games of the season. Similarly, the Washington Capitals are on the precipice of the playoff race, but they’re over four games below their expected wins. With 11 games to go, there’s a good chance they can overtake the New York Islanders (who are 3.4 wins above expectation), and they’re likely to at least maintain their wild card status.

On the other end, somehow, the Buffalo Sabres are obscenely lucky. The worst team in the NHL today is actually 4 games better than its expectation. Full luck standings as of the end of March 16th are behind the cut.

Team | Lucky Wins |

Anaheim Ducks | 5.9 |

New York Rangers | 0.1 |

St. Louis Blues | 0.8 |

Tampa Bay Lightning | -1.2 |

Montreal Canadiens | 1.9 |

Nashville Predators | 1.2 |

New York Islanders | 3.4 |

Pittsburgh Penguins | -0.3 |

Chicago Blackhawks | -1.6 |

Detroit Red Wings | 0.6 |

Washington Capitals | -4.4 |

Minnesota Wild | -1.3 |

Boston Bruins | -0.4 |

Vancouver Canucks | 3.2 |

Los Angeles Kings | -3.5 |

Calgary Flames | -1.3 |

Winnipeg Jets | -1.5 |

Ottawa Senators | -3.8 |

Florida Panthers | 1.2 |

San Jose Sharks | -0.5 |

Colorado Avalanche | -0.7 |

Dallas Stars | -1.1 |

Philadelphia Flyers | -3.2 |

New Jersey Devils | -0.7 |

Columbus Blue Jackets | 2.8 |

Toronto Maple Leafs | -1.3 |

Carolina Hurricanes | -2.4 |

Arizona Coyotes | 2.7 |

Edmonton Oilers | -2.1 |

Buffalo Sabres | 4.0 |

Filed under: Sports Tagged: hockey, luck, NHL, parameter identification, Pythagorean expectation, Sabres ]]>

Batting average has some interesting properties, though. It captures events that have unpredictable outcomes – when you walk, it’s basically impossible to be put out on your way to first. Ditto being hit by a pitch. Of course, BA does have some of those determined outcomes, too – home runs and strikeouts don’t have much dynamic nature to them, although you’ll occasionally see brilliant defense save a sure homer (a la Carl Crawford’s MVP performance in the or a sloppy catcher mishandle a third strike and forget to tag the batter. (I’m looking at you, Josh Paul.) Nonetheless, balls in play – balls that the batter makes contact with, forcing the defense to try to make a play – are a major source of variation in the game.

BAbip is measured as , meaning it takes the strikeouts and home runs out of the equation and (like all sane measures should!) includes sacrifice flies.

Since the ball is out of the pitcher’s control as soon as it leaves his hand, BAbip measures things that the pitcher isn’t responsible for – that is, it’s handy as a measure of pitching luck, or, teamwide, as a measure of defensive effectiveness. The NL team BAbip average was .299, and AL average BAbip was about .298.

**Use Cases for BAbip:**

– **Evaluating hitting development.** If a batter has had a stable BAbip for a while and his BAbip increases significantly, be suspicious! Particularly if his walk rate hasn’t increased, his home run rate hasn’t increased, and his strikeout rate hasn’t decreased, this might be a function of lucky hitting against bad or inefficient defenses. If the biggest part of an increase in production has been on balls in play, your hitter may not have actually improved. On the other hand, if you can see physical changes, or you have an explanation (e.g., went to AAA to work on his swing), you may see a more balanced improvement in OBP.

**– Evaluating pitching luck.** Most of the time, all the pitchers for the same team pitch in front of the same defense. Even with a personal catcher in the mix, expect most pitchers on a team to have similar batting averages on balls in play. If you have one pitcher whose BAbip is much higher than the rest of the pitchers, he may be pitching against bad luck. With that in mind, you can expect that pitcher to improve going forward.

**– Comparing defenses.** In 2014, Oakland had a .274 BAbip and allowed 572 runs – the best in the American league in BAbip and 18 runs behind Seattle – while Minnesota had a .317 BAbip and allowed 777 runs, the worst in both categories in the league. Defensive efficiency (a measure of 1 – BAbip) tracks closely with runs allowed. BAbip can operate as a quick and dirty check on how well a defense is performing behind a pitcher.

Filed under: Baseball Tagged: BABIP, evergreen ]]>

First, league median BAbip was .297. Here are four pitchers who got a little less lucky than the average, since their BAbip was .314:

Player | Year | Tm | |
---|---|---|---|

Randall Delgado | .314 | 2014 | ARI |

Erik Bedard | .314 | 2014 | TBR |

Aaron Barrett | .314 | 2014 | WSN |

Chad Qualls | .314 | 2014 | HOU |

Louis Coleman | .314 | 2014 | KCR |

Then, let’s follow up with the other side: the unlucky hitters who would only get on base 3.14 out of every 10 plate appearances:

Player | HR | Year | Tm | Pos | |
---|---|---|---|---|---|

Alejandro De Aza | 8 | .314 | 2014 | TOT | *78/HD9 |

Michael Bourn | 3 | .314 | 2014 | CLE | *8/H |

Elvis Andrus | 2 | .314 | 2014 | TEX | *6/DH |

Jose Tabata | 0 | .314 | 2014 | PIT | *H97/8D |

In addition, let’s take a look at the two hitters from 2014 who hit the ball 3.14 out of every 10 at-bats:

Player | Year | Age | Tm | |
---|---|---|---|---|

Robinson Cano | .314 | 2013 | 30 | NYY |

Andrew McCutchen | .314 | 2014 | 27 | PIT |

Robinson Cano | .314 | 2014 | 31 | SEA |

Yeah, Robbie Cano managed to hit Pi in 2013 AND 2014. The boy must love his geometry.

Our last mention: This year’s Pi Day mascot is Stephen Strasburg, who had an ERA of 3.14. The league-average ERA for pitchers who started 60% of their games was 3.86, so Stephen was in pretty good shape.

Filed under: Baseball Tagged: Pi Day ]]>