By Danny Blumenthal

On Saturday, April 13, Chris Davis ended the drought. He had gone 54 at bats, 62 plate appearances, and 210 days without a hit, besting Eugenio VĂ©lezâ€™s old MLB record of 46 consecutive hitless at bats. Finally, at bat number 55, he laced a single into right field for his first hit since September. To put Davisâ€™ struggles into context, nearly 600 players recorded hits in that time, including fearsome sluggers like Jon Lester, Greg Allen, and David Price. Anthony Rendon and Christian Yelich each tallied 43 hits, and Khris Davis clubbed 16 home runs over the course of the drought. The disparity between the two Davises was most apparent in last weekâ€™s series between the Orioles and Aâ€™s. Chris went 0 for 9, while Khris hit .368 and crushed 4 home runs in 4 games.

It wasnâ€™t supposed to be this dark for Chris Davis and the Orioles. In 2012, he guided Baltimore to the postseason, and he followed that up by leading the league in home runs in both 2013 and 2015. As a result, the Orioles rewarded him with a 7-year, $161 million contract during the 2016 offseason. However, after one solid year under the new deal, he struggled in 2017. Last year was even worse, as Davis recorded one of the worst years in MLB history. He hit only .168, which is the worst qualified batting average ever. In addition, his FanGraphs WAR of -3.1 suggests that he cost the Orioles 3 wins, even as he accounted for nearly 20% of the teamâ€™s payroll.

Although Davis did not live up to the hype of his contract, the hitless streak was not all on him. Over the course of his drought, he was quite unlucky. In his record-breaking at bat, he crushed a pitch 346 feet, but Robbie Grossman caught it at the warning track. In Fridayâ€™s game against the Red Sox, Davis hit a line drive to right field, which Statcast predicted would fall for a hit 97% of the time. However, Boston had the shift on, and Eduardo NĂşĂ±ez calmly gloved it for the final out of the game.

This inspired us at HSAC to consider how unlucky Davis was over the course of his hitless streak, and how many hits he â€śdeservedâ€ť. One way to examine how unexpected Davisâ€™ hitting drought was is to examine the probability that a hitter of his caliber would record an out in 54 consecutive at bats. Prior to the streak starting, Chris Davisâ€™ 2018 batting average was .175. This provides a baseline for Davisâ€™ initial talent level. To figure out how unlikely it would be for Davis to not get a hit in 54 straight at bats, one can subtract his batting average (updating before each at bat) from 1 and then multiply these results together. This is similar to subtracting the initial batting average from 1 and putting that number to the 54th power, which gives a probability of about 1 in 34,000. Updating prior to each at bat gives a slightly more accurate estimate, and this calculation puts the odds around 5.41 x 10^{-5}. Since the odds of a given .175 hitter recording 54 consecutive outs are about 1 in 18,000 (smaller than the odds of a complete amateur making a hole in one), Davis appears to be very unlucky. However, even this probability doesnâ€™t fully reflect Davisâ€™ bad luck.

Another measurement thatâ€™s useful for determining how many hits a player â€śdeservesâ€ť is expected batting average (xBA). Using the launch angle and exit velocity of a given ball in play, Statcast predicts how likely it is that the ball will be a hit. If a line drive has an xBA of 0.800, one would expect it to result in a hit 80% of the time. It would take an excellent defensive play (or good positioning) to prevent a hit in this situation. To find out how unlucky Davis was during his hitting drought, we gathered the expected batting average of each of the balls Davis put into play. Next, we added the 30 strikeouts he accumulated over the hitless streak, which each have an xBA of zero. Finally, we computed Davisâ€™ average expected batting average during the streak, as well as the probability that he would go hitless for these 54 consecutive at bats. This probability was calculated by subtracting each xBA from 1, and then finding the product of each of these answers.

First, here are some of the balls from Chris Davisâ€™ hitting drought with the highest expected batting average. He hit several pitches very hard, but they either went right into the shift or hung up at the warning track. For more detail on these pitches and Chris Davisâ€™ hitting, check out these results from Baseball Savant.

**Chris Davisâ€™ Unluckiest Non-Hits**

At Bat Number | Pitcher | Exit Velocity (mph) | Distance (feet) | xBA |

54 | Ryan Brasier | 74.9 | 177 | .970 |

17 | Lance Lynn | 109.2 | 210 | .880 |

35 | Joe Biagini | 105.0 | 313 | .680 |

25 | J. A. Happ | 102.0 | 396 | .670 |

51 | Aaron Brooks | 105.1 | 382 | .650 |

The following graph shows Chris Davisâ€™ cumulative expected batting average throughout his streak. Many peaks and valleys populate the graph, as a result of Davisâ€™ high number of strikeouts (which have an xBA of 0). However, as demonstrated by the rising trend, Davis was getting better and better chances as his hitless drought carried on. By the end of the drought, his xBA peaked at .142. Nevertheless, this xBA was still well below the 2019 MLB average, which is around .244.

The next graph demonstrates the probability of Chris Davis going hitless for a certain number of at bats in a row, based on the expected batting average of each at bat. The sharp decline at the 17th at bat is due to the line drive Chris Davis hit off Lance Lynn (2nd at bat listed in the first table) on September 22. Although Statcast expected a ball with a comparable exit velocity and launch angle to become a hit 88 percent of the time, it did not account for the shift. Gleyber Torres was stationed right where he needed to be and was able to make the catch for the final out.

As the graph demonstrates, Davisâ€™ streak was very unlikely. Based on the balls he put in play, it was improbable that he would have 25 consecutive at bats without a hit, let alone more than twice that. Overall, the odds that Davis would go 54 at bats in a row without a hit were approximately 0.000000882, or 1 in 1.13 million. Just writing this number out doesnâ€™t completely reflect how remarkable Chris Davisâ€™ streak really was. To provide some framing for these astronomical odds, one would have almost twice the probability of being dealt a royal flush (1 in 649,740) and would be 90 times more likely to make a hole-in-one (1 in 12,500). In 2012, former HSAC president Andrew Mooney calculated that the odds of an average pitcher throwing a perfect game were 0.00000983, or more than 10 times *more* likely than Chris Davisâ€™ streak.

While Chris Davis might not be as talented as he once was, he was very unlucky to not record a hit at some point over the course of 210 days. Finally, his luck changed on Saturday. Davis stepped up to the plate with the bases loaded, and on a 1-0 pitch, knocked a single into right to score two runs. Overall, he enjoyed a good series against the Red Sox, racking up 4 hits (including one with an xBA of only .140), and had his first home run since August. Things may finally be looking up in Baltimore.

*If you have any questions for Danny about this article, please feel free to reach out to him at dblumenthal@college.harvard.edu*