On July 19, 2017, the Colorado Rockies beat the San Diego Padres by a score of 18-4. Padres starter Clayton Richard left the game after 3 2/3 innings, having given up 14 hits and with his team down 11-0. After the game, Richard took responsibility for his rough outing, but also pointed out that the Rockies may have benefited from some luck. “It just seemed like mis-hit balls found the right spots,” said Richard. Let’s see if Richard is right; let’s try to eliminate the effects of luck and see how this game should have turned out.
Because the score of the game affects how teams play, I am only going to predict what the score should have been after four innings, at which point the Rockies had a 12-0 lead. In lopsided games, teams often rest their everyday players (as the Padres did with Wil Myers) and don’t bring in their top relievers (Kevin Quackenbush, who gave up six runs, relieved Richard with two outs in the 4th), so it would be unfair to use what happened after the 4th inning to estimate what the score of the game should have been.
I looked at Baseball Savant’s hit probability and expected wOBA (xwOBA) of every plate appearance in the first four innings of the game. These stats only consider a batted ball’s exit velocity and launch angle. Although I will generally refer to the difference between xwOBA and wOBA as luck, keep in mind that defensive positioning and defensive ability are also factors that can affect this difference (the Rockies are, in fact, an above-average defensive team, while the Padres are one of the worst in the National League). In the first four innings, the Padres had 16 hitters come up to the plate, and they averaged a .254 xwOBA, compared to an actual wOBA of .281, for a difference of .027 per hitter. I gave Manuel Margot’s first-inning plate appearance, in which he walked but was later picked off, an xwOBA and wOBA of 0. Meanwhile, the Rockies’ 29 hitters averaged an xwOBA of .420 and a wOBA of .664, for a difference of .244 per hitter. Two things are immediately clear. First, the Rockies certainly out-hit the Padres in the first four innings of the game. Second, as Richard noted, the Rockies’ hitters benefited from a lot of luck.
First, I will calculate the number of runs each team would have had through four innings if their wOBA was exactly their xwOBA (this estimate will be a little low for both teams, as xwOBA does not take into account that the game was played at Coors Field). To do this, I will find their weighted runs above average (wRAA), and then add that to four times the average number of runs per inning in the National League.
wRAA = ((wOBA – league wOBA) / wOBA scale) x PA
league wOBA = .320
wOBA scale = 1.25
When calculating wRAA, we run into a problem: we can’t use the actual number of PAs each team had because this number depends on the number of baserunners they had, which should change when we convert wOBA to xwOBA. To come up with an expected number of baserunners, I added the hit probability of all balls put in play and added 1.000 for each walk and hit-by-pitch (with the exception of Margot’s 1st-inning walk). Strikeouts, as you might expect, were worth 0 points. The Padres had 3.24 expected baserunners (.203 xOBP) while the Rockies had 11.70 (.404 xOBP). With a .203 OBP, it would take roughly 15 hitters to get through four innings (15 x .203 = 3.045 baserunners; 15 hitters – 3 baserunners = 12 outs). With a .404 OBP, it would take roughly 20 hitters to get through four innings (20 x .404 = 8.08 baserunners, 20 hitters – 8 baserunners = 12 outs). Therefore, we use 15 PAs for the Padres and 20 PAs for the Rockies (notice that reducing the number of hitters doesn’t ignore what happened to the Padres’ last hitter or the Rockies’ last nine, as I use the average xwOBA of all the hitters that came up and simply apply that to a smaller sample).
The Padres’ expected wRAA through four innings is then -.79 while that of the Rockies is 1.60. The National League averages .5533 runs per inning, which comes out to 2.21 runs per four innings. Add each team’s wRAA to this number and a reasonable score of this game through four innings would be 1.42 to 3.81 in favor of the Rockies. It is still the Rockies’ lead, but nowhere near the 12-run difference that actually took place.
Of course, we know that luck and defense do exist. Let’s say that in one of the oddest trades in MLB history, the Padres and the Rockies decided to swap their luck and their defenses before the game. I will add to the Padres’ xwOBA the difference between the Rockies’ xwOBA and wOBA and vice versa (I will call this new number “swapped wOBA”). I will do the same with the teams’ xOBP and OBP to determine the number of hitters that would have come up through four innings in this scenario. Here’s a chart summarizing all the numbers:
|wOBA – xwOBA||0.027||0.244|
|OBP – xOBP||0.047||0.182|
Using the same process as before, we use the teams’ swapped wOBA to calculate their wRAA through four innings and add 2.21 to each. With the Rockies’ luck, the Padres would have been expected to score 4.92 runs (2.71 wRAA + 2.21) through four innings. Meanwhile, with the Padres’ luck, the Rockies would have been expected to score 4.45 runs (2.24 wRAA + 2.21) through four innings. Not only was the game not as lopsided as it appeared, but with the teams’ luck and defense swapped, the Padres would have held the lead (if you round to the nearest whole number) through four innings. That is a 13-run difference solely due to luck and defense!
Now, there is a slight issue with the calculation I performed above. I took data from only 16 Padres hitters and then applied it to 19, assuming the extra three performed at the same level as the first 16. To fix this, we can look instead at the Padres’ expected run value for only the first 16 hitters. We end up with a wRAA of 2.28. Using their swapped OBP of .385, roughly six hitters would have reached base, meaning that these 16 hitters would have come up in 3 1/3 innings. So through only 3 1/3 innings, the Padres would have had basically the same wRAA as the Rockies would have had through four. This is amazing. If only the Padres were given the luck that the Rockies received on this day, they would have at least been tied through four innings, a far cry from the 12-run deficit they unfortunately had to face.