Making Sense of the Run Differential

After a 3-0 loss in Cincinnati last night to the cellar-dwelling Reds, the Texas Rangers sit at 73-53 and remain 5.5 games up on the Seattle Mariners in the AL West. No, it’s never fun to watch a punchless offense struggle in a National League park, but the fact remains that how you arrive at 73-53 is slightly less important than simply getting there.

Regardless of how you feel about the decision to bunt in the 7th inning of a 1-run game with men on 1st and 2nd with no outs -- I think it’s yet another example of a supposed “analytics oriented” manager not playing the percentages at all -- a single loss on August 23 won’t likely be the one you can point to if somehow, over the next five weeks, things go incredibly awry.

In giving up three more runs than they scored, the Rangers also earned another dubious distinction: their run differential dropped to -2 on the season.

While it’s not all that rare for a team to be above .500 with a negative run differential, what is uncommon is for a team to have such a great record while allowing more runs that it scores. On pace for about 94 wins still, the results and the projections don’t exactly add up.

For starters, the pythagorean wins formula that measures a team’s expected winning percentage based on run production believes Texas to be a .498 team. That is, if you ran them through a computer 100 times, more often than not, you’re going to end up with a team hovering around an 81-81 record.

Sometimes, as is the case with the 2016 Texas Rangers, however, that doesn’t end up being the case. Imagine for a moment that a baseball team is a two-sided coin with one side being “win” and the other “loss”. If you flip it 162 times, you would expect it to come up “win” 81 times. Of course, your actual results will likely end up varying from your expected results.

Following a normal distribution with a mean of 81 and a standard deviation of 6.36, you would expect about 95 percent of your observations to come within two standard deviations of the mean.

That is to say, one time in 20, you would expect a team to win 94 or more games -- or conversely 68 or fewer games -- based on pure luck alone. So the Rangers have been lucky, it would seem.

Now, before you lump me into the “Rangers are just lucky” group, keep in mind that I’m not also saying that the Rangers aren’t good. They are. They’ve simply needed some good fortune along the way to make that happen.

For starters, Texas is 27-8 in one-run games. That is, I think it goes without saying, pretty fantastic. Any number of things can go wrong to flip that in the other direction. A blooper here, an error there. And yet, Texas finds themselves on the winning side of that coin, which on its own could make the difference between Texas being a 94-win powerhouse and something closer to a team hovering around .500. That’s where you’ll see the word “luck” thrown around.

Beyond that, it’s important to note that the starting rotation has been something of a mess this season. Of the 126 games the Rangers have played in 2016, 50 have been started by some combination of Cole Hamels, Colby Lewis, and Yu Darvish. And in those 50 games, they’ve combined to give up 102 earned runs on 317.2 innings pitched. That’s good for an ERA of 2.92.

Then you have everyone else. The Rangers have used 8 other starters in the other 76 games in 2016, and in 408 innings pitched, those pitchers have given up 230 earned runs; an ERA of 5.07.

Pushing aside the fact that bullpen pieces like Tom Wilhelmsen and Shawn Tolleson played their own part in giving up significantly more runs that you’d expect, the starting rotation alone has been a problem area.

Even if those 8 starters could have put up a combined ERA of 4.41 to this point, that would have been around 30 fewer runs allowed, and the pythagorean winning percentage would have the Rangers somewhere closer to 85 wins. No, it doesn’t make up the entire difference, but replacing the production of this pitching staff with something resembling a below-average ERA goes a long way toward explaining any “expected versus actual” discussions.

If you want to have even more fun and imagine, a good rule of thumb is that every 10 runs is worth around one win. Score five more while allowing five fewer? There’s another projected win.

So while projections and formulas are oftentimes correct -- and in most cases, provide useful predictive value -- there’s alway room for statistical uncertainty. No matter the formula, there will always be an outlier, and as a Rangers fan, I’m thrilled that this year’s team -- which now looks stronger on paper than it did a month ago, and looks to get stronger with rotation reinforcements -- is one of those statistical outliers.