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# Where the Royals should be

Math examines where this Royals team should be at in the standings by this point.

The Royals are 40-38 as on June 27th. Historically June has not been a good time for Royals fans to look at the standings. Well...really any month other than the first week of April hasn't been a good time to look at the standings. Last year at this time the Royals were 36-40, two years ago 34-39, three years ago 33-46, and four years ago 32-44. So at least the past two years things haven't been so bad. The team is still in the hunt for the Wild Card and can still see Detroit on the horizon.

Regardless of your opinion of this team, other teams, and even baseball in general, the Royals are 40-38. There's very little math or calculating needed to figure that out. You take their amount of games won and add them up. Then you do the same for the losses. Again, that equals up to 40-38.

Now what can be a little more math intensive is a teams Pythagorean W-L record/expectancy. Essentially it's an estimation of a teams true winning percentage using their runs scored and runs allowed. The rational being that runs scored and allowed is a better estimator of a teams current and future performance. In a vacuum (IE: no trades or injuries) and over a elongated amount of time a teams W-L record should get closer to their Pythag record or match it. Pythag has the Royals at 40-38. Right on the money as their current record.

You can take runs scored and runs allowed and expand upon Pythag even further using BaseRuns estimates. The math on that is even harder.

The problem with using a teams actual W-L record is that sequencing matters when it comes to runs scored or allowed. A team could win one game 10-0 then lose then next game 1-0 and although their offense would look pretty darn good after two games probably, they would be just a .500 team despite having a +9 run differential.

This is where Pythag comes into play, but Pythag only tells half the story here and I'll let Dave Cameron at FanGraphs explain the other half to you.

So, developing an expected win-loss metric that removes the affects of sequencing is a good idea, but pythagorean record only goes halfway to that goal. It removes the timing aspects of converting runs into wins, but ignores the timing aspects of converting baserunners into runs. Evaluating a team by its run differential removes some of the sequencing effects of wins and losses, but leaves plenty of other parts, with no real reason why we should arbitrarily include some sequencing while taking other parts out.

That's why I've always preferred to look at a team's performance based on expected runs scored and allowed, rather than actual runs scored and allowed; this gives us the most context-neutral evaluation of team performance to date.

In comes expected run differential W-L estimator. wOBA isn't too hard of a concept to grasp, in my opinion, and it is the key metric for a lot of advanced stats. Basically it's a linear weight of batting events that gives outcomes a relative weight. Rather than a single being weighted as "1" it's weighted as ~.89, a double as ~1.25, a triple ~1.59 and a home run ~2.05. Note that the linear weights change every season but generally hover near those benchmarks in most normal run environments.

This is contrary to how slugging percentage works as it weights a double as twice as valuable as a single, a triple three times as valuable, and a home run four times as valuable when historically they aren't THAT much more valuable. Then we convert wOBA to wRC so we can get a runs created figure.

So we've taken care of the offensive side. Now there are three parts left to get a full picture.

Since runs can obviously be scored on the base paths we need to use some metric to account for that too and wOBA doesn't include that. In comes the wonderful BsR which is a combination of UBR (Ultimate Base Running) and wSB (weighted Stolen Base) which is the baserunning component of fWAR.

That settles the runs scored side of the ledger, but we also need runs allowed (or in this real case runs prevented).

The first step in run prevention is generally having a good defense. We can use DRS for this because it includes the run values of double plays turned, caught stealing, runners thrown out on base, and bases prevented.

The final piece of the puzzle is the pitching side of things. Again wOBA allowed is used here and converted to wRC.

There you have expected runs W-L estimator. While it, like every other stat, is a perfect evaluation of a team/player, it is the most context/sequence-neutral  W-L estimator available.

The last time this model was run was in May and the Royals were 14 runs better than their expected run differential.

While this model is great in theory, it was tested and broken at the extreme ends. Rather than using a "good but imperfect" model for the W-L estimator, Cameron then turned to BaseRuns.

BaseRuns is definitely more complex, if you could imagine, than the expected run differential model above.

On a high level BaseRuns can be described as:

A*B/(B + C) + D

A represents baserunners; B represents advancement of baserunners; C represents outs; and D represents guaranteed runs (usually just home runs). Thus, Base Runs adheres to the true identity that Runs Scored = baserunners * (% of baserunners that score) + home runs. B/(B + C) is an empirical estimate of the percentage of baserunners that score, and is the main source of potential improvement for Base Runs formulas.

From there you have to plug in the inputs which Tom Tango describes here. The big difference being that the wOBA run estimator uses static weights rather than custom linear weights that BaseRuns generates.

Using BaseRuns the Royals should be 36-42. That's 4 wins worse than they currently are.

 W L W% +/- RDif RS/G RA/G 36 42 .464 +4 -24 3.81 4.12

The +4 win difference is the fourth highest in all of baseball and tied with the Yankees. Only the Brewers (+6) and Rangers (+5) are outperforming their wOBA/BaseRuns more.

On the other side of that is the Rays (-7), Cubs (-5), Astros (-4), and Rockies (-4).

Obviously you want to score more runs than you allow, and in fact research shows that in order to win you must do that. While the Royals actual run differential is 13, their "expected" run differential, using a much more context-neutral and probably exact method, they are -24.

This could make them the Jeremy Hellickson of baseball teams where the question is "how long will they continue to out perform their peripherals and when will they crash?"

Hellickson's ERA crashed pretty hard last year...

Source: FanGraphs