Where the Royals are Baseball’s Fourth-Best Team

It was a dramatic one Sunday in Kansas City. The Royals played the Rangers in a late-season matchup of wild-card hopefuls, and the game was scoreless going into the bottom of the tenth when the Royals loaded the bases with none out. Then, after Mike Moustakas hit, there was one out. Then, after George Kottaras hit, there were two out. Up came Justin Maxwell, and the count ran full, and on what would be either a decisive pitch or a foul, Maxwell swung and lifted the ball out for a walk-off grand slam. A single would’ve done, or an error would’ve done, or a walk would’ve done, but a grand slam is emphatic, and the Royals celebrated like the Royals seldom have over the past however many years.

However, with a week left in the season, the Royals still don’t have much of a shot of advancing. They trail the Indians by three and a half games, the Rays by four. The Rangers are two games in front of them, and the Indians play a soft schedule. Our own playoff odds give the Royals a 1-in-71 shot, so while they’re happily playing meaningful baseball in late September, it’s unlikely there’ll be meaningful baseball in early October. Featuring the Royals, anyway. And that’s too bad for a team that might be one of baseball’s best.

The Royals own baseball’s 13th-best raw winning percentage, at .529. They’re right between the Nationals and the Yankees, and they’ve guaranteed themselves a winning season. In that sense, kudos, Royals. I know this place hasn’t been real kind to the Royals for a while. But look what happens when you sort by total team WAR. The Royals shoot up the table, with a 41.7-WAR sum that puts them between the Rays and the A’s. They’re nowhere close to the Red Sox and Tigers — those teams are running away with it — but the Royals, right now, have more WAR than the Dodgers. They have more than the Braves. They have more than everybody but the Red Sox, Tigers, and Rays, looking in this regard like a legitimate playoff team. The Royals presumably won’t make the playoffs, but they’re off their WAR winning percentage by more than five wins. That feels unfortunate, for a franchise that’s had its share of misfortune.

Let’s look at a table, now, featuring 2013′s ballclubs. There are two statistical categories, each saying the same thing in a different way. Presented is the difference between actual team success and expected team success, based just on WAR. The table is sorted from most positive difference to most negative difference.

Team diffWin% diffWins
Cardinals 0.048 7.5
Yankees 0.046 7.2
Phillies 0.046 7.1
Pirates 0.039 6.1
Indians 0.039 6.0
Padres 0.036 5.5
Athletics 0.035 5.5
Braves 0.033 5.1
Reds 0.028 4.3
Nationals 0.027 4.2
Mariners 0.018 2.8
Dodgers 0.017 2.6
Brewers 0.010 1.5
Twins 0.007 1.1
Astros 0.002 0.3
Orioles 0.001 0.1
Diamondbacks -0.004 -0.7
Marlins -0.006 -0.9
Blue Jays -0.006 -1.0
Rangers -0.017 -2.7
Rays -0.019 -3.0
Mets -0.020 -3.2
White Sox -0.029 -4.5
Angels -0.033 -5.1
Royals -0.034 -5.3
Giants -0.039 -6.1
Red Sox -0.044 -6.9
Cubs -0.050 -7.9
Tigers -0.061 -9.5
Rockies -0.061 -9.6

The Cardinals have an actual winning percentage of .583. By WAR, it “ought” to be .535, and the Cardinals are blowing that away in large part because of their extraordinary success with runners in scoring position. At the other end, we find the Rockies and Tigers, who are off the pace by even more than the Royals. The Red Sox and Tigers have simultaneously been terrific and arguably unlucky, if you consider this somewhat a measure of luck.

I’m not going to dive into examining the differences. That would probably be another post. But, what can we say about the relationship between winning percentage and WAR? Unsurprisingly, the relationship is super strong, because WAR is a measure of productivity, and teams with productive players win more games. Here’s winning percentage against WAR winning percentage over the past century:


Linear, but not perfectly so. No relationships are perfect. Accepting that, in each year, there will be differences, what do those differences mean? What does it mean when a team wins more or fewer games than WAR would suggest?

We can look at this a few ways. Real quick-like, let’s just compare 2012 and 2013. I calculated the 2012 differences between winning percentage and WAR winning percentage, and split into three groups: 10 most negative differences, 10 middle, and 10 most positive differences. How have those groups gone on to do in 2013?

Group 2012diff 2013diff
10 neg -0.039 -0.007
10 mid -0.005 -0.007
10 pos 0.043 0.015

There’s pretty heavy regression: in 2012, between the negative and positive groups, there was a difference of .082. In 2013, it’s .022. Now let’s look at this in reverse. I calculated the 2013 differences between winning percentage and WAR winning percentage, and split into the same three groups. How did those groups do in 2012, before?

Group 2012diff 2013diff
10 neg -0.015 -0.039
10 mid -0.001 0.002
10 pos 0.015 0.038

Between the negative and the positive, there’s a difference of .077 in 2013. Last year, it was .030. Now we might as well look at a way bigger sample.

Consider this the master chart, or something, covering the window from 1998-2013. The chart might look complicated, but it isn’t. On the x-axis, we have a team’s difference between winning percentage and WAR winning percentage. On the y-axis, we have the same thing for the following season. Do we see any hints of sustainability? That is, how consistently have teams beaten or under-performed their WAR?


A relationship exists, but it doesn’t seem to be much of one. And the regression is strong. Over time, winning percentage and WAR winning percentage converge. This is basically along the same lines as examining the relationship between winning percentage and Pythagorean winning percentage. Teams like last year’s Orioles can out-perform their run differentials, because the season stops at 162 games, but going forward, that doesn’t project as a skill. All that matters in the moment is winning. What matters in the future moments, though, are the numbers that underlie winning. This is all stuff you’ve heard before.

So perhaps it’s a silver lining for the Royals. For once, the numbers are on their side, even if the number they care about isn’t. They’ve undershot their numbers in 2013, but they shouldn’t do that again in 2014, given identical numbers. Which, naturally, can’t be taken for granted. Other teams, also, have things to think about. The Angels look better by WAR than they do by record, and for this reason they could be contenders a season from now if Albert Pujols looks more like himself. At the other end, almost the whole National League Central could be examined at length.

The bad news for Kansas City is that they probably won’t make it to the wild-card playoff. The good news is they arguably deserve to, and though that doesn’t soften any 2013 disappointment, maybe next year. For the Royals, the motto has long been “maybe next year,” but this time around it means something a little different.

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Jeff made Lookout Landing a thing, but he does not still write there about the Mariners. He does write here, sometimes about the Mariners, but usually not.

19 Responses to “Where the Royals are Baseball’s Fourth-Best Team”

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  1. David says:

    The Royals aren’t not not out of contention for a playoff spot.

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  2. Chooch says:

    A more meaningful interpretation of the top graph (win vs WARwin) would be to show the error (standard deviation) in WAR. While we try to use WAR as a all-in-one descriptive stat the reality is the weighing of each counting/rate stat that goes into it is still arbitrary (in the true mathematical sense). The standard deviation for Wins Above Replacement is likely high enough to matter and could be taken from this graph. My estimate for standard deviation is +/- 0.5

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    • JMS says:

      The other problem with WAR when comparing teams in different leagues is how it treats the pitcher and DH. Most NL teams–by virtue of allocating about 1/12th of their PAs to pitchers–accumulate about 3 negative WAR per year out of that position. AL teams accumulate a fair [less than anticipated due to the positional adjustment and new trend of using the DH to rest regulars] amount of positive WAR as batters.
      It makes no sense, however,to penalize NL teams for having the pitcher bat when that does not actually produce a disadvantage per se because the other team also has their pitcher bat. This DH/P valuation problem can swing WAR dramatically–two teams with identical true talent levels can be 5 WAR apart. This phenomenon appears to largely explain why AL teams consistently under-perform the winning percentages that WAR would anticipate, while NL teams appear to regularly over-perform.

      This can add up to a 5 war swing between two AL and

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      • Nick O says:

        Is that true? I kinda assumed there was an appropriate positional adjustment couched in there.

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        • JMS says:

          I should retract my comment. As of July, when I marveled at NL pitchers combined -30WAR, it was. It appears that the positional adjustment was added when the offense/defense columns were added.

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    • Jimi says:

      Think about the error associated with just team UZR. It’s calculated by adding player UZRs together. To find the variance of that sum, you have to sum the individual variances. Think about that for a second–That means that the variance associated with any Team WAR score goes up. By a lot. This is further complicated if you believe that UZR can be systematically biased by shifts and therefore teams that shift.

      Team WAR, without significant error bars to account for this variance, means very very little and as an econ/math site, we lose credibility when we use it.

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      • Paul says:

        But it is used constantly on FG, without the slightest mention of the very important caveats you aptly illustrated. I’m no sure under those circumstances this can really be termed a math/econ site. At least not a rigorous one.

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  3. Dayton Moore says:

    The Process has been vindicated.

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  4. Nick O says:

    Couple questions/comments:

    1) Royals WAR is mostly in defense/pitching. Especially given their staff, wouldn’t we expect this to regress pretty heavily?
    2) Royals lead league in UZR despite converting a close-to-average number of BIP into outs. To me it seems like WAR is giving the pitchers’ credit for league-average BABIP and fielders credit for excellent fielding when it should only be crediting one of the two.
    3) With how much team rosters change year-to-year, would you expect much of a long-term correlation between WAR outperformance even if it was some sort of team skill?

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    • Jaack says:

      Well for question 2, since fWAR is FIP based, pitchers are getting no credit for BABIP.

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      • Daniel says:

        Didn’t they just add in IFFBs to pitcher fWAR?


        At least they get some credit for BABIP.

        To help answer question 2:
        Forgetting about IFFBs for a second, pitchers effectively get credit for average BABIP but that is credit against the average anyway (or a +0). The defense/UZR for the players is also credited above average. Essentially, what happens is that the defender gets credit for “all” of the defense above average. There would not be any double counting.

        The first problem would be if the IFFBs get double counted. I would imagine players don’t get much defensive credit for making this play since that is one of the reasons it was added to WAR in the first place.

        The second problem would be if the defenders are getting some credit for defense that the pitcher should get (weak batted ball, etc.). This would not be a problem for this team analysis.

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      • bluejays49 says:

        I’d argue pitchers do get credit for good BABIPs.

        A pitcher who collects no K, BB, or HR over any amount of IP is given a 3.047 FIP. Converting a hit into an out is an event that is worth 3.047 FIP, which is a very good FIP.

        If the ball lands for a hit instead, the pitcher gets a new batter. Yes, this new batter may strike out, but he also may walk or hit a home run. In most cases, the pitcher can be expected to post a worse-than-3.047 FIP against this new batter. Outs on balls in play in a FIP booster.

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  5. D says:

    Curious, what would it look like if you use Baseball Reference’s WAR?

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    • Paul Clarke says:

      Baseball Reference has them at 37.1 WAR, which would remove most of the discrepancy between WAR and the actual win total. One thing that may help explain the discrepancy is that the Royals pitchers have allowed the fourth-highest rate of line drives in the majors, at 22.2%. Lets says your pitchers allow more than average numbers of line drives but your fielders make enough plays to cancel out the extra run scoring that would normally result, leaving you still allowing an average number of runs. fWAR won’t debit the pitchers for allowing the line drives but will credit the fielders for making those difficult plays, so you end up with an above-average WAR while allowing an average number of runs.

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  6. KCDaveInLA says:

    It will be fun to think of what the Royals could have done if not for the epic tank job in May (2.3 team wins – Tigers posted 10.7 during same span), and a full season of Eric Hosmer (post-Brett). A healthy Danny Duffy and Yordano Ventura can effectively replace a sure-to-leave Ervin Santana. I’ll worry most about Moustakas having reached his peak and Jeremy Guthrie’s FIP numbers getting more absurd.

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    • Zsigs says:

      Just as it would be fun to think of what would have happened if the Rangers did not tank in September or if the Rays had not tanked in late August(?)/ early September. Baseball is baseball, and you cannot arbitrarily take away slumps.

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