Saturday, August 27, 2016

Hamilton, Cozart, Votto and WAR

Billy Hamilton, Zack Cozart, and Joey Votto, the Reds' usual 1-2-3 in the batting order (when all three are healthy) have been equally valuable so far this year. According to's Wins Above Replacement, they are tied for 3rd-most WAR on the team with 2.5 apiece. (Dan Straily has been the team MVP so far with 3.3 WAR, followed by Adam Duvall with 2.7.)

How is this possible, when Votto has been the best hitter in the league for three months now, whereas, despite improvements, Cozart and Hamilton are still average or below average hitters? Let's break it down.

On the "player value" table for every player ever, shows how many runs above or below average a player is in hitting, baserunning, grounding into double plays, and defense.

First, hitting:

Player   Rbat
Votto     +32
Cozart     -3
Hamilton  -14

So obviously this is Votto's strong suit. Hamilton has gotten better at getting on base this year, but overall he's still a below average hitter, while Cozart is pretty much average. So far, Hamilton is 46 runs less valuable than Votto, but we're just getting started.

Next, baserunning:

Player   Rbat Rbaser subtotal
Votto     +32     -2      +30
Cozart     -3     +1       -2
Hamilton  -14     +9       -5

Here's where Hamilton shines - he's created nine runs more than an average player just with his baserunning exploits. That narrows the gap, but he's still in last and 35 runs behind Votto.

Double plays grounded into:

Player   Rbat Rbaser Rdp subtotal
Votto     +32     -2  -1      +29
Cozart     -3     +1  -1       -3
Hamilton  -14     +9  +2       -3

With his speed, Hamilton is also especially hard to double up. He's now tied with Cozart, 32 runs behind Votto.


Player   Rbat Rbaser Rdp Rfield subtotal
Votto     +32     -2  -1    -12      +17
Hamilton  -14     +9  +2    +13      +10
Cozart     -3     +1  -1    +10       +7

Now things are getting much tighter. While Votto has been Votto with the bat, his formerly solid defense at first base has been abysmal this year (at least according to WAR). Meanwhile, Cozart and Hamilton continue to be Gold Glove-caliber defenders.

But wait, we're not done. WAR also includes a positional adjustment. An average hitter who plays shortstop is more valuable than an average hitter at first base. WAR accounts for this, so players at more offensive positions, like first base, left field, and DH, get a penalty, while players at more defensive positions, like shortstop and catcher, get a bonus.

Player   Rbat Rbaser Rdp Rfield Rpos  RAA
Hamilton  -14     +9  +2    +13   +2  +12
Cozart     -3     +1  -1    +10   +5  +12
Votto     +32     -2  -1    -12   -7  +10

With positional scarcity accounted for, Hamilton and Cozart close the gap and pass Votto, But they're all pretty even - each have been worth 10 or 12 runs more than the average MLB player.

Finally, to find true value, WAR adds eplacement runs to account for the difference between an average player and a "replacement" player. The theory being that if a player went down with an injury, how many runs (and wins) would you be giving up by replacing him with your best option from AAA or waivers? An average player over a full season is much more valuable than two weeks of an above-average player, while a replacement-level player is, by definition, worthless.

Replacement runs is a set number based on a player's playing time. Votto has been in the line-up more often than Hamilton and Cozart this year, so he gets slightly more Replacement Runs. Runs Above Average and Replacement Runs are added together to get Runs Above Replacement, which is then converted to Wins Above Replacement (roughly one win for every 10 runs):

Player   RAA Rrep RAR  WAR
Hamilton +12  +14 +26 +2.5
Cozart   +12  +15 +27 +2.5
Votto    +10  +17 +27 +2.5

I hope my brief explanation of Wins Above Replacement made sense to the uninitiated. If you're interested in a detailed explanation, here's's version.

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