Mathenaging: The decision to have Jonathan Broxton face Khris Davis was not a bad one

The St. Louis Cardinals trailed for much of Sunday's contest against the Milwaukee Brewers. But the Redbirds fought their way back into the ballgame. Matt Carpenter punctuated the Cardinals' comeback with a three-run home run—his seventh round-tripper in his last 11 games—which gave St. Louis a one-run lead in the top of the seventh.

Unfortunately, things went sideways for the Cardinals in the bottom of the eighth.

Kevin Siegrist started the inning on the mound for the Cardinals. Pinch-hitter Jason Rogers led off the home half with a single to left field. Milwaukee manager Craig Counsel then pulled Rogers for pinch-runner Logan Schafer. Former St. Louis farmhand Shane Peterson laid down a sacrifice bunt that advanced Schafer from first to second.

With the tying run on second base and one out, Cardinals manager Mike Matheny was faced with a decision: Stay with the lefty Siegrist or bring in the righty Jonathan Broxton. Matheny elected to give Siegrist the hook in favor of the hefty veteran. Broxton entered the game to face the righthanded-hitting Khris Davis. Davis homered off Broxton, which gave the Brewers the lead and their margin of victory.

Matheny's decision has drawn the ire of many of the best fans in baseball on Twitter, so I thought we might take a look at the variables at play to see how bad, good, or meh Matheny's choice was.

Davis's Platoon Splits

It appears that Davis's platoon splits have fueled the outrage over Matheny's decision to remove Siegrist, a southpaw, in favor of the righty Broxton. Matheny's choice of Broxton meant a righty-versus-righty matchup for St. Louis. But Davis has enjoyed success against same-handed pitching this season while putting up bad numbers against portsiders.

2015

61 plate appearances is a sample size so small as to be meaningless. I hope that Matheny would not make any managerial decision based on 61 PAs. I also hope he would not make a substitution based on 189 PAs. Moreover, the gulf in Davis's production against lefties and righties appears to be one that is by and large driven by BABIP—which makes it even more specious.

Of course, there is no reason to artificially limit ourselves to Davis's 2015 stats. Davis has played baseball before this year. If Matheny limited himself in such a way, he would deserve criticism for basing his decision on numbers that are unreliable with respect to measuring true talent. The more information, the better. Especially when it comes to a player's platoon splits. So let's consider Davis's career splits as a big-leaguer.

Major-League Career

This chart shows a smaller gulf in Davis's production against lefties and righties. It's also interesting to note that he has hit for more power during his brief major-league career against lefthanded pitching than righthanders. But these stats are also based on a rather small sampling of PAs. Thus, the chart provides a cloudy reflection of Davis's talent as a hitter. More information would be better.

Davis did not come straight to MLB. He spent time on the farm, plying his trade in the minors. And we have access to his splits from 2011 onward via Minor League Central. Unfortunately, Minor League Central does not have wOBA or wRC+ for a player's minor-league splits, but it does have the other stats found in the major-league charts above.

Minor-League Career

As with Davis's major-league stats, the sample size is too small to draw any definitive conclusions about Davis's true talent for hitting righthanders or lefthanders. With that caveat in mind, Davis hit better overall against lefties in the minors than he did righties while hitting for more power (as measured by ISO) against righties. In other words, Davis's minor-league stats reflect results that are the opposite of his major-league stats.

There is no statistical reason to believe that Davis is better at batting against righthanded pitchers than he is lefthanded pitchers. Especially given the backdrop of MLB-wide trends. Decades of information regarding major-league batter splits suggest that it is highly unlikely that Davis has a true reverse-platoon-split skill. Over the last decade, the gap has been around 10-15 points of wRC+. To believe that Davis is an exception to this MLB-wide reality due to his major-league stats to date is essentially to base your rationale on the vagaries of batted-ball luck. That's unsound ground upon which to stand.

To summarize, Davis's big-league platoon splits during his short time in the majors provide little reason to launch a full-throated attack on Matheny for his decision to bring Broxton into the game on Sunday. And that's without considering Broxton's stats.

Broxton's Platoon Splits

Another dynamic in a relief substitution is the pitcher's platoon splits against hitters. There are several ways to measure this. We can look at the traditional defense-independent stats like Fielding Independent Pitching (FIP) and its component parts. We can also look at hitter results. I won't waste anyone's time on Broxton's 2015 stats, which are a tiny sampling. Instead, we'll look at career numbers.

Career Pitching

Broxton is a better pitcher against righthanded than lefthanded batsmen and it isn't particularly close. Interestingly, Broxton's FIP against righthanded hitters of 2.73 is roughly on par with Siegrist's 2.60 FIP against righthanded batsmen. (When we're dealing with a sample as small as 303 PAs as in the case of Siegrist, 0.13 worth of FIP isn't much.) Now let's look at batter results by handedness against Broxton.

Batters vs. Broxton: Career

Broxton has enjoyed more success against same-handed batters than opposite-handed batters. This is not particularly surprising. And while righthanded hitters have hit better against Broxton than they have against Siegrist (.175 BA/.252 OBP/.322 SLG/.256 wOBA), that has been over just 303 PAs, as noted above, and needs some serious regression if the aim here is to identify just how good a pitcher's talent is for retiring righthanded batsmen.

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All of this is to say that it's hard for me to come down on the side of the folks who are declaring Matheny to be an idiot for pulling Siegrist and having Broxton face Davis in the bottom of the eighth inning on Sunday. Yes, Davis homered, but hindsight is always 20/20 and is consequently rarely a strong foundation for questioning a decision. Based on what we know about the players involved, the correct decision is not as clearcut as some have made it out to be. In fact, after considering all the information to which we have access, I'm not convinced that Matheny's decision was the wrong one.

Correction: The original version of this post recounted Matt Carpenter's go-ahead homer as a two-run dinger. In fact, it was even better: a three-run round-tripper. It has been corrected.

FanDuel

SBN and FanDuel have entered into an exclusive partnership regarding daily fantasy baseball. The Rockies no longer have Troy Tulowitzki. For the year, Colorado has hit .249/.281/.396 on the road. They travel to New York on Monday to face the Mets at Citi Field, a pitcher-friendly ballpark. Consequently, I like the otherwise underwhelming Jon Niese, who starts for the Mets, as a value play. You can play FanDuel here.