The Braves fired manager Fredi Gonzalez. No word on his replacement but, chances are, the new manager won’t be any better.

That’s not because Gonzalez is a particularly good manager. Rather, it’s because only a handful of managers have been empirically proven to make much of a difference for their teams. Firing Gonzalez isn't likely to make the Braves any worse but the new manager also isn't likely to make them much better.

That’s according to the best available evidence collected by "sabermetricians" and others who have crunched the numbers and tried to answer the question: How much do managers contribute to winning? Their conclusions:

Russell A. Carlton at Baseball Prospectus (2014): "I started out by trying to answer the question of how much of an impact a manager might make on a team with his strategic decisions. It turns out that while the answer isn't zero, most of the things that we obsess over with managers aren't really that powerful. But we do obsess over them."

Dennis Smart, Jason Winfree and Richard Wolfe in Journal of Sport Management (2008): "In summary, our results are supportive of the Smart and Wolfe (2003) finding that field managers have very limited influence on MLB team performance."

There have been some attempts to rank managers by their influence on winning by comparing the expected wins for a team against actual wins. Here's one by Adam Darowski, last updated before the 2012 season. Here's another one by Jon Sheperd calculated before the 2014 season. Notice that Gonzalez rated favorably back then, before Melvin Upton, Dan Uggla and Chris Johnson sucked up payroll without producing and then the eventual veterans-for-prospects swaps.

Analyses such as Paine's and Carlton's study strategic decisions that are within a manager's control and have measurable outcomes. They don't capture every factor that contributes to winning but it's illogical to base conclusions based on what we don't know. Studies such as those by Paine and Carlton offer the best available evidence of a manger's impact.

Using those studies and others as my guide, my view is that Gonzalez’s strategic decisions usually were OK if not always optimal. More importantly, a new manager isn’t likely to improve on his areas of weaknesses. Certain statistically dubious strategies are so ingrained in baseball culture that finding a manager who will think outside that box will be difficult—and that's assuming the Braves would even want a radical strategist.

For example, I though Gonzalez sometimes adhered too strictly to the conventional thinking on lefty-righty matchups without considering other pertinent factors. But pretty much all managers do that. Gonzalez too often relied on small sample sizes of data to make decisions, such as when evaluating batter/pitcher matchups or reacting to "hot" or "cold" streaks, but which managers don't do the same? Gonzalez sometimes didn’t use his best relief pitchers in high-leverage situations before they are "supposed" to pitch (see Kimbrel, Craig, 2013 NLDS) but most managers hew closely to the specialist/setup/closer formula.

But even if Gonzalez had been better in those strategic areas, they only provide incremental advantages that take time to accumulate into wins (and Paine found that most managers don't get enough time to prove whether they are better or worse than average). In other areas, I thought Gonzalez was right where others thought he was wrong.

Some Braves fans got upset when Gonzalez said he didn't favor "small-ball" for this team. But, generally speaking, the numbers say sacrifice bunting by non-pitchers is a bad idea. There are some situations in which it can be a good call but the advantages typically are small and often offset by defensive adjustments. Gonzalez's explanations for why he didn't sacrifice in specific situations made sense and were generally supported by the numbers.

Gonzalez’s critics also complained about his handling of pitchers, usually because they felt he pulled starters too early. But much of that criticism was after-the-fact: the decision didn’t "work" because of the outcome, so it was a bad one (and when the outcome of the decision is positive critics say it worked in spite of Gonzalez).

Anyway, how do you judge what would have happened had he let that starting pitcher go longer? It's folly to focus only on outcomes because good decisions can have bad results. For Gonzalez with this team, it often came down to choosing the least bad option.

As for Gonzalez’s leadership, that’s an intangible factor that’s difficult to evaluate objectively. Managers must handle personalities and relationships while helping to establish the clubhouse culture. You can't quantify those things, though, and so many subjective criteria come into play when you try to do judge leadership.

Chris Jaffe, author of "Evaluating Baseball's Managers," told the Star Tribune that most managers have little impact on wins but that a good manager might be worth three to five wins in a season and a bad one might cost three to five wins.

“Maybe that doesn’t sound like much, but it’s a lot," Jaffe said. "Not many players can affect a team that much, maybe only a couple per position every year. But even still, there’s a feeling that part of (the manager influence) is accounted for by chemistry, which is really hard to quantify. It’s a word we hate in (sabermetrics).”

Many fans seem to think chemistry has something to do with the outward demeanor of the manager. I heard complaints from Braves backers who wanted Gonzalez to “show more fire” while sitting in the dugout. They wanted him to “stick up for his players” with umps and do other demonstrative things.

According to these critics, who no doubt are influenced by fond memories of Cox's style, if Gonzalez had done these things he would have motivated professional ballplayers to perform better. Is that true? Maybe. It's possible that "showing more fire" is part of the reason why managers such as Cox, LaRussa and Weaver were able to get more wins out of their teams than expected over the long term. But, again, there's no good way to know for sure.

I suppose the Braves could hire a manager with a more forceful personality and see if that makes a difference. But unless the Braves somehow can identify and hire one of those rare managers with non-quantifiable gifts who can get a team to play over its head, I'm thinking the new guy won't make much of a difference until better players are added to the roster.

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