Spring training is getting underway, which means while we aren’t yet into the regular season, we are into projection season. Depending on what you’ve been looking at, there’s been a lot of talk about the White Sox, and there’s been a lot of talk about the Royals. Those teams have received some somewhat controversial projections, but not everything is so up for debate. For example: it’s universally agreed the Cubs look really good, and it’s universally agreed the Phillies look really bad. These statements are practically givens.

The White Sox became a topic of conversation because of USA Today. The Royals are back in the spotlight because of Baseball Prospectus and PECOTA. This is FanGraphs, so let’s take a look at what’s being published on FanGraphs. Here’s our projected standings page, based on Steamer projections and the depth charts, and you see the Cubs projected for an MLB-best 94 wins, and the Phillies projected for an MLB-worst 66 wins. These projections won’t cause any arguments — the numbers agree with consensus opinion.

Projections, though, are midpoints, at least when you see them published. Ranges exist around them. Sometimes pretty big ranges. And both the Phillies and Cubs will employ major-league baseball players, who are elite talents when it comes to their craft. The Cubs will win a bunch of games, and the Phillies will win a bunch of games. What are the chances the Phillies win more games than the Cubs?

This could actually be super easy. If I were a smarter person, I’d run a bunch of season simulations, and then I’d just calculate the rate of those simulations in which the Phillies finished with a better record than the Cubs. For some people that would be a trivial assignment, but I’m not one of them. And besides, I don’t love that methodology, because simulations don’t account well for potential transactions or injuries. Let’s deal with real life, and then let’s make some simplifying assumptions.

To start with: we’ll peg the Phillies at 66 wins, and the Cubs at 94. Okay!

By coincidence,Jeff Zimmerman also just looked at historical projections. I have a sheet of the same stuff, stretching back to 2005, and here’s how the projections have matched actual win totals, over the 11 seasons:

Pretty good, not great, I don’t know, it all depends on your standards. The projections have clearly been measuring something real, but there’s been plenty of variation. In terms of the differences between actual win totals and projected win totals, the standard deviation stands at 8.7. That leaves a lot of wiggle room for under- or over-performance.

Time to simplify a bit. Let’s hold that standard deviation steady. Let’s assume it applies equally to teams projected to be either good or bad, even though that’s not quite true. What we see is worse teams might have a slight tendency to over-perform, and better teams might have a slight tendency to under-perform, but we’ll keep things easy. Let’s also assume the Phillies and Cubs are pretty “normal” teams for teams projected at those records. With the simplified method, you can construct something like the following plot. The Phillies’ line tracks the chance the team wins at least that many games. The Cubs’ line tracks the chance the team wins at most that many games.

Phillies bad, Cubs good, etc. We’re interested in where the Phillies end up with at least one more win than the Cubs. For example, there’s a 0.9% chance the Phillies win 81 games. There’s a 5.4% chance the Cubs win no more than 80 games. There’s a 0.05% chance of both those things happening. It’s just a matter of running through these calculations for each potential Phillies win total, and then finding the sum.

My sum is a hair over 0.8%. In other words, by this method, there’s a 0.8% chance the Phillies end up with more wins than the Cubs do, based on their projections and based on how projections have worked out historically. Another way of saying that is the Phillies would end up with a better record than the Cubs in about one of every 123 seasons. Another way of saying that is the odds are roughly equal to last year’s odds of Alexi Amarista hitting a home run in a given plate appearance. On the one hand, Amarista was awful. He was an offensive black hole. On the other hand:

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It does happen. It did happen. Amarista didn’t hit zero home runs, and the Phillies don’t have a 0% chance of outplaying the Cubs. Nobody thinks it’s going to happen, the Phillies included, but it’s not impossible, and in reality the odds are probably even higher given how bad teams have over-performed and good teams have under-performed. We’re not dealing with perfectly normal distributions, and truer odds might be more like 2%. To say nothing of the Phillies’ young talent, or the Cubs’ various injury risks.

You might say the Phillies’ upside is represented by the 2012 Orioles. The 2011 Orioles won 69 games, and the 2012 Orioles were projected to win 70 games, but they really won 93 games, fueled by an outstanding bullpen. It’s easier to recall bad or mediocre teams who were projected to be good. Last year’s Nationals won 83 games, after being projected for 95. The 2012 Red Sox won 69 games, after being projected for 91. These collapses are never likely, and they’re almost impossible to see coming, but they always manage to make sense in retrospect. If the Cubs were to underachieve, we’d get it. We wouldn’t get it now, but that’s only because we don’t yet know what would’ve gone wrong. So many things can go wrong!

The Phillies are bad, relatively speaking, and the Cubs are good, relatively speaking. Relatively speaking, these are arguably the worst and best teams in baseball. The overwhelming likelihood is that the Cubs finish at least one game better than the Phillies, but there exists some real chance the reverse of that happens, in which case, we’ll talk about what went wrong with the preseason projections, even though these probabilities always exist. At the end of the day, all of them are damn fantastic baseball players.