What Are the Chances the Phillies Outplay the Cubs?

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:

actual-vs-projected-wins

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-cubs-simplified-win-curves

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:

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.



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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.


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Roger McDowell Hot Foot
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Roger McDowell Hot Foot
3 months 12 days ago

I head-scratched for a moment just taking this as an estimation exercise before I read the article, and guessed 0.5%. Not bad. This would’ve been an interesting subject for a pre-article reader poll!

Shirtless Carson Cistulli
Member
3 months 12 days ago

About the same odds as me pitching the final out of this year’s World Series.

Owen S
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Owen S
3 months 12 days ago

It always amazes me how paradoxical theorizing over probability can be. That’s probably (definitely) why there are so many heated debates on topics that hinge on probability, like projections.

For instance, I think we can all agree there exists some percentage chance the Phillies will end up with more wins than the Cubs. Some may say 2%, others 0.5%, and still others, O.01%. But despite this overarching agreement, if such a scenario actually comes to fruition, there will inevitably be people, people who agreed such an outcome was possible, who will insist the projections were wrong. People who will insist Fangraphs missed something, or several somethings, that were of critical importance.

And this is where the paradoxical part comes into play: people will acknowledge the theoretical possibility of both the Phillies besting the Cubs AND the projections being right, unless the former ACTUALLY occurs, in which case the latter assumption will be assumed incorrect.

novaether
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novaether
3 months 12 days ago

They’ll probably also conclude that the Phillies just “wanted it more” and that the Cubs didn’t have any “clutch hitting”.

BenRevereDoesSteroids
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BenRevereDoesSteroids
3 months 12 days ago

Or there could be some extreme circumstance, like the Cubs having a 2014 Rangers situation where they lose 2000 days to the DL and under perform the projections by 20 wins. Then maybe people will just shrug their shoulders and move on.

Sleepy
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Sleepy
3 months 11 days ago

Don’t forget about “heart” and “grit.” Invaluable skills, those.

vivalajeter
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vivalajeter
3 months 11 days ago

To be fair, if the Cubs finish behind the Phillies there’s a good chance that they *didn’t* have any clutch hitting.

Roger McDowell Hot Foot
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Roger McDowell Hot Foot
3 months 12 days ago

I get what you mean and agree, but it’s hardly a paradox — more like a set of hard-to-dislodge cognitive biases in how people think about causation and probability.

Oneear
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Oneear
3 months 12 days ago

So you’re saying there is a chance.

MickO
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MickO
3 months 12 days ago

Came here to say this. Glad you did

j6takish
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j6takish
3 months 12 days ago

You’re doing God’s work Jeff.

zaxell
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zaxell
3 months 12 days ago

Also note that the Phillies play the Cubs 6 times in 2016, so their respective win totals aren’t independent; this might bump the Phillies’ odds all the way up to 1%!

Hank G.
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Hank G.
3 months 12 days ago

And this is where the paradoxical part comes into play: people will acknowledge the theoretical possibility of both the Phillies besting the Cubs AND the projections being right, unless the former ACTUALLY occurs, in which case the latter assumption will be assumed incorrect.

The converse: if things had gone well for the Nationals last year, no major injuries, everyone played up to their expectations, and they won the World Series, no one would be touting the projections because it would have been “obvious that they were the best team”.

Big Matty 24
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Big Matty 24
3 months 12 days ago

When I look at that line chart with the win probabilities, I read it as the phillies have a roughly 5% chance of winning 81 games, and you listed it as 0.9%. What am I missing? Or did you accidentally pull prob of phillies winning 91?

formerly matt w
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formerly matt w
3 months 12 days ago

The chart shows the chance that the Phillies win at least 81 games, but for the calculation Jeff is doing, he needs the chance that they win exactly 81 games.

srpst23
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srpst23
3 months 11 days ago

but why would he need exactly 81 games, if the Phillies won 84, and the Cubs won 80, wouldn’t it still be the same scenario?

Schmidt Happens
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Schmidt Happens
3 months 11 days ago

In order to answer the question, “What are the chances the Cubs win fewer than X games?”, you have to set a value of X.

In this case, we don’t know the value of X, because we don’t know how many games the Phillies will win. So the easiest way to answer the question, and what Jeff did, is to start at some very small value of X (Phillies wins); calculate the chances of the Cubs finishing below X wins; increase X by 1 and repeat the calculation; then add all those individual chances together.

I mean, I suppose you *could* construct a giant 163×163 grid with every probability combination of Phillies and Cubs wins (e.g. Phillies win 84, Cubs win 80), calculate all 26,569 probabilities individually, then add up only that subset for which PW > CW. But Jeff’s method seems … less insanely complicated.

jrl133
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jrl133
3 months 12 days ago

How did you factor in the variety of curses in play over the past 100 seasons of Cubs baseball?

The Ghost of Johnny Dickshot
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The Ghost of Johnny Dickshot
3 months 11 days ago

Cubs projected for an MLB-best 94 wins, and the Phillies projected for an MLB-worst 66 wins.

****

This difference is roughly 1 extra win per week of the season for the Cubs.

MajesticOwl
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MajesticOwl
3 months 11 days ago

How many weeks are there in the season? A lot, right? At least 24.

Playing the rest of the season normally and setting aside one extra game per week to be determined by a coin flip, the chances of getting a W on all 24 coin flips would be about 1 in 17,000,000.

Winning one extra game in one week isn’t anything. Winning an extra game every week isn’t luck at all. Yet we often see “Just one extra game per week!” as if it’s something insignificant or something that can be accounted for by luck.

MajesticOwl
Member
MajesticOwl
3 months 11 days ago

One thing that sticks out in this article is the 8.7 standard deviation. That’s really high! That would be unrealistically high if we were talking about simulating seasons using fixed rosters.

When I run simulations of a team that wins a bit more than 95 wins per season (real simulated seasons, not just simulated coin flips), I get a standard devation between 6 and 7 very consistently. For a .500 team, I get a standard deviation slightly less than that. (The league run environment makes a difference, too, but I haven’t explored that variable much!) Oversimplifying a team into a weighted coin flip gets us about the same number, so this is a plausible value.

How do we account for this difference? I think part of it is measurement error when we’re evaluating teams (i.e., the projections are off by a bit, so the standard deviation of actual wins would be smaller than the standard deviation of the difference between actual wins and projected wins!), plus roster changes and player improvement and decline, injuries, et cetera. All the stuff I haven’t put into this simulation model yet (except for the measurement error, when I’m simuluating a platonic ideal of a team with a certain talent level instead of a real team), because that wasn’t the point of the model I’m using, so I need to get around to updating it.

When the real data have a standard deviation almost two wins higher than more basic simulations or coin flips, that makes a BIG difference when we’re comparing stuff that happens at the margins. We’re already looking at the Cubs falling about two standard deviations below their talent and the Phillies climbing two standard deviations about it (approximately). Basically, if we restrict ourselves to cases where the Cubs don’t have something drastic like a major injury happen and the Phillies don’t strike gold with a player breakout, the Phillies’ odds are a bit longer.

But we already knew that. If Arrieta and Harper are both hurt, or Franco starts hitting like Babe Ruth, then we’re no longer looking at the same Cubs or Phillies.

On the one hand, freaky things like that DO happen. On the other hand, I’m not sure how interesting it is to think about them, since we’re talking about the Cubs and Phillies teams as they are, not necessarily how the Cubs and Phillies could be.

I guess the point is that the chances of the Phillies beating the Cubs without something strange happening are even lower than they look in this analysis, but also, the reason for this could tell us something interesting about how we estimate the quality of a baseball team and how likely teams are to change significantly during a season.

Baseball4ever
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Baseball4ever
3 months 11 days ago

I hope the Pirates surprise everyone and win the division. It would be even better if the Cubs didn’t make the playoffs. 109 seasons and counting would be fantastic.

Nats Fan
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Nats Fan
3 months 11 days ago

You know if the Cubs fail to make the Postseason this article could become as important as a certain billygoat is to Cubs Cubs fans.

Scott Lindholm
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Scott Lindholm
3 months 10 days ago

.8%–never would have guessed that high. Should be a good year to have a daughter who lives blocks from Wrigley.

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