Note: This article will be continually updated to take into account game results each day, so continue to check it out and scroll to the bottom to see the latest matrix of outcomes / probabilities.

The Colorado Rockies entered the final week of the 2017 season in control of the second Wild Card, but with the Milwaukee Brewers and St. Louis Cardinals right on their heels. In order to keep track of all possible scenarios that would lead them to clinch the Wild Card spot, I wrote an article that showed all possible outcomes and how their probabilities changed until the Rockies finally clinched on the final Saturday of the season.

We now find ourselves in the final week of the 2018 season, and somewhat remarkably, it is again the case that things are coming down to the wire for the postseason chances for the Colorado Rockies (85-70) as they battle it out with the St. Louis Cardinals (87-69) and Los Angeles Dodgers (87-69).

But this year, things are a bit more complicated than in 2017, namely because the NL West is still simultaneously in play along with the NL Wild Card. So in reprising my article from last year I had to find a way to expand my original matrix to track dual outcomes for various NL West and NL Wild Card combos (and ties!).

Before we get to the matrix, I want to explain an important simplifying assumption I had to make in order to make the sample space manageable: I am not going to include the Milwaukee Brewers (89-67) or Chicago Cubs (91-64) in my analysis since I will be assuming (for now) that they both will make the playoffs without issue.

Given that both teams have at least a 99% chance of making the playoffs according to FiveThirtyEight, that hopefully shouldn’t be too controversial, but just to cover all my bases I’ll explain the scenarios where this assumption would break down.

The Cubs are in an extremely good position to make the playoffs at 4.5 games ahead of the Cardinals and Dodgers and 6 games ahead of the Rockies, so the only way they would not make the playoffs outright would be if they went 1-6 or worse while the Rockies and Dodgers both simultaneously went 7-0 and 5-1. Given that the Cubs play 4 games against the Pittsburgh Pirates this week, the chance of this happening is so absurdly low it’s not worth considering.

The Brewers are also in a very good position to make the playoffs at 2 games ahead of the Cardinals and Dodgers and 3.5 games ahead of the Rockies, but their situation is a bit more precarious because they are playing the Cardinals on the road. Namely, if the Brewers are swept by the Cardinals this week (unlikely but possible), suddenly the Brewers could become in danger of missing the playoffs entirely and it would come down to their performance in their final series against the Detroit Tigers and how well the Rockies play.

So although I didn’t include the Brewers in the analysis at this stage, I will certainly have to add them in my mid-week updates if they do start losing. For now, I’m thinking of them as basically being guaranteed to win at least 3 games (which isn’t hard to imagine given they play 3 games at home against the Tigers), which makes them unlikely to be the team the Rockies would oust from making the postseason (as they’d have to win out to tie them).

So now that we’ve taken care of the caveats, we are ready to discuss how to build the matrix to track which of the Dodgers and Rockies will win the NL West and then which of that other team and the Cardinals will win the NL Wild Card for every possible record that the three teams can have over the final week. Since each cell needs to encode both an NL West winner and an NL Wild Card winner, I have used a vertical bar where the left-hand side is who would win the NL West in the given scenario and the right-hand side is who would win the second NL Wild Card. In the case of ties, I used a hyphen for the tying teams.

Since each cell is containing these multiple possibilities, to aid in the visualization I have also used a nifty gradient effect to show the winners. (With only two-color gradients at my disposal it was a bit of a struggle to capture the tying. scenarios, but I did my best...)

Here are the 10 scenarios and their descriptions:

I understand that this is a lot to take in, so the first thing I want you to note is that of these 10 possible scenarios, only the top one (“LAD | STL”) is very bad news for the Rockies. Every other scenario in this chart means that the Rockies would play beyond Game 162 in either a tie-breaker or make the playoffs outright, so keep that in mind when looking through the rest of the article.

Note also the various tying scenarios for the NL West come in three flavors depending on the Cardinals’ record:

If the Cardinals have a better record than the NL West tie, then you get the “COL-LAD | STL” option which means the loser of the Rockies @ Dodgers Game 163 would miss the playoffs entirely. If the Cardinals have a worse record than the NL West tie, we have the “COL - LAD” scenario and the Cardinals would be eliminated outright, and the loser of the Rockies @ Dodgers Game 163 would be the WC winner. Finally, if the Cardinals have the same record as the NL West tie, then we would get the zany three-way tie scenario “COL-LAD-STL” where the loser of the Rockies @ Dodgers Game 163 would go to St. Louis to play Game 164 that would decide the WC winner.

The last thing I will note is the final option “LAD | STL & COL” – the only time I include the Brewers in this analysis, thereby breaking my own assumption. However, this scenario was necessary because it would be what occurs in the crazy situation where we go 7-0, but the Cardinals go 6-0 and the Dodgers go 6-0 (i.e. the bottom-right-most square in the matrix below). If this were to happen, the Cardinals going 6-0 would guarantee the Brewers go at best 3-3 and finish with at most 92 wins, ensuring the Rockies would at least tie the Brewers for another WC spot even though they never caught the Dodgers or Cardinals.

So this scenario shows us the Rockies do still completely control their own destiny – even if the worst possible outcome (Dodgers 6-0 and Cardinals 6-0) were to occur, they can still make the playoffs by winning all of their own games.

Of course, none of this is at all likely to happen, but hey, there is something comforting about not actually needing to rely on anyone losing to make the playoffs.

Now that we have all the scenarios down, we are ready to construct the full matrix showing when each scenario would arrive for a given record combination of the Dodgers, Rockies and Cardinals.

Unlike in 2017, none of the three teams are playing each other so there are 392 (8 * 7 * 7) record combos possible, and that is how many cells are in the matrix below.

One thing misleading about trying to use the matrix in this form to determine how likely various scenarios are is that not all cells are equally probable to occur – records like 7-0 are much harder to have than records like 4-3, so fringe results are over-represented.

Therefore, the best way to contextualize these outcomes is to compute the joint probability of every cell, which means finding the probability that each team ends up with every possible record combination.

Using game probabilities from FiveThirtyEight, I simulated each of the 3 teams’ records over the final week 1 million times and computed the joint probabilities, which I put inside the cells of the matrix below, and included the marginal probabilities for each row and column on the sides of the matrix.

Then, I rolled these joint probabilities up to compute the chance that each of the color-coded scenarios would occur and included that in the table on the upper right.

Finally, taking any tiebreaker games as 50-50 coin flips, I also computed the probability of various “COL Results” to give the final probability of the Rockies making the playoffs and winning the division when all is said and done. Note that my results agree with FiveThirtyEight (as they should since I used their game probabilities) in giving the Rockies a 21% chance of winning the NL West and an 39% chance of making the playoffs.

But there are some more interesting takeaways from the scenario breakdown - note that there is only a 50% chance that our season ends after Game 162, and there is nearly a 30% chance that we are involved in some type of tiebreaker, including a 4% chance of the three-way tie.

Finally I derived what I find to be the most useful output: the conditional probabilities of the various scenarios and COL results given the Rockies records over the final week.

Because at the end of the day that’s kind of what we’re all wondering – if the Rockies go 4-3 or 5-2 is that likely to be good enough? Or do they need to go 6-1 or 7-0?

As the table above shows (and as one would expect), a record of 3-4 or worse is bad news for our playoff chances, although 3-4 is still not quite as bad as I’d expect, since we’d still have a 15% chance of playing in at least a tie-breaker.

At 4-3, we’d have a worse chance than our chance right now (that shows that the game probs are bullish on the Rockies winning slightly more than 4 games on average), so 5-2 is where things start to get very interesting.

At 5-2 we’d have an 83% chance of controlling our own destiny and playing at least a tiebreaker, and we would interestingly have roughly equal chances (33%) of winning the NL West, winning the NL Wild Card and missing the playoffs.

At 6-1, we would be in a very good situation – 64% chance to win the NL West, and a 98% chance to control our own destiny, and that last figure is actually low given that I’m not including chances that the Brewers lose more than 3 games (which would be likely if the Cardinals went 5-1), so in some of those 2.25% “LAD | STL” situations we actually tie or pass the Brewers and still make the playoffs.

At 7-0, as mentioned earlier we have a 100% chance of controlling our own destiny, and an 88% chance of winning the NL West.

So: the ultimate conclusion: At 5-2 we have a good shot to play beyond Game 162 and if we can do better than that, we should expect Rocktober.

As the games come in this week, I will update this article with the new matrices to show how the probabilities change so be sure to keep checking back here throughout the week!

UPDATE: Sunday Morning, Sept 30

Rockies: (5-1); Dodgers (3-2); Cardinals: (1-4)

On Saturday, the Rockies finally had a bad day for the first time in over a week as the Dodgers beat the Giants 10-6 and the Rockies got destroyed by the Nationals 12-2. The Cardinals also won, something that is inconsequential for our purposes as the Dodgers win eliminated them (although that win did impact the NL Central race). Even though they no longer matter, I will still include them in the main matrix for consistency’s sake.

The Rockies and Dodgers are now tied on the final day of the season, and there’s now a little over a 50% chance that we play the NL West tiebreaker game in LA on Monday. Of the two remaining scenarios, the Dodgers are slightly more likely (27% vs 22%) to win the division outright given that 538 thinks that they are a bit more favorable to win today (61% vs 56%).

In the above matrix I have included two versions that give different results for the Rockies’ NL West probs: one with the Rockies having a 50% chance of winning the tiebreaker, and the other with the Rockies having only a 33% chance of winning the tiebreaker.

Since it’s been announced that if we do play the tiebreaker German Márquez will be on the mound, I really think that our chance in that game should be closer to 50% even though the Dodgers will counter with Walker Bueheler, but I include the 33% scenario as that appears to be the win probability for the game that 538 is using (as I can now solve for it exactly because they give the Rockies a 39% chance of winning the NL West, and that is what the tiebreaker would have to be for that to happen).

We control our own destiny in the narrow sense that if we win today and tomorrow we win the division, but let’s hope that we get lucky today and have one final optimal day to win the division outright.

UPDATE: Saturday Morning, Sept 29

Rockies: (5-0); Dodgers (2-2); Cardinals: (0-4)

Yesterday was yet another great day as the Cardinals lost again and the Rockies beat the Washington Nationals for their eighth straight win, clinching a postseason spot and thus officially vanquishing all scenarios that involved them possibly missing the playoffs. Even though they had a 97% chance of making the playoffs before the games started, there is still a huge relief associated with actually clinching and knowing that no heart-breaking collapse is possible to end up at home for the postseason.

Notice that the matrix is suddenly dramatically less red, and that is because today was a really bad day for the Cardinals since the Dodgers also won – the Cardinals’ only path to the playoffs now is to win the next 2 while the Dodgers lose the next 2 and then to win the Game 163 tiebreaker.

As much as we would all love to see this happen, realistically the Cardinals are probably done, so the 3 team race for 2 spots is now effectively a battle of two teams to win the NL West.

Despite the Rockies win today, notice that our NL West probability barely improved, and that is because the Dodgers winning the game of the three that they were least likely to win against the San Francisco Giants all but neutralized our good outcome.

The Dodgers are heavy favorites for the final two games of that series, and are thus almost ~40% likely to sweep at this point, so we will likely have to take care of business ourselves to clinch the West. Doing this against Strasburg and Scherzer will not be easy, and note that 538 doesn’t know Scherzer is probably going to pitch, so our probabilities for Sunday would be much lower if that was confirmed, which may mean that our chance at winning the West actually decreased from yesterday despite our victory.

If we go 0-2, then we only have a 10% chance to win the division without going through Game 163, and have a ~40% chance of finishing behind the Dodgers after Game 162 (not ideal).

If we go 1-1, that gives us a 60% chance to win the West outright, and guarantees us a divisional tiebreaker in that 40% chance the Dodgers sweep.

Although 2-0 seems like too much to ask for after 8 straight wins, it is honestly probably necessary if we expect to win the NL West without a high chance of playing a Game 163.

In the end, the situation is also simple enough that our magic number of 2 tells you all you need to know: in the 4 remaining Rockies and Dodgers games, if 2 or more go our way we win the NL West, if 1 goes our way we play the Game 163 tiebreaker, and if 0 go our way we lose the division outright.

UPDATE: Friday Morning, Sept 28

Rockies: (4-0); Dodgers (1-2); Cardinals: (0-3)

With the Cardinals and Dodgers off, the Rockies held on for a 5-3 victory to complete the 4-game sweep of the Phillies, giving them a 2 game lead in the WC and a 1 game lead in the division with 3 to play.

They’ve now cleared off the matrix of almost all of the bad scenarios, and the only way they could now have their season end after Game 162 (i.e. the dreaded “LAD | STL” scenario) would be if they go 0-3 while the Cardinals go 3-0 and the Dodgers go 2-1 or 3-0. The chance of this happening is down to 0.50% (recall on Monday it was a staggering 100 times more likely to occur: ~50%)!

Now, even going 0-3 gives them an ~80% chance of making the playoffs and a 94% chance of still playing at least a tiebreaker, but if they can even go 1-2, this will guarantee them a WC tiebreaker and give them a ~60% chance of the division.

At 2-1, they clinch the playoffs and at least a division tiebreaker and would have an ~80% chance of winning the division outright, so really one final series victory is all that is likely to separate the Rockies from their first-ever division title.

UPDATE: Thursday Morning, Sept 27

Rockies: (3-0); Dodgers (1-2); Cardinals: (0-3)

Amazingly, for the second straight day the Rockies had another ‘optimal day’ where the Dodgers and Cardinals both lost, and they absolutely eviscerated the Phillies.

Things are suddenly looking very good for the Rockies, with a ~97% chance to play beyond Game 162, a ~93% chance to make the playoffs and a ~64% chance to win the NL West.

Note that the truly dreadful scenarios are gone – even if they go 0-4 (although let’s please not), they would still have a 60% chance of playing beyond Game 162, and going 1-3 would still give them an 94% chance at this, and an 80% chance at making the playoffs.

At 2-2, they have a 100% chance at playing beyond Game 162, a 98% chance at making the playoffs and a ~60% chance of winning the division (although the most likely single scenario would be the divisional tiebreaker).

At 3-1, they’d be guaranteed the playoffs and at least a division tiebreaker, as it would force the Dodgers to sweep just to tie.

One thing to notice is that the Cardinals are underdogs in their remaining three games against the Cubs while the Dodgers are favorites, so if you add up the marginal probabilities you can see that the 1.5 GB Cardinals have only a ~9% chance of sweeping the Cubs while the 0.5 GB Dodgers have a ~20% chance of sweeping the Giants.

So the Rockies are probably in a safe place for the wild card barring their own collapse, but they’ll have to keep the pedal to the metal if they want to win the division outright.

UPDATE: Wednesday Morning, Sept 26

Rockies: (2-0); Dodgers: (1-1); Cardinals: (0-2)

Tuesday turned out to literally be the optimal day for the Rockies, as they dominated the Phillies again 10-3, the Cardinals got blown out by Milwaukee 12-4 and the Dodgers lost 4-3 on a walk-off to the Diamondbacks. And for good measure, the Cubs also lost to the Pittsburgh Pirates for the second straight day to put them only a half-game ahead of the Brewers, which is great for the Rockies as it makes it more likely that the Cubs will play the Cardinals this weekend with a greater sense of urgency.

With all these outcomes going their way, everything about the matrix improved for the Rockies – they now have almost an 80% chance of making the playoffs, an 88% chance of playing after Game 162 along with nearly 40% chances each of winning the NL West and the NL Wild Card.

With 5 games to play, if they can even go just 3-2, they would only have 2% chance of their season ending after Game 162, and a 90% chance of reaching the playoffs in some fashion.

Going 4-1 would make the playoffs all but guaranteed and give them a ~70% chance at the division, although interestingly the most likely outcome in that scenario would be a tiebreaker game in the “COL – LAD” scenario.

And if they can somehow go 5-0, that would now not only guarantee them a playoff spot but also at least a tie for the NL West crown (along with an ~88% chance of winning it outright).

UPDATE: Tuesday Morning, Sept 25

Rockies: (1-0); Dodgers: (1-0); Cardinals: (0-1)

The Rockies had a dominating victory against the Philadelphia Phillies and the Brewers rallied to beat the Cardinals, so everything was shaping up to be an optimal day for us until the Arizona Diamondbacks blew a 7th inning lead against the Dodgers.

Alas, the Cardinals loss puts us in a better place to make the playoffs – we now have a ~55% chance to make the playoffs, and a ~67% chance of playing beyond Game 162.

And if we can go 4-2 to finish the week 5-2, we have a ~75% chance of making the playoffs and an ~88% chance of at least playing beyond Game 162.

The NL West probabilities took a bit of a hit with the Dodgers’ win, so we really need some help for the Diamondbacks. One hopes that they will be able to avoid the sweep and an ugly 1-8 final homestand, but in all honesty they look so bad right now that it’s hard to see anything other than a Dodgers sweep.