The fallacy of the maturity of baseball chances is the belief that because your favorite team has lost more frequently than expected in the past that the team is more likely to win in the future to restore balance to The Force. The underlying assumption is that the past team and the present/future teams are similar enough in constituency that maintenance of this belief isn't largely a function of improved components.
Depending on your source of choice the Cardinals have a 2-2.5% chance of making the playoffs. The numbers are based on algorithms, 1000's of simulations, and 2 kids from Hufflepuff rolling a 21-sided die on the floor of a bamboo hut. Mind you, those chances are just to get a foot in the door which does not guarantee a seat at the cool kids table.
Playoff odds aren't terrible predictors, and they do have a modicum of science behind them. Half of that sliver of science is based on probability which I'm choosing to bastardize and distort to my own liking. I don't actually know probability theory at all, but I did fall asleep in the parking lot of a Holiday Inn Express one night. At least I think I probably did. Odds are fairly good that I did. Well they probably are. Whatever.
Probability is the likelihood of an event happening.
Probability does not care about historical precedence. Today's results and tomorrow's results are statistically independent of previous outcomes as well as each other. The odds of winning tomorrow aren't changed by the win/loss outcome of today's game. The chances of winning tomorrow may be impacted by today's injuries, weather, reactions to winning/losing and a whole host of other things but not by winning or losing.
The probability of a team overcoming a 7 game deficit in the last 15 games of the season to win their division are the same whether they've done it before or not. Hint: The probability is very, very not good.
If you roll a die and get "6" on 5 consecutive rolls, the chances of rolling a "6" on the next roll are 1 in 6. That's probability. It's not the be-all and end-all. At least that's what William Shakespeare wrote in the second issue of Baseball Prospectus in 1604.
According to the law of large numbers, the larger the sample size the closer the average of the results should be to the expected value. I refer to this as "much more results make more better accuracy". Winning 3 of the first 5 games isn't a solid indicator of the probability that the team will play .600 ball the entire 162-game season. Winning 30 of the first 50 games is a slightly better indicator, and winning 72 of the first 120 is even more better. So if .600 is the expected value, then maintaining exactly that pace is as close to the expected value as you can get. Even so, that 72-48 record only indicates that there is a relatively high probability of finishing close to .600.
Similarly, a team that is 51-51 has a significantly higher probability of finishing at .500 than it does at .600. Conveniently, a .500 team at this point in the season lends itself to the application of a very crude version of the coin flip probability calculation mechanism. That is to say that the outcome of each game averaged over the last 60 games has a higher likelihood of resulting in a 30-30 record than any other single record pairing possible. For 60 games the probability of getting exactly 30 wins in a coin flip reality is 10.26%. The probability of getting something other than 30 is obviously higher, but 30 is the peak of a symmetrically distributed mountain.
Obviously, baseball isn't a coin flip. Thank goodness for that.
The Mets (54-47) are currently in possession of the 2nd Wild Card spot in the NL and improving as I type this. Consider their win rate applied over the balance of the season with the result conveniently rounded down because I'm a petty tyrant about such things, and their projected final record is 86-76. It's possible that the Cardinals can catch the Mets. Plausible even.
The problem is that it isn't just about catching and/or passing the Mets avec Baez. The Cardinals also have to catch the Reds and outrun both the Phillies and the Braves. It's reasonable to argue that if the Cardinals take care of business that they will simply take what is not given. It's equally reasonable to argue that the other teams can do the same, and there are more of them than there are of the one.
The real obstacle in arguing either side to a satisfactory conclusion is that the final results are a combination of independent and non-independent events. The teams in question play against one another, and that complicates matters. The fact that they don't play each other in a round-robin fashion with equally fair pairings makes it practically impossible to promote meaningful discussion about predicting this particular set of futures.
If I had to arbitrarily choose a starting point for what ultimately seems like an incredibly boring circular discussion, I'd take strength of schedule. The Cardinals play a lot of games in August against the Royals, Pirates, Tigers, Pirates, and the Pirates. Unfortunately, September is stacked with a series against the Mets, a series against the Padres, 4 games hosting the team that employs Trevor Bauer, and 38 games against the Brewers.
The flaw in this particular starting point is that strength of schedule is based on what has happened which preceded a bunch of other things happening. Some teams are worse off than when they played the Cardinals. Some are better. A Pirates team that was already awful doesn't help the Cardinals a lot by getting worse. The Cubs are a different story, and the Cardinals play them 7 times in the last 10 days of the season. The Royals are probably worse than their record suggests after dealing Danny Duffy, and that could result in two extra games in which the Cardinals face someone who isn't as good as Danny Duffy.
Feel free to play this game at home. Microadjustments are fun for the whole family. They are also difficult to quantify unless you consider "bad to worse" a quantification somehow. If nothing else, you may choose to selectively bias yourself by favoring August over September or simply by finding whatever bias floats your baseball boat.
You may tell yourself that getting Mikolas and Flaherty back will boost the Cardinals in a hurry. There could be a lot to that since both are starting pitchers and neither is named "Oviedo". It's like trading for two All-Stars and such. It's possible that the Cardinals could have actually traded for two All-Stars in the traditional way. Maybe they should have. Maybe not.
Former minor league shortstop and NASA astronaut Ralph Waldo Emerson once wrote that "A foolish consistency if the hobgoblin of little minds, adored by little statesmen and philosophers and divines." He was referring to reluctance or refusal to adjust one's thinking based on new information revealed by the passing of time.
At the end of May when the Cardinals were part of a tug-of-war for the division, entertaining the possibility of making deals made a lot of sense. After a 10-17 June doing so probably made a little less sense. Nearing the end of a mediocre July and having gained practically nothing or less than nothing, the Cardinals have even less time to overcome deficits than they did back in May or June.
This is where the "foolish consistency" thing applies. As odds get worse, it's a bad idea to keep making the same bet or any bet at all. It's like Blackjack. If you find yourself in desperate need of an ace but know that at least 21 aces out of a 6-deck stack have already appeared 1/3 of the way through the stack, you don't bet on pulling an ace. Or at least you should be aware that odds are astronomically worse than they were immediately after the shuffle. If you don't know that, then you probably should avoid gambling altogether to be honest, and you definitely shouldn't take out a second mortgage to cover a larger bet.
The Cardinals find themselves in an even worse position. They are nearly 2/3 of the way through the stack, the already small number of aces is dwindling with every passing minute, and snagging one doesn't even guarantee them a win. They CAN still snag one though. The cost is really high and time is short (35 minutes). The probability of the best possible outcome is incredibly low. Considering all this in addition to the moves being made by other teams, I find it difficult to criticize them for opting to become conscientious objectors this year.
But some will because they set the lofty expectations they never properly adjusted, and they will air their frustrations replete with profanities and vulgar, personal attacks on their MySpace pages.
That's where the Gambler's Phallusy comes into play. You have to be a real dick to expect a management team to bet all its chips on really long odds and trash them when they don't.