As October gets closer and closer, baseball fans have some shopworn sentiments to trot out:

  1. This is the exciting part of the season—there’s a lot more tension as teams jockey for position.
  2. Or it would be, if it weren’t for that gall durned wild card.

Players and teams that perform well down the stretch are viewed as clutch, because later on in the season the games allegedly matter more. But do they really? And has the wild card really drained the drama from the stretch run?

Logic would suggest that the number of games you win matters far more than the order in which they are won—to the extent that games late in the schedule seem more important, it’s because it’s far more apparent at that point how many games a team needs to win in order to make the playoffs.

It’s also far more apparent which teams are in the playoff hunt at all, which leads to a counterintuitive finding—it’s actually the games early on in the season that have the greatest effect on a team’s playoff chances. To measure a team’s playoff chances, we can simply look at a team’s position in the standings after each game and see how often teams in similar positions made the playoffs.

What we see is that very early on, teams are lumped into two groups—contenders and non-contenders. Around seventy games into the season, half of all teams have odds of winning the division below ten percent, and over three quarters of all teams have odds of winning the division below thirty percent. The remaining teams have division odds squarely between sixty and seventy percent. The handful of teams still contending can see their playoff odds shift dramatically, but the teams at the bottom typically don’t have odds that are going to move much at all.

So, games later on in the season can be more dramatic—for teams that are in the race. But for many teams, the race ended back in late May or early June, and late-season games aren’t exciting at all. Therefore, the “average” team sees a lot more excitement early in the season, because with only a few games on the books, nobody can put together an insurmountable lead. What’s interesting to note is that as you progress through the season, you see fewer and fewer average teams—teams will move to one end of the spectrum or the other fairly quickly, and teams in the middle are rare to nonexistent.

There are two reasons for this. The first is that teams that get out to a lead early tend to be better than teams that fall behind early. Notice I said tends—there are certainly good teams that stumble out of the gate and recover (like the Red Sox this season, for instance.) But they’re less common than teams that stumble out of the gates and then continue to stumble for the rest of the season. If you give better teams a lead, they tend to hold onto them; they don’t even have to play better than the other teams the rest of the way, because they already have a lead. The other reason is that teams in contention behave differently—they make deadline deals, they’re more likely to start the service time clock of a top prospect if he fills a need, and so on. Teams out of contention are more likely to deal away players for prospects and to try “playing the youngsters” in preparation for next season.

How does adding the wild card to the mix change things? The obvious effect is that more teams make the playoffs, and so more teams are competitive in some sort of playoff race later in the season. This means the average change in playoff probability for any given game is higher—introducing the wild card increases the average change in playoff probability for a single game from two percent to three percent.

Even after we control for that effect, we see the wild card boosting the volatility of a team’s playoff odds late in the season. Looking at the average change in a team’s playoff odds percentage (on the y-axis) by days into the season (on the x-axis), both with and without the wild card:

Looking just at a team’s division odds, we see a pronounced dip right around the 120-game mark, following a long and steady decline. After introducing the wild card, we still see the long and steady decline, but instead of plummeting after 120 games, the volatility in playoff odds stays much steadier through the end of the season. Looking at the last forty-two games of the season, there’s roughly 20 percent more movement in a team’s playoff probability with the wild card than without it.

So if one wild card makes late-season games more interesting, what would a double wildcard do? If we assume the second place wild card team would have also gotten a playoff berth, we can look at how our leverage index shifts:

Having a second wild card tracks very closely with having a single wild card; you end up with additional playoff teams, so in that sense a larger number of fans are invested in the playoff race. But in terms of uncertainty of outcome, a second wild card would have no effect; it wouldn’t increase the impact of late-season games relative to early-season ones.

A version of this story originally appeared on ESPN Insider Insider.