Baseball

My previous mathematically-oriented baseball posts

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I’ve been away for a while.  But I’m returning.

Where have I been the past year?  Mostly over here, and sometimes commenting over here.  But during that year, I’ve done a lot of mathematics to study questions I had about the baseball I was reading about and following, and some of that has filtered into some of those posts.  I thought I’d provide a selection here of some of the more interesting ones.  Some of these contain hints to posts I plan on putting up here in the coming weeks, posts that will include discussions of the math of streaks, and just how much a small sample size actually tells us.  There will be other new topics too, not previewed in any of these posts.  Stay tuned.

Here is that selection of my mathematically-oriented posts of the last year or so:

A post from August 2014 explaining why batting 15 points above league average is sometimes actually hitting at league average. This in the context of examining one upcoming player.

A comment titled “Expected frequency of reverse platoon splits exceeds the actual numbers” to the article “Are reverse platoon splits sustainable?” on Beyond The Box Score. In this comment (scroll to the bottom of the comments section) I used binomial theory to come up with what would be the expected number of players, based on random chance alone, having a reverse platoon split in on-base percentage for the years 2012 and 2013. I show that the actual numbers were less than the numbers you’d expect by random chance, seeming to indicate that reverse platoon splits are unsustainable.

A comment titled “No, because starters face more batters” to the article “The Hidden Perfect Games of Relievers” on Beyond The Box Score. In this comment (scroll to the next-to-last comment), after making two points about the right way to compare starters and relievers for the purpose of the article, I discussed my first attempts at producing an expected number of “wrap-around” perfect games that will occur in a given season for starters and relievers, to help clarify any meaning that might be attached to the reported results. I did complete that work, which I plan to publish later on this blog, in a post about the math of streaks.

A post from September 2014 that argues that a certain young player is better than his overall numbers say he is, by analyzing his advancement as a hitter at each new level he played at.

A post from September 2013 explaining why one baseball team’s chances of making the playoffs were ridiculously close to, but not quite exactly, 100%.

A post from later in September 2013 which explains (in more detail than anyone probably cared to read) why that same baseball team’s chances of having home-field advantage were about 7 out of 11 (washing dishes at night gave me a lot of time to listen to baseball and think about this stuff).

6-team AL wildcard race now looking like a 3-team race

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It’s been exciting watching the wild card race in the American League evolving these last couple of weeks, with 6 teams having a real shot.  With division leaders pulling away, making the division races relatively uninteresting, and with the National League’s 5 playoff entrants pretty much a done deal (with only positioning remaining a question), this race has provided most of the late-season playoff race drama.

But as we approach the last week of play of the regular season, 3 of those 6 contending teams now look like outside longshots.

Each of these 6 teams has either 7 or 8 games remaining in the season.  It’s not likely that any of them will lose more than 3 or 4 of these remaining games.  However, the Yankees, Orioles, and Royals, each with 73 losses, will require at least two of the Rays (now at 69 losses) , Indians, and Rangers (70 losses each) to lose 3 or 4 games just to have a chance at tying.  Were the Indians and Rangers both to lose exactly 3 of their remaining games, one of the 73-loss teams would have to win all their remaining games just to tie.  Not unheard of; the 2007 Rockies faced this sort of scenario with just over 2 weeks to go that season, needing to win their last 15 games to make a wild card berth probable; they won 14 of those 15 to tie for the wild card and force a one-game playoff for the spot (which they won).  These streaks would be half as long, and with 3 teams poised to try for it, it’s not too out-of-the-question that one may do it.

At this point, scheduled opponents can make a big difference.  The Orioles seem to have the short end of the stick here, with 2 of their remaining 8 games against the Rays (who are fighting to keep their slim wild card lead). and 3 against the Red Sox (who will likely be trying to maintain their lead for home-field advantage against the other division leaders, Detroit and Oakland).  The Yankees also have 3 games against the Rays, but otherwise have an easy schedule, with 3 games against the bottom-dwelling Astros.  The Royals seem to have the best schedule of all though, with today’s game against the Rangers their only one against a contending opponent.

Though the Rays have the best record right now by a slim margin, if the Yankees or Orioles make a charge now, the Rays’ position in the standings will fall rapidly, while the Rangers and Indians, with easier schedules, would most likely stay put at the lead of the wildcard race.  Unfortunately for the Yankees and Orioles, this would only allow them to leapfrog one of the three leading teams; not enough to take a wildcard berth.

In the end, two of the 3 leading teams must falter, and that just doesn’t seem all that likely.  The Yankees, Orioles, and Royals are all positioned to make it interesting by winning, but won’t likely catch a wild card berth even if they do.