## Xander Bogaerts back on pace to reach 200 hits, win AL batting title

Back on Wednesday morning, I showed that Xander Bogaerts and Miguel Cabrera were hitting at paces that would cause Bogaerts to (most likely) surpass Cabrera for the AL batting title. Though I didn’t mention it at the time, these projections also showed that he’d reach 200 hits even if he sat out a couple of games, and a few more than that if he played all the remaining games. After a pair of low-hit games knocked Bogaerts off that pace, his 3-for-4 performance last night has put him right back on it.

In trying to project future totals using “the pace at which a player is producing right now”, how many games do you use to determine what that pace is? The last 5? The last 10? 20?

I circumvent that question by using all of them … I calculate his pace of production over his last 5, 6, 7, 8, etc. games, then use that pace applied over the remaining number of games to be played to see what final numbers he’s headed for. This gives a big collection of possible final numbers; you then choose one in the middle.

On Wednesday I did that for Cabrera and Bogaerts using their paces of production as established by their last 8, 9, 10, etc. up to their last 20 games. That gave 13 paces of production for each player. I then applied these to their remaining games assuming they’d not sit out any games, and then again assuming they’d each sit out two games. I got these results:

If playing all remaining games
Bogaerts Cabrera
Low 0.327 0.324
Median 0.329 0.326
High 0.332 0.331
If sitting out two games
Bogaerts Cabrera
Low 0.327 0.326
Median 0.329 0.328
High 0.331 0.332

In all but one of these 26 projections, Bogaerts would end up with at least 200 hits.

I just updated these numbers, and now they look like this:

If playing all remaining games
Bogaerts Cabrera
Low 0.327 0.325
Median 0.329 0.326
High 0.330 0.332
If sitting out two games
Bogaerts Cabrera
Low 0.327 0.327
Median 0.328 0.328
High 0.329 0.332

Here are Bogaerts’ projected numbers of hits:

Bogaerts projected 2015 hits
# of recent games used If playing all games If sitting two games
20 204.0 200.8
19 203.3 200.2
18 203.0 200.0
17 203.3 200.2
16 203.6 200.5
15 204.0 200.8
14 205.1 201.7
13 204.9 201.5
12 203.8 200.7
11 204.4 201.1
10 204.0 200.8
9 204.7 201.3
8 204.3 201.0

Longer term projections (based on his last 40 or more games) almost all have him finishing with 200 hits exactly if he sits out 2 games, 203 hits if he plays all remaining games, and a .327 average.

If they play it out, and stay on pace, Bogaerts probably will win the batting title and will get to 200 hits.

Thanks to Baseball-Reference.com for the gamelog data I used for this article.

## My previous mathematically-oriented baseball posts

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).