How often does leadoff man get a hit?

The other day at the pub there was an argument whether Joe Maddon preferred beer or wine.  Since he is spokesman for Binny’s Beverage Depot holding a glass of wine people thought that was proof of his preference for wine.   That led to a question about the Binny’s leadoff man promo:  How often does the leadoff man get at hit?

Since I don’t get event data for this year until December from retrosheet.org I can’t tell.  Luckily there’s this site called Google that has answers to every question imaginable.  Here is  current year data according to Binny’s Beverage Depot.

binnys2

As of August 10 the Cubs played around 114 games so 28/114 = 0.245.   Binny’s has a payout ratio of around 1/4.  If you were to bet the Binny’s leadoff man promo this would be good to know.  It seems low however.   Usually managers put the hottest hitter in the leadoff spot because the leadoff hitter bats the most.  Mathematically you want your best hitter to get the most plate appearances.  There are always exceptions.

The 0.245 above is not a batting average and since retrosheet.org does not publish current year event data until December we don’t know how many walks there are this season at the leadoff spot.  We know there are always exactly 0 sac bunts and sac flies for the first batter in every game.  We have event data from past years.  Here is a table compiled for the year 2017.

Year Hits Binnys % CUBS BA LEAGUE % LEAGUE BA
2017 41 0.253 0.270 0.243 0.265

Second column shows Binny’s paid out on 41 hits with a win % of almost exactly 1/4.  The  LEAGUE % column is if Binny’s had to pay out for every team in every 2017 game.  It is lower than the Cubs which should be expected because the Cubs had a good team last year.

The fourth column incorporates walks into the BA stat and it’s 0.270, also higher than league average.  But what does this mean?  There are a bunch of tables In Part 5 of our OPS series.  Scroll down to second table and you will see the average league wide BA from 2010 – 2017 is 0.262 which is almost matches the LEAGUE BA column  above.

What does that mean?  I don’t know.  Here is a complete table from 2010 – 2017.

Year Hits Binnys % CUBS BA LEAGUE % LEAGUE BA
2010 33 0.204 0.213 0.238 0.258
2011 49 0.302 0.327 0.241 0.261
2012 40 0.247 0.265 0.242 0.262
2013 37 0.228 0.245 0.236 0.257
2014 40 0.247 0.263 0.244 0.263
2015 35 0.216 0.240 0.244 0.262
2016 52 0.321 0.382 0.260 0.284
2017 41 0.253 0.270 0.243 0.265

One of the baseball constants used in this data model is  1 game = 38.4 plate appearances.  PA is a measure of playing time and that’s how you convert PA into games.  Pitchers have a baseball constant used forever which says that there are exactly 9 innings to a game.  A game is not always 9 innings but they kept the math simple because they didn’t have calculators when Ted Williams played.  In the end it doesn’t matter.  Nine innings/game is close enough just like 38.4 PA/game.

The leadoff hitter then represents 1/38.4 = 0.026 = 2.6% of all plate appearances.  This lack of data leads to a large year to year variation in payouts which you can see in the above table.  Binny’s had to payout almost a third of the time in 2016.

Not sure what the above is supposed to mean however.  New series with the Brewers tomorrow so we’ll have a look see into their team.  Until then ….