THE BOOK--Playing The Percentages In Baseball

That was a great catch.  FWIW, that doesn’t happen in the WPA spreadsheet.  I must be applying your math differently.

You can generate the WE tables empirically.  Although that can result in some quirks as well with states with very small N, it still is useful to have for comparison purposes.

It is useful, but, you will get ALOT of quirks, especially if you use single-year only.

Click on my name for empirical that spans multiple years.

This link is also useful:
http://www.tangotiger.net/innwin2.html

No, a single year is not very useful.  But if the run environment doesn’t change drastically, it is possible to get multiyear runs that generate sufficient N for almost all states.  I think it is important not to assume that all differences between empirically generated tables and simulation generated tables are due to the sample size problems of the empirically generated tables.  Some (like the example above) have strategically related logical reasons for occuring.

Personally, I think there are too many problems comparing empirical tables to tables generated by math.  The sample sizes in cells vary too much, even with five years worth of data.  You can certainly assume that not all the differences are due to sample size, but which results should you assume that for?

To me, the “sanity check” is the best approach, a in the linked thread, or perhaps checks between tables generated two different ways (such as my spreadsheet and Tango’s tables).

Few people, least of all me, would assume “all differences”, applies to anything.

It’s rather clear what the differences are, with first and foremost being the sample size.  Other differences are the quality of players in each batting slot, the use of relievers in close/late situations, and the strategic use of small-ball weapons.

When I run my sims, I need to run 1 million trials to get the win percentage to less than .001.  This can be easily shown by sqrt(.5*.5/1,000,000) = .0005.  So, 95% of the time, you’ll get it to within .001.  And with my process, I only need it to generate the 24 base/out states.

If you go to “multi-years” with a similar run environment, you are still at only 20,000 games played, but certainly not each of the thousands of states will have 20,000 observations.  You’re talking more like 1000 observations, using 5-year data, if you are lucky.  That gives us the 95% band of +/-.032 wins.

Clearly what needs to happen is a better understanding of when/how relievers and small-ball strategies are used, and incorporate those as states and figure out the appropriate event-frequencies and state-to-state transitions.

I’ve long thought that a systematic comparison of empirical WE results with mathematically-based WE results could be very interesting.  To avoid small n problem, you’d want to focus on inning/score categories, not specific states—for example, how often does the home team win when up by 1 run at end of 8, vs. how often ‘should’ the home team win?  Up by 2 after 7?  The first thing you would need to correct for is quality of the teams, as teams with a lead would tend to be better.  But after that, I would think it could shed some light on how effective modern bullpen usage is.  Might also be interesting to see if there have been changes over time.

Guy,

You can answer the question yourself, as I provided a link to answer that very question.

http://www.tangotiger.net/innwin2.html

If you click that, you will get not only the empirical, but also the Markov/probability numbers as well.

I should also mention that batting order plays a role.  In the second inning, it’s the bottom of the order that is due up, so when you do the comparisons, you have to be aware of that.