THE BOOK--Playing The Percentages In Baseball

You probably need HUGE amounts of FTA to see anything.  You’re looking for maybe a difference of 1 in 1000.

If you had 100,000 FTA on each side, the SD of the difference would still be 2 in 1000.

So I mean it more theoretically than practically.

Let me ask Justin anyway, and see what we can get.

King Yao left some numbers in the comments to my post.  There’s a .002 to .003 HFA in the first three quarters, but a negative HFA in the fourth quarter.

That’s on roughly 125K attempts per team.

The overall numbers were somewhat in line with your expectations!

Yeah, but a little higher ... the third quarter was 8 points higher, where I suggested 1.5 or maybe a bit higher.

But somewhat in line, yes ... the important thing is evidence that the HFA actually exists on roughly the predicted order of magnitude.

Right, which is great stuff.

I think we need to keep hammering the “confrontations” aspect to home side advantage (or really ANY advantage).

When Federer or Nadal plays someone, it’s clear they will win more in best-of-5 than best-of-3 or best-of-1.  Or even a single-serve.  It compounds.

Maybe that’s a good name: compounding confrontations.  They each build on the other.

I love the idea your showing that the compounding is not only by number of confrontations but number of participants per event.  It’s obvious now, but it’s a great way to put it.

Right.  You could still call it the number of confrontations if you look at it like every player is involved in a confrontation even if the ball is elsewhere.  Trying to get away from your defender is definitely a confrontation, although, for some reason, only in football is it ever explicitly talked about.

It also depends on the relative importance of those participants.  In baseball, there are nine guys on the field, but most plays are “controlled” almost completely by pitcher and hitter. 

In hockey, there are 12 guys, but you’d probably want to try to treat the goalies separately.  But how do you do that?

Anyway, just rambling.

Great, great stuff Phil!  I think that the insight here is not so much the magnitude of what the HFA should look like in any individual play (like player FTM), but that the reason the authors found no difference was the fouling of poor FT shooters late in the game.

Which emphasizes another thing that a good sports researcher has to do when he is comparing team results across two different groups - and this comes up all the time.  Control for the quality of the two groups!  You can usually not assume that the two groups have the same quality of players on the field.  There can be a random inequality or there can be a reason why there is a natural inequality (in this case, because, as Phil says, the road team is more often losing at the end of the game and has to foul the other team’s worst foul shooters).

Another thing that blows the authors’ (of Scorecasting) claims of umpire bias (being he primary cause of HFA) out of the water.

"Phil is proposing that we should be able to see a home advantage if you look at individual players, and weight their home and road splits equally.”

I am not sure where you get that from, and why that is useful.  If you just look at home and road stats, like the Scorecasting authors did, you might find that the FT% is equal, because the player pools are not the same.

If you look at it using the delta method (adding up individual home and road splits), then you should find a difference no matter how you weight them, no?  And the only reason we don’t weight equally when using a delta method for almost anything is that we want to minimize the effect of someone who only played a little but had a big split.  For example, in this case, if a player made 3 FTA at home and 1 on the road, and his H/R FT% split were 100/0, if we give that equal weight we are going to screw up our results.

So using the harmonic mean, the total, or the lesser of the two opportunities is fine in this case (and in most other cases).  We’ll still come up with the correct HFA for free throw %.

I guess my quote wasn’t clear enough.

If Jordan had 1000 FT at home and 900 on the road, we’d weight his FT success at 900 opps.

If Kobe was 700 and 750, we’d weight his at 700 and so on.

At my post, King Yao figured out HFA for pre-season games in various sports.  They’re the same as for regular season games.

Very interesting result, I think.

I uploaded the data to a google spreadsheet: http://is.gd/y3yKF5

Thanks, Ed.

For every player/year, I took the higher number of attempts (home or road) and reduced it to the lower number of attempts, but the same success percentage.

Results, if I’ve done it right:

.7569102 Home
.7545445 Road
----------------------------
.0023657 Difference

Less than the HFA you get from King Pao’s raw numbers for the first three quarters.

Er, King Yao, not King Pao.

#14, that cracked me up.  Perhaps you had Chinese food (Kung Pao chicken) on your mind!

I am going to send the FT “delta” results to Professor Moskowitz.  Hopefully, I am not overwhelming him.

I’m on a “referee” panel with Jon Wertheim at the MIT Sloan conference this weekend.  If free throws come up, I’ll mention it ...

Looks like Toby Moskowitz will be there too, speaking on home field advantage:

http://www.sloansportsconference.com/panels-2/2011-2/invited-speakers/

I’ve been called a lot worse!

Interesting Phil.  Let’s see if I get any response from them this week.  If not, perhaps you can ask them about my letters.

I received an email response from Prof. Moskowitz about the basketball data only. I don’t know why he didn’t address my earlier email about the baseball stuff that I articulated on the other thread.  I am not going to post his response on this blog until I get his permission.  Their free throw data was from 05-09.  The stuff that Phil computed (weighted average H/R difference among all players) was 01-10, I think.  The quarter by quarter stuff from Kung Pao - I don’t know the years.

2006/2007 season to the 2009/2010 season.  Regular season and playoffs.

Thanks.  I like your new handle!

King, can you post quarterly results including OT for the 05-09 seasons (I am not sure which seasons those are, but that is what the authors used)?

There were 133,568 attempts in their database if that helps.  Thanks!

I am shocked that the pre-season games have a home-field advantage, and one that matches the regular season ones.

For all intents and purposes, those pre-season games are being played at neutral sites.  If not completely neutral, at least much more neutral than the regular-season parks.

Entirely consistent with the testosterone theory, though, no?  Dunedin is the Blue Jays’ spring home.  It’s theirs.  Doesn’t matter if it’s only temporary, it’s where they spend every spring.

I don’t have data for the 2005-2006 season.  I only have it for the 2006-2007 season through the 2009-2010 seasons.  I also am not sure what they mean by the 2009 season - do they mean the 2008/2009 or 2009/2010?  It doesn’t matter really, I’ll just post the data I have by year by quarter. 

2006/2007
1Q A 4647/6250 74.4%
1Q H 4862/6523 74.5%
2Q A 6007/7950 75.5%
2Q H 6230/8286 75.2%
3Q A 5983/7978 75.0%
3Q H 6492/8599 75.5%
4Q A 7678/10155 75.6%
4Q H 7857/10462 75.1%
OT A 316/415 76.1%
OT H 355/446 79.6%

2007/2008
1Q A 4469/5940 75.2%
1Q H 4728/6240 75.8%
2Q A 5730/7738 74.1%
2Q H 6161/8215 75.0%
3Q A 5913/7858 75.2%
3Q H 6439/8382 76.8%
4Q A 7493/9860 76.0%
4Q H 7759/10260 75.6%
OT A 190/237 80.2%
OT H 226/287 78.7%

2008/2009
1Q A 4451/5792 76.8%
1Q H 4991/6478 77.0%
2Q A 6078/8001 76.0%
2Q H 6280/8265 76.0%
3Q A 6011/7754 77.5%
3Q H 6368/8196 77.7%
4Q A 7357/9543 77.1%
4Q H 7786/10120 76.9%
OT A 277/335 82.7%
OT H 321/394 81.5%

2009/2010
1Q A 4774/6243 76.5%
1Q H 5100/6653 76.7%
2Q A 5961/7913 75.3%
2Q H 6255/8284 75.5%
3Q A 6027/7969 75.6%
3Q H 6167/8047 76.6%
4Q A 6861/9108 75.3%
4Q H 7341/9741 75.4%
OT A 181/230 78.7%
OT H 206/274 75.2%

All years combined for OT

OT A 964/1217 79.2%
OT H 1108/1401 79.1%

The difference in the number of free throws in OT seems pretty high.  There were only 306 games, so on a per game basis, that’s 4.6 free throw attempts for the home team and 4.0 for the away team.  Assuming a 79% rate for both teams, that’s a difference of 0.475 points. 

In those 306 games, the home team only outscored the away team by 0.43 points on average!  (12.76 vs 12.33).  The home teams were only 161-145 in games that went to OT, so it seems like the FTA disparity was the main reason.  Could that be ref bias?  I don’t know...maybe the refs were calling it correctly and the home teams just had a bigger advantage in OT which led them to getting fouled more often.  306 games is a very small sample size - definitely compared to the 5000 games for the quarter data I have, but still, it raises an eyebrow, especially since the Home team seems to get many more FTA in each year (does the consistency from year to year make it more likely this is not just an anomaly?) Of course, there is another possibility --- maybe I have bad data.  I don’t think that’s the case, but always possible.

Hmmm ...

Overtime is shorter, but the end-game is the same length.  So any deliberate fouling effects will be larger in the data.  So if home teams are more likely to be deliberately fouled, because they’re winning, it will look like a larger proportion.

What if you look at it by subtracting instead of dividing?  In overtime, it’s 0.6 extra opportunities per overtime game.  Do you know what it is for the fourth quarter?  Wait, I can kind of figure it out ... it’s about 0.3, if I’ve done it right (eyeballing an average for all years).

That still seems a little high:

-- In overtime, all games are close so there may be deliberate fouls.  In the fourth quarter, not all games are close.  So OT should be significantly higher.

-- In overtime, HFA is lower, because it’s a much shorter “game”—home teams were .526.  So OT should be somewhat lower.

-- In overtime, teams are more likely evenly matched.  That doesn’t make a difference, right?

-- And then there’s lots of random chance, because of small sample size.

I dunno, it seems to me like 0.6 is out of line, but not that far out of line.  But then you have the fact that FTs seem to be almost the entire overtime HFA, as General Tao King Yao points out.

What does everyone else think?

Phil: except there’s a ton of NRI (non-roster invitees) there as well.  For some, it’s the first time they are there.

All I’m saying is that you have Wells at Rogers 81 games a year, and he’s 10% of the hitters, and all the other regulars have a big share as well.  What share are the veterans at Dunedin?  So, wouldn’t you expect the veterans at Rogers to have more of a HFA than a bunch of veterans mixed with NRI at Dunedin?

Or is it simply the idea that you are at “home” enough to establish the HFA?

>Or is it simply the idea that you are at “home” enough to establish the HFA?

Right.  I don’t think it takes long for your brain to register a place as “home”.  If you go out of town, and stay in a hotel, how long does it take before you start to think of your room as your temporary home?  Not long, at least for me.  I could go into a colleague’s room in the same hotel, with exactly the same layout, but ... it feels a little foreign.  It’s his room and his stuff, not mine.

Anyway, that’s just a gut argument.  I could be wrong.

One way to test it is to look at pre-season performances by “first-timers” or NRI.  Compare the home/away splits.

Who would have thunk it, that pre-season data would be valuable…

"One way to test it is to look at pre-season performances by “first-timers” or NRI.  Compare the home/away splits. “

NFL Preseason may be interesting in this regard because the 4th quarter is almost always played by backups and players that may not make the regular season roster.  Maybe the 4th quarter in preseason NFL can be used as a proxy for the NRI you mentioned. I have scores by quarter for the NFL preseason and regular season games.  There is a bit of time-frame difference, but I don’t think it matters.  The Regular season data is from 1989-2010, the preseason data is from 1996-2010.

Preseason 4th Quarter: 925 games
Home teams outscored away teams by 0.34 points: 5.10 to 4.76. 

Regular Season 4th Quarter: 5,493 games
Home teams outscored away teams by 0.56 points: 6.07 vs 5.51. 

When it has been a close game (defined as a game where neither team has a greater than 7-point lead at halftime),

Preseason 4th Quarter “close game”: 555 games
Home teams outscored away teams by 0.17 points: 5.06 to 4.89. 

Regular Season 4th Quarter: 3,030 games
Home teams outscored away teams by 0.58 points: 6.21 vs 5.63

If one were to believe this data (I do think there is a lot of variability around these numbers so I wouldn’t use them as “the truth"), I think one could conclude that the NRI/first-time players don’t feel quite at home as the regular starters.

Phil’s comments about feeling at home in his hotel room compared to another person’s room is interesting.  It makes me wonder if there are any non-sports, but competitive events where one could measure home field advantage....especially with no referee involved in the event.  I’m pretty sure there is a home advantage in events like the Olympics or World Cup, but what about in business/government/politics?  If two countries are negotiating a trade treaty in person, does it help to be the host country?  For people that have couples night and play games like charades, do the host couple win more often than they do on the road?

I’m thinking about doing a home/road study on beer pong.  It is on my list of things to do.  I’ll let you guys know when I get around to it…

As far as preseason baseball, you have to rememeber the home teams are more frequently playing their more talented players (or projected starters), than the visiting teams are.  I think that has something to do with the preseason HFA. Often times, the visiting teams will not travel with many from the opening day roster.

Good point, even though you are so late to the party, everyone else has either gone home or is passed out on the floor!

Very true, just finished reading the scorecasting book, so was checking all posts involving their book to get your guys thoughts.  Was most specifically interested in the HFA portion of the book.