Sunday, August 31, 2008

On Base Percentage

I'm not a big baseball fan any more, but this is interesting stuff. Just from reading the posts of baseball fans around the Oiler blogs, I know that on base percentage (OBP) for teams has a strong correlation to winning. This seems a bit counter intuitive, because the power numbers aren't factored in at all, especially so for someone who started watching baseball when Earl Weaver's Orioles were winning a lot of ball games on the back of three-run homers.

Just looking at overall team stats, adding the hits+walks+hitbypitch numbers, then dividing those by the same surrendered by the team's pitching staff/defense; that gives the OBP ratio. This is the convention used by sabrmetric types, no? And the correlation to winning is enormous, and the correlation to runs ratio (runs scored divided by runs surrendered) equally so. A sample correlation of .90 or so, for any season or portion of it, this is typical. And it is obviously huge.

Now baseball isn't much like trivia craps at all. The better team on the day usually wins. Whereas over 40 matches of trivia craps, I would guess about a quarter of the players will actually have won more money in matches where they did worse at the trivia. Stuff happens.

My question is; how does it predict? If a team starts the year with a disappointing record, but a strong OBP ratio, should we suspect that they've just been a touch unlucky, and that they will start scoring more runs, allowing fewer, and winning more games in the future? And the answer is yes, or at least I can't find a baseball stat that has stronger predictive value, not with a quick search of the web, anyways.

For the 2003, 2005, 2006 and 2007 seasons the predictive value of OBP to the runs ratio, from one half of the season to the other, it averages a correlation of .43. As a point of reference for baseball fans, this is a touch better than the .38 predictive value of runs ratio to future wins ratio over the same interval (which is the essence of Bill James' Pythagorean Expectation) .

I have the even strength face off zones for the NHL for these same seasons, that's why I picked them. And obviously in both sports there are trades at the deadline, injuries, young players that get better with experience, differences in schedule difficulty from one half to the next, teams that are out of the playoff picture so start playing youth in situations that they wouldn't otherwise, etc. And in hockey especially, the bounces are still going to have a big say in the results.

The chart below shows the average repeatability and predictive correlations for these four seasons. I used face off zones because to my mind it is a strong indicator of meaningful possession in hockey, and the even strength zone time ratio and corsi ratio (shots directed at net ratio) aren't available for all of these seasons.

If you sum the first half of these four seasons, and compare it to the sum of the back half of these same four seasons (which I did accidentally at first, due to a script error) then both metrics grow stronger.

In the case of OBP, repeatability climbs to .70, prediction rises to .62.

In the case of face off zone ratio, repeatability climbs to .87, prediction rises to .57.

And in the case of face offs the correlation to immediate results, averaged over these four seasons, is a fairly weak .35 . With the four seasons combined, however, the benefit of the larger sample causes correlation of face off zone ratio to scoring ratio to climb to .71.

I know I'm painting with a big brush here, this is a bit rough. And I'm sure that baseball stats guys have done a tremendous amount of analysis of OBP and other team stats. Still, to my mind it's a comparison that has value. In large part because Pythagorean Expectation and OBP are fairly established metrics in the minds of a lot of the Oiler fans who hang out on the Oilogosphere.

Possession certainly isn't everything, but it's a lot of it. And is the foundation for any sensible endeavour to place reasonably accurate expectations on hockey teams at even strength, and hockey players as well.

As an aside: is a terrific resource for baseball stats nuts. Everything is laid out for you, it takes minutes to write an excel macro that scrapes off what you need, and for any range of seasons. It does not have pitch counts by inning though, or even pitch counts by game. Does anyone know where this is available? I suspect that the reason OBP is such a strong indicator of present and future success is because it is an indicator of pitch count, and the ability of a team to get weaker pitchers (middle relievers) into the game. Tthough I'm certainly not sure of that.


Blogger Lowetide said...

This is beautiful stuff, Vic. Outstanding.

To one of your points, OBP predicts well because it gives your side more opportunities if youre good at that portion of the game. If we treat each plate appearance like a sortie, then a really good team in terms of OBP will get many more sorties over a season.

I have no idea how much better you'd have to be at hitting home runs to get things back to do with a team that is superior at OBP, but quite often in MLB history good home run hitters also walk a lot.

Anyway, carry on and terrific stuff. This is the other side of the mountain, with ERA/pitching equalling SP/goaltending so once you suss this out we're away.


8/31/2008 1:40 pm  
Blogger Vic Ferrari said...

Thanks LT. And that OBP analogy makes sense. Still, if you give a bit of extra credit for extra base hits in the OBP equation, then it weakens the value in terms of what we are looking at here. Which really seems upside down to me.

That's why I wondered if OBP is more of an indicator of an important part of winning baseball games, rather than the important element in it's own right. Again though, I don't know a lot about baseball. And results be results, OBP works.

On NHL goaltending at even strength; straight craps, the dice weighted to the EV save% of the goalie over the past 4 or 5 years. It's just stunning how well that works.

I mean really we should be looking at three dice games with 25%, 10% and 5% dice weightings (ish), and more throws with the more lightly weighted dice. Because that mirrors scoring chances. But practically that is nearly the exactly the same spread of results as a the simpler dice game (every shot on goal as a dice throw, 8.5%-ish dice weighting, depending on the goalie). So we keep our life simpler and just use the latter.

9/01/2008 8:58 am  
Blogger Lowetide said...

I think you'd find (going over many MLB seasons) there would be a few outer marker seasons that don't resemble each other (good hitting, bad hitting teams or teams playing their home games in the Baker Bowl) but generally speaking it should work all down the line.

If I understand correctly, you would be looking for:

*a very good OBP team
*that still finished under .500
*despite having an average pitching staff.

Is that what you'd be looking for to disprove the point you're making? I'll have a look, starting with the 1970s Houston Astros who are a team you would have loved.

9/01/2008 9:56 am  
Blogger Lowetide said...

That should read "good hitting, bad pitching" teams above.

9/01/2008 9:57 am  
Blogger Vic Ferrari said...

Not really Lowetide, I wasn't clear at all.

I'm thinking that if you went back over the years when you watched baseball, and picked the few teams from each season that had deep bullpens. The bullpens whose middle relievers were actually pretty good. I don't know how many teams per year would qualify, but I trust your judgment.

If we took all of the season splits for these team-seasons, the the OBP predictive value would drop a bunch, and the Pythagorean Expectation would climb a lot I think.

It's a quality of competition issue in hitter/batter matchups.

The exact opposite for teams with a really weak bullpen, especially if they had one great closer in amongst the riff raff.

Again this just by my intuit, which certainly shouldn't be trusted with baseball. I'm not asking for math here :), I'll trust your memory, and if you do a quick scan through the old rosters and pick the squads that best match, I'll run the numbers.

9/01/2008 11:12 am  
Blogger Lowetide said...

I'll give you some teams straight off the top of my head and then maybe add a few over the next few days:

Great bullpens
*1987 Montreal Expos
*1975 Cincinnati Reds
*1969, 1973, 1986, 2006 Mets
*1982 Cardinals
*2002 Braves

I think it was 1998 Yankees who had a dominate Mariano and garbage everywhere else. Mike Marshall's career with Montreal and LA would be of interest to you and the 1984 Tigers had some interesting things in the bullpen.

I'll come back later, and I'll also look forward to the other baseball nuts contributing. :-)

9/01/2008 11:58 am  
Blogger RiversQ said...

Isn't there a weighted OPS that should handle all your concerns Vic? LT is right - slugging matters but I think it's generally accepted that conserving outs matters more, so "they" use x*.OBP + .SLG, although I don't know what "x" usually happens to be.

Anyway, most people these days would use regular OPS (OBP + SLG) anyways to account for extra bases.

9/01/2008 8:59 pm  
Blogger mc79hockey said...

Gross Production Average is what you're thinking of.

9/01/2008 9:45 pm  
Blogger Vic Ferrari said...


Thanks guys, I looked up Gross Production Average on Wiki and applied it. It works a lot better than what I was doing, which was adding one extra to the numerator of OBP for every double, two extra for every triple and three extra for every home run.

It's still not as strong as simple OBP by the way I measured in the post. But it's close on all counts.

9/02/2008 8:42 am  
Blogger Vic Ferrari said...


Thanks. So I ran those eight team seasons, and the relationship of runs scored to OBP for these teams offensively, for the 16 half-seasons, it's strong, as you would expect. .80.

For seven of the eight teams though, they soundly outperformed the opposition OBP in both halves of the season.

correlation of opposing OBP to runs allowed should also be .80, the lowest half season that I saw in the past 20 years was the from half of 1987, at .66.

This group is a touch under .50. And if we take out the 2006 Mets, which are clearly the odd one of this bunch, then the correlation drops to .31, and the predictive value of OBP for these teams, defensively, it becomes negligible, actually a smidge negative (.03 going forward and -.21 looking back).

Makes sense, no?

Now it's a really small sample, you may just be remarkably lucky in the teams you've chosen. Still, plenty enough to look further I think.

We could look at playoffs, because relief pitching, esp mid relief is much stronger then. Largely because they are teams that likely have stronger bullpens to start with, plus they'll use better pitchers, 4th or 5th starters or better, to come in for that gig. It stands to reason that OBP has less impact there.

We could look at the pitch count if it's available. That would be the bomb I think. It would be like hockey if goalies started fading badly after going to there knees 40 times in a game. The best thing about throwing a lot of rubber at Luongo would be the ECHL goalie that would come in to start the third period if he was worn out.

Or we could look at the number of innings that starters lasted against teams on average. I wouldn't be surprised if we could outdo OBP with just that and slugging%, but I don't know.

Off topic from hockey I know, but it's the sort of process that we should go through when pegging hockey. And something I'll get to shortly in a reader participation thing. I'm sure it will leave me shaking my head a the lack of participation, but what the hell, I'll have a go.

9/02/2008 9:11 am  
Blogger Vic Ferrari said...

At this point I'm probably talking to myself, but I'll add one bit anyways.

As stated, The Lowetide Eight seem very resistant to opposing team OBP. So if you looked at the opposing team OBPs for them from one half of the season, you'd predict bad things for the other half. You'd expect them to do far worse in terms of run differential. But it doesn't happen. And they outperformed their opponents OBP in both halves as well.

OTOH, the Oakland A's looked to be very vulnerable to teams with strong OBPs, at least over the past 12 seasons that I looked. A staggering .95 correlation of OBP to runs allowed.

Odd that.

9/02/2008 4:29 pm  
Blogger Vic Ferrari said...

Edit for above, that last sentence should read:

A staggering .95 correlation of opponent OBP to runs allowed.

Unless of course I've made a mistake somewhere in my script, which is very possible. I'll post the season splits for all teams for the last 40 seasons online, hopefully someone can check my sums.

9/02/2008 4:32 pm  
Blogger Vic Ferrari said...

The OBP splits are uploading as I type this. They can be found as such:

Just change the year in the url to go back as far as 1968. As I say, I'm not certain that these are error free.

9/02/2008 4:38 pm  
Blogger Vic Ferrari said...

One more thing before I leave the computer for a few hours, in case I'm still on a baseball kick when I return.

The correlation of a team's OBP to it's run scored is much stronger in the first half of the season than the latter half (.83 first half, then drops to .61). And just scrolling through the seasons it is obvious that this happened in the vast majority of the past 40 years. I don't think it could be script error, because of the way it's written ... plenty of other things could be a mistake on my part, but not so much this.

The same applies to opponent OBP and runs allowed, and in the same measure. (.84 first half, then .63 on the back end of the season).

What could cause that, year in and year out?

9/02/2008 5:04 pm  
Blogger Lowetide said...

Wow. Just wow. Well, one theory would be that the fastball pitchers hit their stride in the warm weather and by end of May big league teams have quit on any starters/relievers who aren't getting it done no matter how famous they are.

Plus that's enough time for minor leaguers to establish themselves enough to make it to the show.

But those are old timey reasons and I can't really say if they're true.

One thing I would suggest if it's easy to do: take out the Cubs and Rangers from your survey. Hot weather wears those teams down.

9/02/2008 6:28 pm  
Blogger Vic Ferrari said...

You know, LT, I've looked through some of this baseball stuff and it's madass. How in hell anyone can make sense of this is beyond me. I mean even a fool could predict the midpoint for a group, but the spread is crazy. And the Sabrmetric stuff I've found through google seems insane to me. I mean you can't just divorce stats because they are in separate columns, not if they can't be separated on the field.

Back to point: Slugging percentage takes on an increased value in the second half for most teams, it's stealing some of the value from OBP, even though they are obviously tied together, there is a clear shift towards power there for most teams. For and against. So I think maybe it's bats heating up, LT. And the 'maybe' can't be boldened enough. Probably a matter of heavy bats heating up more than the pitcher's arms (on average). And surely the other things you mention.

The Oakland A's, since Billy Beane took over as GM, in the first half their correlation of slugging% to runs scored is .69, averagish. And in the second half it's a bizarrely high .96.

Go figure. I thought he was the OBP guy, no?

The expos of my childhood, 1977 to 1983 (never watched much baseball after my dad died, he was a huge expos fan though) the results of those teams, in this light, well they were bonkers. Maybe that explains my own intuition on the game, I dunno.

The correlation of OBP to runs scored for the Spos was negative over that timeframe in the back halves of the seasons, which I assume is an oddity. Plus those are most of the games that probably stick in a guy's mind. Walks and singles weren't driving the bus for those teams after summer arrived, not even a little bit.

BTW: Did anyone check to make sure my season split numbers are right? Or can they drop a link to a site that does these?

9/03/2008 11:17 am  
Blogger Vic Ferrari said...

Edit for above, it should read "bizarrely high .92"

9/03/2008 11:42 am  
Blogger Vic Ferrari said...


The numbers for the individual teams are right, I think. But I erred when summing up the totals for the OBP correlations in a spreadsheet. D'Oh! So there isn't the big drop in OBP importance in the second half for teams as a whole.

I'm impressed with how well slugging percentage meshes with offense though, for most teams anyways. And for some teams, like the Yankees, much moreso than OBP. Odd stuff, it's all magic to me. I can't see rhyme or reason in much of it.

I'll show myself out now.

9/03/2008 3:23 pm  
Blogger Lowetide said...

Vic: I swear to God one day people are going to flock to this stuff like they do now to a Bill James Abstract.

The truth is out there!

9/03/2008 6:03 pm  
Blogger Bruce said...

Interesting read, Vic. However, contrarian bastard that I am, I must take issue with one of your original assumptions:

Now baseball isn't much like trivia craps at all. The better team on the day usually wins.

One could argue (simplistically) that the team with the better pitching/goaltending on the day usually wins; they're the great equalizers. The key difference between the two is that pitching is proactive, goaltending reactive.

Only in baseball does the defending team start in possession of the ball. A well-pitched ball game results in few opponents on base, no matter how powerful a batting order they might have in theory. So a simple calculation of OBP at game's end will likely confirm that stipulation of "the better team on the day".

Whereas the hockey goalie who shuts down a strong opponent will do so by responding to opposition scoring chances and stopping them. The opponents might rack up big numbers in secondary stats like shots on goal, and if you use those numbers to determine who is the better team on the night then sure hockey appears more random. But the key distinction is the hot goalie is at the end of the scoring chance, whereas the hot pitcher stops those scoring chances before they begin. So it's not entirely a fair comparison.

9/03/2008 10:51 pm  
Blogger Vic Ferrari said...

All valid points Bruce, and Joe Torre is with you. I saw him interviewed after the Yankees had been beaten by Boston in the playoffs, I think that they had been leading the series 3-0.

He said he couldn't complain, that the Yankees had caught a lot of breaks in the playoffs for a few years in a row. He could remember game winning hits that just barely squeaked through the infield, a foot either way and the Yankees would have lost the game and possibly the series. Bloop singles that fell where nobody was, that sort of thing.

And I would imagine that he's right.

In hockey we know where it comes from though. The spread of the players away from their career averages will be nearly identical the the spread of a bunch of dice rollers (each throwing the same number of times as one player's shots, and having dice weighted to that player's average EV shooting% over the past three years).

It's just spooky how close the results are, in terms of the right number of guys overachieving and underachieving on the year, and by what amount. Plot it out and it's two bell shaped curves almost on top of one another.

Do that with most baseball stats and they are a mile apart. So either we need a better analogy or we have to accept that there is a lot of real estate available for clutchness, team chemistry and it's cousins to live on in baseball.

Hockey is a simple game. Baseball, not so much.

9/04/2008 8:04 am  
Blogger Doogie2K said...

Do that with most baseball stats and they are a mile apart. So either we need a better analogy or we have to accept that there is a lot of real estate available for clutchness, team chemistry and it's cousins to live on in baseball.

Hockey is a simple game. Baseball, not so much.

Funny, I've historically argued the opposite based on the fluid nature of hockey versus the relatively discrete and consistent nature of baseball. Besides, I defy you to really argue that chemistry and clutchness do not exist, full stop, in hockey. Sportscaster cliches or not, they're a fact of sport.

9/04/2008 6:28 pm  
Blogger Oilman said...

Baseball is so far ahead of hockey in terms of stats that clutchness is actually measurable. ie...average with runners in scoring position, average in 9th, average when tied or trailing. We'll never see a Shooting Percentage when down by 1 with under 5 minutes remaining in hockey. Hell, we'll never even see shooting percentage based on chances instead of shots (which would be pretty cool I think)...but it's just the nature of the games. Baseball has that full stop after every event which makes it a statisticians wet dream - the breakdowns are endless.

I remember seeing a stat regarding Chacin of the Jays and how opposing players batting average went up dramatically against him throughout the game...the batting averages went something like .150 in the first plate appearance, .280 in the second, .360 in the third and so on and it was kind of attributed to his choppy delivery. The first time facing him was tough but once you saw him release the ball a few times his stuff was pretty easy to hit. I'd expect a guy that gets 3 shots from the slot in a game is more likely to score on the third shot (all things being equal - like if every shot was from 60'6"), but again, hockey will never be tracked that deeply.

9/04/2008 8:36 pm  

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