Rough Translations: Is the traditional OBP formula the most suitable?

Thanks to a recent Sports Illustrated article and Baseball Prospectus interview, I stumbled across the website for the Grupo Independiente para la Investigacion del Beisbol (GIIB), a group interested in applying sabermetric principles to Cuban baseball. Their website is very interesting, but it's in Spanish. In order to spread their very useful approach, I'm putting my loose translation here, in the hopes that (even if it's not 100% accurate) it will at least be an improvement over what you can get for free through something like Google Translate.

DISCLAIMER

• All content is property of the GIIB and is not my own. I claim zero rights to it. If they get mad about this translation, they just have to contact me and I will absolutely take it down.
• I also claim zero responsibility for the accuracy of these translations. I am not a native Spanish speaker, but I did take Spanish in high school and am currently a level-17 Duolingo user, for whatever that's worth. Any missing Spanish knowledge (of which there is a lot) will be supplied by Google Translate.
• Because my understanding of the original is limited, the translations will probably not be exact. I hope to at least capture the spirit of the article, so others who don't know Spanish can still read the GIIB's research. Sentences or phrases I can't get a good handle on will be denoted by italics. You're welcome to leave corrections or other constructive feedback in the comments.

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¿Es la fórmula tradicional del OBP la más idónea? (Is the traditional OBP formula the most suitable?)
Is the OBP formula the most correct way to measure the probability that a batter reaches base? Is not the sacrifice bunt an opportunity to get on base? Why does the OBP formula ignore when a batter reaches base on an error?

OBP = (H+BB+HBP)/(AB+BB+HBP+SF)

H: Hits
BB: Base on Balls
HBP: Hit by Pitch
AB: At Bats
SF: Sacrifice Flies

The formula for OBP is too focused on the analysis of the individual hitter and not what he really contributes to the team. One piece of evidence for this last statement is the fact that the OBP formula excludes the sacrifice bunt from the denominator. Suppose a batter comes up with runners on first and second with no outs, and grounds out to second, allowing the runners to advance. What is the difference between this at bat and a sacrifice bunt? Are the two actions not worth the same to their team? Then why does OBP make a distinction between them? Defenders of OBP argue that, because the sacrifice bunt is ordered by the bench, it should not be seen as an opprotunity to get on base and therefore should be excluded from the denominator. But is this true? Are all sacrifice bunts ordered? Should OBP distinguish between sacrifice bunts put on by the manager and other sacrifices? Of course note; and even if we consider all sacrifices as ordered from the bench, the sacrifice isn't an opportunity to reach base? Really?

Let's return to the previous situation: runners on first and second, no outs. Suppose the batter bunts the ball and reaches first safely, getting credit for a hit; is this bunt not an opportunity to get on base? In other words, if the bunt goes for a hit, it is a positive action, but if it advances the runners (which could also be accomplished by other means as shown above) and the batter is thrown out at first, it doesn't count as an opportunity to get on base? This is incongruous.

Now we analyze another important aspect of OBP: the exclusion of times the batter reached on an error.

Suppose a batter reaches on an error. The batter accomplished one of his goals (to get on base), and has become a runner and an opportunity for his team to score. Any runner represents a great opportunity for a team to manufacture runs, regardless of whether he has reached by error, hit, or walk. But the basic OBP formula doesn't see it this way. According to the basic OBP formula, reaching on an error is a negative action. When a batter reaches first by an error, according to this formula he is not credited with reaching first safely but is credited with an at bat. In other words, the times when a batter reaches on an error, it is counted as a failed opportunity to reach first. This is difficult to understand.

Let's analyze this from a different perspective. For some, the error has nothing to do with the offensive player; it is true that the error is a bad defensive acction, but does this mean the batter has no influence? What is the difference between a hit and an error? Subjective concepts; first, the positioning of the defensive player, and then if the scorer considered there to be an opportunity for an out. Is a Texas leaguer to center field worth more than to connect on a shot to third that the fielder can't handle? In general, baseball rewards speed and placement and not force, but is this really important? Imagine your favorite team, losing by one in the ninth, with two outs and the tying run on third. The batter reaches on an error and the game is tied. Does it really matter how the game was tied? Would you rather lose?

It is true that errors are sometimes just bad defensive plays, where there is not a hard-hit ball or fast players to rush the defense and force them to make risky throws. But is the HBP not an error by the pitcher? The HBP is in most cases a mistake by the pitcher, a pitch that gets away from him; but it is nevertheless counted in the traditional OBP formula as a positive offensive action. It takes a lot for us to understand how a HBP is worth more for the batter than to reach on an error.

We now return to the initial question: is the traditional OBP formula the best way to measure the probability of a batter reaching base? Briefly, OBP does not count when a batter reaches on an error and doesn't consider a sacrifice bunt as an opportunity to get on base. We therefore calculate OBP in an alternative way and call it gOBP.

gOBP = (H+BB+HBP+ROE)/(AB+BB+HBP+SF+SAC)

ROE: Reached on error [Trans. note: abbreviated EE in original]
SAC: Sacrifice hit

To capture the reality of the concepts we must move away from the moralistic way of thinking that still exists in baseball analysis. If we want to know the real probability that a batter reaches base, then we have to count all opportunities and all successful actions. Each turn at bat is an opportunity to reach base; and of course, every time the batter reaches first safely, it is a positive result for him. We exclude only interference or obstruction from this analysis, because the probabilities of these actions occuring in a baseball game is around 0.0027 [~0.27 percent]. That is to say, it is such a small sample that it is negligible.

For now, enough philosophical discussions about baseball. We will concentrate on mathematical tools that allow us to demonstrate which of these two statistics is more useful when analyzing the offensive prowess of a team.

For this we compiled statistics from the last 15 Cuban National Series. We calculated both variants of OBP and found the linear correlation of both with runs scored per game.

This is the scatterplot of the traditional OBP vs. runs per game. These statistics show a linear correlation of 0.93. But we are not questioning the proven utility of the classic formula, but we are analyzing which formula is the most suitable.

We next show the scatterplot of gOBP with respect to runs per game.

These statistics show a linear correlation of 0.95.

Although the difference is not very high, it is not possible to deny that gOBP is slightly closer to reality than OBP, at least numerically. We remember that correlation does not explain causation between variables. But we consider gOBP the optimal indicator to measure the probability that a batter will reach base. This is why STRIKE, as well as other projects that derive from it including StatsPlay, includes gOBP in its reports and recommends it over OBP to measure this concept.

Regards, friends.

Bad Beats: Getting Back on the Bowl Prediction Horse

Last year I used the Sagarin pure points method and found the games with the biggest discrepancy between the spread Sagarin predicted and the actual spread. I charted this for all of last year's bowls and finished around .500.

This year, I'm using The Prediction Tracker, which aggregate predictions from a number of systems. Treat the picks as independent and assume they fall in a normal distribution (warning: this is probably a terrible set of assumptions, but roll with it). Then, we can see how many standard deviations each spread is from the mean predictions. The ones that are furthest away are the best values.

Let's run through the Chick-Fil-A Bowl (Duke-TAMU) as an example. There are 48 picks with a mean of TAMU -6.54 and a standard deviation of 4.2. The current spread at the LVH is TAMU -12.5, approximately 1.42 standard deviations away from the mean prediction. The high Z-score demonstrates that there's value in this line, and that TAMU is overvalued. And that's why I picked Duke.

For reference, I put all the scores in a Google Document so you can bet against them as you will.

There haven't been many updates here lately, but that doesn't mean I haven't been working. Expect another update soon with a bunch of news.

Super Bowl Hype Drive: Room for Squares

The run-up to the Super Bowl leads to a lot of great traditions -- parades! weird bloggers at media day! the disfiguration of millions of chickens! -- but high among these is the office squares pool. You've probably seen them; they look something like this:

You sign your name to a square, and once all the squares are filled, someone picks row and column values. Say you end up with the square (3, 1). That means that, at the end of any of the four quarters*, you win money if the score is X3-Y1 -- e.g., 21-13, 31-3, 41-33, etc.

* - Actually, the fourth quarter one usually includes overtime periods too, so if you had Ravens 8, Broncos 5 as a square in the AFC divisional playoff game, you would've won once Justin Tucker made that kick in the second overtime.

Obviously, the odds of every combination aren't equal, and you know intuitively that multiples of 7 or 3 are more likely to come up. Wouldn't it be nice to know what your odds of winning were compared to someone who drew, say, 7-7?

To determine the odds, I used Pro Football Reference's Score Index to find the score by quarters of all playoff games dating back to the 1994-5 season, when the NFL added the two-point conversion. This gives you a 20-year sample that (with this season included) encompasses 208 total games. Here are the total number of times each combination of numbers has occurred.

	0	1	2	3	4	5	6	7	8	9
0	62	16	6	66	65	6	25	112	7	7
1		5	3	13	20	6	7	27	10	3
2			0	3	4	1	4	9	3	1
3				19	35	3	11	64	6	8
4					20	8	9	43	9	11
5						1	1	7	3	1
6							1	14	2	3
7								41	9	6
8									2	3
9										1

Divide by the total number of quarters of football played (832), and you get percentages:

	0	1	2	3	4	5	6	7	8	9
0	7.5%	1.9%	0.7%	7.9%	7.8%	0.7%	3.0%	13.5%	0.8%	0.8%
1		0.6%	0.4%	1.6%	2.4%	0.7%	0.8%	3.2%	1.2%	0.4%
2			0%	0.4%	0.5%	0.1%	0.5%	1.1%	0.4%	0.1%
3				2.3%	4.2%	0.4%	1.3%	7.7%	0.7%	1.0%
4					2.4%	1.0%	1.1%	5.2%	1.1%	1.3%
5						0.1%	0.1%	0.8%	0.4%	0.1%
6							0.1%	1.7%	0.2%	0.4%
7								4.9%	1.1%	0.7%
8									0.2%	0.4%
9										0.1%

So, from the looks of things, (7, 0) is the best combination to get, right?

Not so fast. These numbers include ALL scores, both X0-Y7 and X7-Y0. In typical versions of this game, you only get one of the two squares. How can you determine which of those are more likely to occur? You can't really use home/away, since the playoffs include the neutral-site Super Bowl, and the home/away designation isn't meaningful for those games*. So let's just split it down the middle: if you have (7, 0) and someone else has (0, 7), 50% of the time you'll be on the right side of the pairing and 50% of the time you'll be on the wrong side.

* - Unless you really, REALLY like coin flips.

If you have (0, 0) -- or any of the other pairs along the diagonal -- you're in luck; there's no one else to split the odds with. That means that, overall, your best bet is that (0, 0) square, and THEN one of the (0, 7) or (7, 0) squares. The top five, by percentage:

Square	Pct
0,0	7.5%
0,7	6.7%
7,7	4.9%
0,3	4.0%
0,4	3.9%

The bottom five, of course, remains the same, with (2, 2) as the kiss of death with zero occurences.

Good luck, everyone. I for one will be rooting hard for a 42-12 final.

Bad Beats: Sagarin's Predictor Rankings and the Bowl Games

I promised more updates, but that obviously hasn't happened. There are three reasons behind this: first, the million distractions of the holidays got in the way, as tends to happen; second, I've been working on my Evolution of Sport proposal for the upcoming Sloan Sports Analytics Conference, and third, it's harder than you'd think to type with these broken thumbs.

Maybe I should explain.

A coworker of mine is in a weekly football pool: for each NFL game, guess which team will cover the spread to win fame and fortune, etc. The pool keeps going into the playoffs, but since there aren't that many playoff games, he's also required to pick any six college bowl games against the spread. Last year, he told me, he used some good guessing and coin flipping to go 3-3. This year, he wanted to do better.

A Richly-Deserved Beating: CFB ATS Update

At the beginning of the college football season, I asked whether you could use a team's recent against-the-spread (ATS) history to predict how they would do against the spread this season. I came to the conclusion that

[T]he perpetually underperforming teams (like Tulane) and perpetually overperforming teams (like Boise State) are a function of luck* rather than some underlying market inefficiency.

Well, the season's over (except for the bowl games). Was I right?

Bad Beats: The Predictive Power of Past Years' ATS Record

Last week, I used this space to complain about losing money to my friend Dave by betting against Tulane football.

Faaascinating, I know. But it gives me a chance to make an Important Point about the predictive value of statistics.

My confidence in my bet was based on the fact that, from 2003 to 2011, Tulane covered just under 40% of their games against the spread. Winning 60 percent of your bets would make the average professional bettor salivate, so I was happy to bet based on this big trend.

There were two things I ignored: first, that one game is the smallest of sample sizes, and second, that past results are no guarantee of future performance. The second point is the interesting one, so let's focus on that: if a team has done better/worse than average against the spread in the past, does that tell us anything about its performance against the spread in the future?

Bad Beats: Rutgers at Tulane, Sep. 1, 2012

I owe Tulane football an apology. It seems I underestimated this year's team.

When the opening line for the season opener against Rutgers was listed at 17, I immediately jumped on Twitter.

At work today: "Tulane is 17.5-pt underdogs in their home opener vs Rutgers!" "That's it? Take Rutgers."
— Bryan Cole (@Doctor_Bryan) August 9, 2012

Even when confronted with the one other Tulane football fan on Twitter, I refused to back down.

“@jbr1657: Rutgers didn't even score 17 at home against Tulane in 2010” // Forgot about this. Prediction: Rutgers 14, Tulane -6 #rollwave
— Bryan Cole (@Doctor_Bryan) August 9, 2012

And it seemed Vegas agreed with me, kind of: by the week of the game, the line had moved to 20, though the over/under still suggested Tulane's score would be a natural number.

Euro 2012 Tournament Odds

The European Championship pits the best 16* international soccer teams on the continent against each other, producing better matchups than the World Cup and fun Eurozone debt crisis proxy fights. The 16 teams are divided into four groups of four. Each group plays a round robin, with the top two in each group advancing to a single-elimination tournament.

* - Okay, 14 best teams and 2 host teams. But even the host nations are pretty good: There's no North Korea losing games 7-0.

The group stage just finished, and the tournament is about to get underway. Of the eight teams remaining, who has the best chance of winning it all?

For baseball and basketball games, you can calculate the expected win probability for a single game from the two teams' Pythagorean records using the log5 method. For international soccer, you can use the Elo ratings to determine the expected win probabilities. The formula looks like this:
We = 1 / (10(-dr/400) + 1),
where dr is the difference in Elo rankings between the two teams.

Once you know the probability that a team wins its first game, you can compute the probability that team wins its second game using conditional probabilities. Like this:
P(wins first game)*(P(beats potential opponent A)*P(potential opponent A wins first game)+P(beats potential opponent B)*P(potential opponent B wins first game))

Keep doing that and you eventually get win probabilities for the entire tournament:

	Elo	Semis	Finals	Champs	Odds (x-to-1)
Spain	2110	83%	67%	44%	2.3
Germany	2063	85%	59%	32%	3.1
England	1950	61%	25%	10%	10.1
Portugal	1883	65%	18%	6.1%	16.4
Italy	1871	39%	12%	3.7%	27
France	1839	17%	9%	2.5%	40
Czech Rep.	1779	35%	6%	1.5%	68.3
Greece	1763	15%	4%	0.9%	112

And you're never going to believe this, but the teams with the best ratings are the ones with the highest chances to win. You can see that the probabilities depend a bit on matchups: France has only a 17% chance of knocking off Spain in the first round, but a 2.5% chance of winning the championship, whereas the Czech Republic has a 35% chance of beating Portugal but a 1.5% chance of making the finals, since they'd have a lower win probability against the remaining teams if they did advance.

Comparing the odds to the betting markets, it looks like Spain might actually be a good wager: if you believe this method, their odds to win are 2.3-to-1, but the books have them listed at 2.6-to-1. Practically everyone else is overvalued, but laughably so for Portugal (listed at 7.5-to-1), Italy (9-to-1), and France (12).

UPDATE #1: June 21, 4:45 p.m.
Here's what the odds look like after Portugal's win over the Czech Republic:

	Elo	Semis	Finals	Champs	Odds (x-to-1)
Spain	2110	83%	64%	41%	2.4
Germany	2063	85%	59%	32%	3.1
Portugal	1901	100%	29%	11%	9.3
England	1950	61%	25%	10%	10.3
Italy	1871	39%	12%	3.6%	27.3
France	1839	17%	7%	2.1%	47.6
Greece	1763	15%	4%	0.9%	117

Note that everyone else's odds change, despite not playing, because of the improvement in Portugal's ranking. Portugal now has an 11% chance of winning the tournament, leapfrogging England, who obviously still has to survive the semifinal matchup. France, a bad bet to begin with, becomes a slightly worse bet now that they have to beat both Iberian Peninsula teams to get to the finals.

UPDATE #2: June 22, 4:45 p.m.
Here's what the odds look like after Germany's demolishing of the Greeks:

	Elo	Semis	Finals	Champs	Odds (x-to-1)
Germany	2074	100%	70%	39%	2.6
Spain	2110	83%	64%	39%	2.6
Portugal	1901	100%	29%	9.6%	10.5
England	1956	62%	21%	8.4%	11.9
Italy	1871	38%	9%	2.7%	36.9
France	1839	17%	7%	1.8%	54.8

Germany are* technically the favorites by half a percentage point over Spain. But, again, Spain still has a first round match to play; with their odds somewhere in the 11-to-4 range (2.75-to-1), they still look like the best bet.

* - This always looks wrong to me, but everyone else does it. My least favorite thing about soccer.

UPDATE #3: June 25, 9:15 a.m.
Here's what the odds look like after this weekend's games, including the first upset of the knockout stages as the favored England side screwed up some penalty kicks to lose to Italy in a shootout:

	Elo	Semis	Finals	Champs	Odds (x-to-1)
Spain	2123	100%	78%	49%	2.0
Germany	2074	100%	73%	36%	2.8
Italy	1902	100%	27%	7.6%	13.2
Portugal	1901	100%	22%	7.2%	13.8

This is the last update here, but I'll still post updates on Twitter. Italy's odds are slightly better than Portugal's, just because Germany has a lower rating than Spain's. I do like the fact that every German game from here out (vs. Italy, then vs. Spain/Portugal winner) is another Bailout Bowl, though some of that has to do with the woeful state of the Eurozone.

The Pain from a Future Wound: Betting on Mad Men Season 6

In sports, futures bets are a popular way for casual fans to get in on some sweet season-long action and casinos to take advantage of the eternal optimism of Cubs fans. What's more, future odds for next season are up mere minutes after the previous season ends. And while you can't place many entertainment-related bets in Vegas, you can certainly place them online. With all that in mind, The Feats of Strength proudly presents the first lines posted* for the sixth season of Mad Men.

* - God, I HOPE they're the first lines posted. What is wrong with you people?

Bracket Showdown, Day 10: [Title Vacated]

With Kentucky's dismantling of Kansas in last night's national championship game, the first ever Feats of Strength Bracket Showdown has come to an end*. A comical 28 entries correctly put Kentucky on the final line. As I said on Twitter last night, I have never seen more experts pick the same team to win a championship -- and be correct -- in a long time. Then again, maybe I just haven't been paying attention.

Anyway, the Aluminum Pole for best performance** goes to Jerry Palm at CBS Sports, who picked 3 of the Final Four, both finalists, and Kentucky to win for a total of 146 points.

Congrats, Jerry; you've earned this.

Bracket Showdown, Day 9: Domeward Bound

RISD alumna and mascot-bracketeer Ashley MacLure illustrates the Louisville-Kentucky matchup.

No one, they say, wants to hear about your fantasy sports teams or your bad gambling losses. At the risk of losing my one reader, then, I'll refrain from complaining about the Ohio State Buckeyes, who snatched defeat from the jaws of victory and cost me a shot at my bracket pool. Fortunately, I had the catharsis of the Bracket Showdown, so as the Buckeyes stood around bewildered on the Superdome floor, I grimly set to work tallying up the points from tonight's semifinals, drawing larger-than-usual X's through the incorrect predictions.

Let's move on, and see how our panel of experts fared in the Bracket Showdown. As usual, the rules of the showdown are here, and the updated scoreboard is here.

Bracket Showdown, Day 8: ...Step 3 = Kentucky.

After a weeklong vacation in Las Vegas, Bryan triumphantly returns to the blog with an update on the 36-entry Feats of Strength Bracket Showdown.

After two glorious weekends, four teams are headed to New Orleans to compete for the college basketball championship. Sixty-four other teams are not headed to New Orleans or, at least, if they are, will be mostly limited to drinking hurricanes on Bourbon Street. Let's look back at our Bracket Showdown and see how our contestants are doing. The full scoreboard is available in this Google Document.

Bracket Showdown, Day 2: Where the hell is Lehigh anyway?

"Sir, the possibility of St. Bonaventure winning the tournament is approximately 3750 to one!"

The first round of the tournament is in the books, and my bracket is in enough disarray that I can stop worrying about winning my office pool (which was never going to happen anyway) and start rooting for chaos. Let's go Mountain Hawks!

Anyway, let's check in on our team of experts and computer simulations and see how they're doing:

Bracket Showdown, Day 1: Barack, Chalk, Jayhawk

The greatest first day of the tournament I ever had was back in 2008. Between a series of brilliant thefts of other people's deductions and some good old-fashioned dumb luck, I actually got all 16 games correct. Like a pitcher in the middle of a perfect game, I refused to talk about it, but spent a good part of the morning going back to ESPN's bracket challenge page to admire the score.

It wasn't long, of course, before I got my first loss of the tournament. It was all downhill from there, and I finished somewhere between "mediocre" and "flipping coins" that year.

All of which to say that March Madness is not a mad dash, but rather some kind of mad marathon*. Still, it's never to early to jump to conclusions! Let's take a look at the scoreboard and discuss the results of day one:

Bracket Showdown: Just the FAQs, Ma'am

As the NCAA college basketball championship gets underway, The Feats of Strength will be hosting a showdown between dozens of brackets from college basketball experts, analysts, celebrities and more. Winner gets an aluminum pole -- very high strength-to-weight ratio*.

"No decorations. I find tinsel distracting."
Today, I explain the rules of the contest. What better way to do that than the ol' Frequently Asked Questions gimmick? Well, except that no one's reading this blog, let alone asking questions, so let's call it the "Fruitlessly Anticipated Questions" section.

Announcing the Feats of Strength Bracket Showdown!

The header on this blog might lead you to believe that actual analytics will show up on this blog someday. For a variety of reasons, that day is not today, and it's probably not tomorrow, either. As a cop-out, I'm taking a page out of junior high science fairs everywhere and seeing which laundry detergent works best* whose March Madness bracket predictions are best.

I've compiled 34 36 brackets from four categories: experts, celebrities, analytical systems and simulations, and a miscellaneous group of controls. The current list is below the jump.

EXPERTS
Nicole Auerbach, USA Today
Jay Bilas, ESPN
Jeff Borzello, CBS Sports
Dennis Dodd, CBS Sports
Gregg Doyel, CBS Sports
Jeff Goodman, CBS Sports
Andy Katz, ESPN
Tony Kornheiser, ESPN
Matt Norlander, CBS Sports
Jerry Palm, CBS Sports
Gary Parrish, CBS Sports
Peter Tiernan, CBS Sports
Eddie Timanus, USA Today
Scott Van Pelt, ESPN
Dick Vitale, ESPN
Michael Wilbon, ESPN

SYSTEMS
Massey Ratings
Ken Pomeroy
Prediction Machine
Jeff Sagarin
Nate Silver
Joel Sokol
Stat Junkies
Tiernan high-risk
Tiernan medium-risk
Tiernan low-risk
What If Sports

CELEBS
Common
LeBron James
Barack Obama
Rajon Rondo
LaMarr Woodley

MISC
CBS Users' Bracket
Harvey Dent (a.k.a. the coin-toss bracket)
Chalk (i.e., highest seed always wins)
Mascot fight

Not all brackets are currently available. As the missing brackets get uploaded, I will paste in the links here.

Details about the scoring system will be posted tomorrow. Check back after each round for an update and see who wins!

Now, I know what you're saying, O reader, because I've hacked into your computer and have a live feed coming from your camera. You're saying, "Wait, what the hell?", but before that, you were saying, "This isn't very scientific! What good is a sample size of one?" And that's true. But like I said, this is more fun than anything else. Everyone makes these predictions every year, and wouldn't it at least be nice to go into next March knowing who did the best last year? Nevertheless, Operation Frantic Googling may yet reveal some past predictions to add to our sample. Rest assured, we have our top men working on it.

"Who?" "Top. Men."
___________

*-I've seen like a hundred of these and the winner is always Tide. Always.

Thinking Out Loud: Point-Shaving Detection

Those knee-deep in the hoopla of NCAA conference championship tournaments might not have noticed, but Yahoo! Sports reported yesterday that Auburn guard Varez Ward was being investigated by the FBI for point shaving. Auburn, that upstanding institution of higher learning whose athletics program has always followed the straight and narrow before, joins an august group including Boston College, Northwestern, and (my alma mater) Tulane.