1. A reliever for the Arizona Diamondbacks?
2. A bully who picked on Nerdtron in his youth?
3. The Robert Goulet Memorial Mustached American of the Year?
4. Both 1 and 3

That’s right, in addition to putting together a nice 50+ innings in the desert, Zavada deservedly took home the Mustached American of the Year. The American Mustache Institute put out a press release, which included a curious claim about players sporting the ‘stache.

The mustache’s enhancement of a player’s skills has stirred controversy in the sport as an internal report produced by Major League Baseball reportedly said it believes Zavada’s mustache was responsible for at least 42 of his 52 strikeouts in 2009

Here at Nerd Central we don’t hide our affection for those who tout the lip sweater a bit less gracefully than Zavada. So we went about investigating whether a mustache truly could improve a baseball player’s ability.

There are 100 nerds in the nerdbase, but not all of them managed to play in the season of their card. One of the nerds is a manager (who got fired partway through the season of his nerd card). Another nerd is Pope John Paul II, who had to be thrown out because a VORP (Value Over Replacement Pontiff) of infinity skews the results. We’re left with 49 nerds without the facial hair tag, and 39 with it. The easiest way to compare them is to look at their ERA+ or OPS+ (depending on position) as a comparison of how they did relative to their peers in the league, and a rough way to put pitchers and position players on the same scale. We end up with the results below, where the two boxplots show the clean shaven and the razor phobic. The scale on left is ERA+/OPS+, and you can see each group contains some sorry baseball players.

The mustache is worth about 4 points of OBP+/ERA+ over the shaven, and the nerd can use all of the help he can get. It’s not statistically significant (sadly), but there are still the intangibles that come with the mustache. We’re looking forward to the time when statistics friendly GMs start realizing the benefit of fielding teams of players who look like this, and strongly encourage you to keep a facial hair column in your fantasy baseball draft spreadsheet.

Brian Downing in the 1970′s
Brian Downing in the 1980′s

Mr. Cubbage hit for the cycle on June 27, 1978. Mets fans may remember him as their interim manager for seven games in 1991, and Red Sox fans may remember him as their interim manager after Joe Kerrigan was fired in spring training of 2002.

Congrats to the 2009 Nerd-All-Stars, and starting with Mr. Cubbage, new nerds will be eligible for the 2010 Nerd-All-Star-Team.

Price Per WARP via Free Agency

Let’s get the grains of salt out of the way…this table only takes two seasons of free agency/performance into account (thats how many years of free agency data I was able to find on ESPN.com). For some teams that’s only a half-dozen signings, not the biggest sample size. I only considered free agents who were given guaranteed major league contracts. If players were traded mid-season, I had no way of tracking how much of the remaining season salary was paid by the original team (though I don’t think that these few occasions would have had much effect on the overall numbers).

Despite these caveats, there are some interesting numbers to be found in the above table. First of all, the average price per WARP paid to free agents over the past two years was $2,374,331. This is not far off from the median price, which was $2,285,947. Of the major market teams, the Cubs have done the best job of finding value in free agency. Only the Dodgers, Braves, and Pirates fall more than one standard deviation from the mean (approx $4M…not including Atlanta’s infinite price).

Since these three teams are pretty big outliers, I ran the standard deviation numbers again without these teams involved (we’ve already identified that they’ve done an extraordinarily poor job over the past two years). Without them, the mean only dropped to $2,309,728, but the standard deviation dropped to $895,192, and some more interesting comparisons can be made.

In this set, the Marlins, Rays, Phillies, and Rockies all fall outside one stdev on the “finding good value” side of the curve. Of those four, the Rays, Phillies, and Rockies were World Series representatives during that same time period.

On the “we’ve been wasting money” side of the curve, the Mariners, Nationals, and White Sox fell outside one stdev, and the Twins fell over two stdevs of the mean! While the Mariners and Nationals had abysmal 2008s, Seattle did have 88 wins in 2007, and the White Sox and Twins actually tied for the 2008 AL Central title before their one game playoff (being in the same division was certainly beneficial for these two).

Back to those outliers…In the case of Pittsburgh, the team only spent about $6.6M in free agency over the past two seasons. However, their $22M per WARP shows that this money was not spent very efficiently. My initial reaction was to give them some additional leeway since they are a small market team, and don’t have the funds to target the top free agents, or mask any mistakes with additional signings. However, Oakland, Tampa Bay, and Florida all had lower payrolls than Pittsburgh, and they each paid less than $1.75M per WARP. Pittsburgh fans, avert your eyes. Otherwise, take a look at these signings by the Pirates: Tony Armas got paid $3.5M for 0.6 WARP, Yosian Herrera got paid $1.28M for -0.4 WARP, Chris Gomez got $1M for 0.1 WARP, and Byung-Hyun Kim got $850K for 0.0 WARP. If there’s any slack left to be given, it’s that the lack of recent success and the wild Pittsburgh nightlife and weather don’t stand much of a chance of attracting those lower-salary free agents against South Beach or the Bay area.

The Dodgers, on the other hand, have no excuse. Major market attraction? Check. Sunny California attraction? Check. Laid-back west coast attraction? Check. Enough money to mask mistakes with more transactions? Check. Recent playoff appearance? Check. Yet over the past two years, the Dodgers have spent over $122M on their free agents’ salaries, and still have an average price per WARP of over $9.5M. Juan Pierre at $8.8M per, Nomar at $9.25M per, Jason Schmidt at $15.7M per, and Andruw Jones at $18.1M per, I’m looking at you…No wait. Actually, Ned Colletti I’m looking at YOU. No one better complain about Manny’s contract when he’ll be the one high-paid player on the Dodgers who actually puts up big numbers.

One major surprise for me was that the Giants didn’t have a terrible price per WARP. I would’ve thought that the Rich Aurillia, Dave Roberts, and Barry Zito contracts would’ve created a hole that was too deep to dig out of. And Atlanta…what happened? Paying $11M over two years for the production of replacement players is quite an accomplishment

So where to go from here? It will be interesting to revisit this list after the current season, when so many teams spent so much less on free agents, and the Yankees spent so much more than usual but signed three players with star potential. It would also be interesting to track this data from the start of each current GM’s reign, and ranking their careers in free agency signings. Anyone know where I can find all of this data easily?

Regression in a nutshell

To look at run prevention, I went to the same regression approach as before.  I like this because it lets us use what Doc Nerd calls parsimonious stats.  They are stats easily counted and hopefully found in the box score.  The other nice thing about regression is that the output is pretty straightforward.  It’s the y = mx + b thing that comes up in high school.  In a regression, y is your predicted outcome, and x is your predictor.  There can be multiple predictors, leading to a formula like y = m1x1 + m2x2 + m3x3 + b.  The coefficients (m1, m2, m3, etc.) tell you how to weight each of the contributing factors.

The boring part

Looking at pitching and defense ended up opening up a lot of interesting paths for studying.  These paths are arranged in layers.  Just as the bottom tier of the standings is the least interesting, looking at the foundation is a lot like looking at the Nationals.  What I found was a lot of common sense: a team that wants to prevent runs needs to (A) not give up hits, (B) not give up walks, and (C) keep the ball in the yard (Nerdstradamus: this time we used best subsets to get the order).  This simple formula will explain over 90% of the variance in allowing runs, with a high degree of confidence.  That 90% is about as good as we are with offense, and is generally considered very high.

Here’s the raw output:

Yes, that model looks like it’s missing some things to me too, but I want to hold that thought and first look at who over- and under- achieved last year.  The one major over-achiever was the Phillies.  That’ll be good news for the Mets fans that hang out around here.  The underachievers were the Rangers and the Diamondbacks.  The Rangers gave up 967 runs last year.  That is worst in MLB, and truly horrible.  The model predicts them at 913 runs, which would have been worst in MLB and truly horrible.  The model sees the Diamondbacks as a very good pitching and defense team; it’s too bad their offense is so unconvincing.

The three true outcomes?

When I look at this model, I’m surprised by the parts that aren’t there.  Namely, strikeouts.  Strikeouts show back up in the second level of the analysis, when I look specifically at what prevents hits.  But for now, teams that allowed fewer runs didn’t necessarily strike more players out; strikeouts are not a direct predictor of a teams prowess in preventing runs.

Second, errors aren’t there at all.  Team errors do not predict allowed runs at all (nor do they predict hits allowed, but that’s for another day).  This takes me to one of my favorite soapboxes.  Earned runs are not a useful statistic.  Any run is a product of the interaction between the pitcher and the defense.  The errors behind a pitcher do not give any meaningful information in how the pitcher fared.  There may be good ways to measure defense, but errors are not among them.  The case will get stronger when I look at hits.  The bottom line is that a pitcher should be uniformly punished for any run that is given up.  That penalty need not be as harsh as currently assumed for an earned run, but the pitcher bears a degree of responsibility for every run that crosses the plate.  A more enlightened approach is slightly more forgiving to pitchers for any run allowed, but indiscriminate on how that run came to pass.  Fantasy baseballers, take note.

Pitchers have direct control over the amount of HR they surrounder and the amount of free passes they give up.  The question now is how much control do pitchers have over the amount of hits that they give up?  That’s for next time.

While looking at some of the contracts given out this winter, I was wondering what some of the worst (and best) returns teams might expect from their investments. I decided to look at the top 50 player salaries for 2008, and compare this with their WARP1 (wins above replacement player, normalized for the season…this metric also rewards/punishes a player for their defense) performance. I chose WARP1 because I was only interested in 2008 salary/production. Read on to find out which players were a good value per WARP, and which player would’ve been more valuable for his team if he was playing for someone else…

Ok, so here’s the top 50 highest paid players in MLB in 2008, their salary, their WARP1, and how much they were paid per WARP that they contributed:

WARP for the 50 Highest Paid Players (2008)

Things to note: teams paid these former “big ticket” free agents an average of $3.35M per WARP that they contributed. This was calculated after I threw out the data for Jason Schmidt, John Smoltz, Mike Hampton, Jorge Posada (all due to missed injury time), and Andruw Jones (negative WARP would’ve messed everything up). The average would’ve been several hundred thousand higher otherwise. Once again, Pujols leads this list, as his 13 WARP only cost 13.8M…the best bargain on the list.

From here I moved on to the 53 (meant to do top 50, but kept going by accident) highest WARP performing players from 2008. Here are those players:

Top 53 WARP Performers (2008)

Here, the top 53 players last year (according to WARP), were paid an average of just about $710,000 per WARP that they contriubted. You’ll also notice that only ten out of those 53 come from the highest paid list. I guess this can be viewed as the price of free agency…Ryan Howard is the only guy who had a crazy-high arbitration salary (and he’s neither among the top 2008 WARP performers nor arbitration eligible anymore). During the period where teams can control a player (their early years through their arbitration years), they can add the majority of their projected wins at a relatively low cost (as long as they identify the right players). And while there is some overlap in the lists, once top-50 salary level players hit free agency, interested teams are probably going to have to pay about four or five times more for the same production ($700K per WARP vs $3.4M per WARP). Probably not a big newsflash, but interesting to see what teams are actually paying for.

It turns out a simple linear model can explain team run scoring a little better than OPS.  What’s nice about this approach is that by using this method to rank players, we’re also directly seeing how players contributed to their respective teams.  So, who were the leaders last year?

Linear team runs predict team run scoring, and were derived in my last post.

LTR = -419.14 + 1.50 * HR + 1.46 * 3B + 0.94 * 2B + 0.50 * 1B + 0.21 * BB

Linear runs created (LRC) uses the same formula without the intercept.

The (AA) columns stand for above average.  LRC is accumulated so, obviously, playing a lot helps rack up the runs.  To put this in perspective, we can look at how many runs a player creates in a single at bat.  Pujols is a god among men, and I can’t believe Nerdius got him in the third round last year of our draft.  Stupid injury rumors.

I’m not sure what to make of this order of players.  The top 10 makes sense to me, but they’re not in the order that I would choose if I were just to figure things off the cuff.  On the other hand, the weights that lead to the formula were developed in the most impartial way I can imagine.   It’s also important that LRC is a counting stat.  Just like a player who racks up the ABs will get more hits, the same player will rack up LRC.  Some of these players get to the plate a whole lot.  LRC like walks, but it isn’t as enamored as some other methods I’ve seen.

Reyes is the real surprise here.  We’re not accounting for his steals at all, and LRC has him as the third best player in 2008?  LRC loves triples, it seems that this is the way it accounts for speed.  LRC also has no park adjustment, so Reyes park could be giving him some help here.  Last summer I made it to my first Mets game, and sure enough, I witnessed one of Reyes 19 triples.  It was very exciting, and my computer obviously understands this.  Hopefully Jacoby’s efforts this summer can bring in a little more excitement.

What about some free agents still left?

If I were running a team and had an open OF slot, I would be trying my hardest to get Manny for two years.

Update The Angels just grabbed Abreu for one year @ 5 mil, which is an absolute steal.

Update 2 Dunn is now gone for 2 years @ 10 mil per.  I’m not as high on Dunn as some of the other nerds, I think his game is tied to a set of skills that require the right kind of context.  Walking and hitting solo dongs for the Nats don’t really strike me as the key to contention.  That said, he’d improve any number of teams, and the Mets contingent is probably annoyed to see him off the board.  I still contend that whoever decides to put up with the Manny circus will be the real winner.

It also turns out that I’ve been tasked with learning R, an open source statistical package, for work.  Namely, I need to figure out how to do a multiple regression.  This is a statistical technique that allows you to model an outcome based on multiple inputs.  So, to learn how to use the software, I decided to model offense in baseball, and finally figure out how good our league’s scoring system really is (for offense, at least).

Here’s a warning.  It gets really nerdy from here on out, so if you’re just interested in the answer, here it is.  Our method is pretty good.  We overvalue walks.  If you’re for some reason interested in R vs. SPSS, R is an adequate replacement.

So what is this scoring system?  It’s point based for various baseball events.  We’re only talking about the offense, so here we go:

To figure out how our weights stack up, I looked at the 2008 run scoring for each of the teams as a measure of offense (i.e., the outcome variable).  The planned inputs were everything shown above, plus strikeouts.  However, some of the measures ended up being dropped.  Strikeouts didn’t make the final analysis because it’s bimodal (what’s going on there?), and regression demands normal distribution.    Triples are positively skewed, but I kept them in anyway without a transform.  RBI and GDP I dropped because they’re context dependent.  Obviously, RBI and R are closely correlated.  There is nothing Earth shattering by saying that the trick to scoring runs is driving them in. GDP is equally misleading.  A team with a high GDP has a lot of runners on base, which is actually a good thing.  SB and CS didn’t end up being a significant predictor of runs in 2008, so they’re not in the final analysis.  A league that treats steals as anything more than a footnote is interested in Fantasy baseball, not fantasy Baseball.  If your real-life MLB team is built around steals, take a moment and go weep.

I’m sorry I’ve offended the member of the Willy Tavares fan club.  The output of the modeling is in the table below.

What does this mean?  This is a linear model, of the form y=mx + b.  Y, in this case, is predicted runs.  B is the intercept, and listed under each model.  Don’t read into the negative intercepts, it’s mostly a statement that real baseball teams don’t have zero offense.  The rest of those numbers are the coefficients for each event.  In model number five, where all five events are used, we predict that a homerun will produce 1.5 runs, and a double will produce 0.94 runs.  Triples are also productive, but we have to take that 1.46 with a grain of salt because the original data was skewed.  Finally, a walk is not as good as a single, but getting on base at all is still very valuable. (Don’t worry about something being more significant than something else.  Significance is a yes/no proposition.  If something is reported as more significant, that speaks to the confidence in the coefficient, not the magnitude of the coefficient itself).

None of this is actually new, and all it really does is confirm that we’re on the right track with our league weights.  We could stand to knock BB down a bit, I guess.  It’s also pretty amazing that these 5 stats describe 90% of the variance in run production.  Finally, the Twins scored 60 more runs than the model predicts.  They were the only over-productive outlier.   I would expect fewer runs out of them this year.   San Diego and St. Louis under-produced by about 40 runs.  The SD result shows that not including park factors could be a real problem if this were anything more than just fooling around.  STL will probably just score more runs this year.

Now how often can I get nerdly baseball pursuits to count as work?