During one of our irregular, meandering internet conversations today, I offered the following prediction to Pepe: The Cubs would very likely be in serious contention for the NL Central this season up until the end of the season, and I don't believe it's out of the question that they could actually win the damn thing. Cue incredulous scorn from my counterpart, who mentioned three reasons why he doesn't believe this is the case:

1) The Cubs are currently 8.5 games out of first place in the Central;

2) The Cubs sucked in 2006;

3) The players on the Cubs suck, at least in contrast to current front-runner Milwaukee.

The first two are obvious truths, and the third is a subjective claim. I'll get to No. 3 in a minute.

Currently, the Cubs' record sits at 32-39, which is good for third place in the putrid NL Central. There is no question that, for a team that spent a total of $300 million during the offseason, this is a disappointment (and further evidence that spending and success in baseball do not share a direct correlation). If the Brewers continued to play at this pace, the Cubs would have to sport a .652 winning percentage for the rest of the season, which is greater than the Red Sox's current pace (.648). That is unlikely, to say the least. So, if one were to formulate his or her opinion of the Cubs' playoff chances based purely on W-L records, it would appear safe to stick a fork in the North Siders and crown the asses of the Milwaukee Brewers.

But that would assume that W-L records are useful as predictive tools, and there's no reason to think that's the case, particularly in this situation. First, the Brewers and the Cubs have played 71 and 70 games, respectively, which is roughly 43 percent of the season. That's far from a large enough portion of the season to draw reliable conclusions about what will happen for the remaining 67 percent of the season (particularly considering that remaining part of the season is likely to include a large number of roster changes, via trades, injuries or call-ups). If Prince Fielder breaks his jaw on an overbaked hoagie tomorrow, and misses a couple of weeks while being fed intravenously, one cannot expect the Brewers to keep playing this well. Conversely, if the Cubs finally give touted prospect Felix Pie enough at-bats for him to start playing to his potential, the Cubs could begin playing better both offensively and defensively (more Pie = less Jacque Jones). So, there are a lot of variables that will determine these two teams' fates for the rest of the season.

But there's also the issue of what a current W-L record is based on. While a W-L record is the only measure that matters to a team when it's all said and done, that doesn't mean it's an accurate indication of how well (or poorly) a team has played to date, or how well/poorly one can expect that team to continue playing from here on in.

So, what is? A couple of things. Most notably, there's the concept of a team's Pythagorean Record, a concept created by Bill James that has since been modified to allow for more factors, including run-scoring environments (See here for a rather dense explanation). A Pythagorean-based calculation results in First-Order Wins. Then there are two other measures, referred to as Second- and Third-Order Wins. These are based on Equivalent Runs, a measure that attempts to place value of an offensive performance of players based on playing time and position. Second-order wins are a stepping stone to Third, which used Adjusted Equivalent Runs, a measure that takes into account to opposition and environment (for example, the value of a HR off Jake Peavy in PETCO park is greater than the value of a HR off Woody Williams in whatever the fuck they call Enron these days). I'll be honest and admit that the how of arriving at these numbers is a little mind-boggling — it bears mentioning that the people who came up with these formulae are not only way smarter than me, but also highly educated in the field of statistics and mathematics — but that doesn't mean the what is any less valid.

Here is BP's adjusted standings page, which list the first-, second- and third-order wins of all the teams in the major leagues. It takes a second to process everything, and I suggest looking at the legend to clarify exactly what it is you're looking at.

Now, I know what you're saying: "So the fuck what? Just because some nerds have come up with a measure doesn't mean that it means anything. A team's W-L record is what's important, because that's what determines post-season eligibility." And that's obviously the case. But what we're attempting to do here is figure out, with some measure of accuracy, what teams are going to do for the next 67 percent of the season. I know that some people still scoff at the notion, but luck has played a role in the success and failure of teams so far this season. The Brewers, for instance, started off the season like gangbusters, and built a massive lead early on. Obviously, the team couldn't support that rate for the entire season, and regressed. Conversely, the Cardinals were absolutely horrible to start out the season, but eventually began playing better because they weren't really that bad. However, those small periods of time still have a massive effect on the W-L records we see now, because those unsustainable streaks have yet to be adequately buttressed with periods of normalcy, or even equally-unsustainable winning/losing streaks.

Based on what the BP chart tells us, the Cubs have played baseball at a level that is more likely to result in a 37- or 38-win record than a 32-win one. And — surprise, surprise — the Brewers have played at virtually exactly the same level. The BP charts indicate that the Cubs and the Brewers should be in a tie for first place in the win column, with the Brewers roughly one loss back.

I think the results that show on the BP chart are indicative of the usefulness of the measures; it's fairly accurate in nailing what the actual standings are, in most cases, and that accuracy rate will likely increase as the season goes on and the effect of random variation is reduced. I can't find the chart for 2006, but when I find one, I'll post it; it was quite on-point.

Luck isn't the entire story for teams that play below or above their Pythagorean records. Beyond possible inequities in strength of schedule thus far, the Cubs exemplify the kind of team that is highly susceptible to this kind of difference, mainly because of a poor record in close games. That usually is an indicator of a bad bullpen and a shaky defense, which fits with the Cubs. Furthermore, teams with low OBPs tend to be more slump-prone, as the success of an offense becomes more dependent on power and surges in hitting. That applies to the Cubs as well.

However ...

Teams that have a variation of more than a game or two between the actual W-L record and the Pythagorean records are outliers; it just doesn't happen all that often, because runs scored vs. runs allowed are easily the best single indicator of a team's quality. With that being the case, it is highly likely that there will be a correction over the course of the season for the Cubs, as well as the Brewers (to a lesser degree, since they're only playing roughly 2 games over their Pythagorean). It's likely that the Cubs will need to have a hot streak or two where they play above their heads, but that's not abnormal at all, almost to the point where it's to be expected.

At this point, the always-entertaining BP Playoff Odds Report (based on Monte Carlo simulations) shows the Cubs as having a 20 percent chance of winning the NL Central. I would suggest that the chances of the Cubs being "contenders" — a designation that Pepe set at being within two games back or less with a week or so left in a season, which is sensible — are much higher than that. The one thing I will back off on is that I'm not sure those chances are even-money or better; I can't begin to do the math needed to arrive at that kind of conclusion with any reliability. But I'm going to e-mail Davenport and see if he can shed any light on making that kind of conclusion.

## Thursday, June 21, 2007

### By the powers of Ron Santo

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## 7 comments:

Are you implying that JJ Hardy

won'thit 54 home runs this season?Actually, my fuzzy math says he's on pace to hit 39 HRs.

Are you saying JJ Hardy

won'thit 39 home runs this season?I'm supposed to trust your fancy statistics when you think 67 percent + 43 percent = 100 percent?

Hahahahahahaha. That is excellent. The Cubs are going to give 110 percent this year, fellas.

I could correct it, but it's so much better leaving that dumbass mistake. I'm going to blame it on IMing with Mutter while I was writing the post.

On the BP page, the deltas for the Cubbies are pretty large. The varying and sometimes large deltas in general on the BP page suggest (so far) that the Pythagorean model has been neither accurate nor precise. Would you say that this is due to poor modeling, or bad luck thus far for the Cubs?

Knowing the answer to that question, I will pose a second order question: Is linear statistical analysis proper for such a stochastic system as baseball? I seem to recall from an earlier conversation at 16th Street a declaration that the playoffs in baseball are essentially luck-based. By extension, would that not also apply to the regular season? If so, isn't game theory or (as you mentioned) Monte Carlo sims more appropriate than Euclidian geometry? I acknowledge that baseball cannot simply be relegated to a coin flip, but where significant chance based elements are involved, I'm not too thrilled about a linear (or even quadratic) analysis.

I believe that you make a very insightful statement that the 'how' does not necessarily affect the 'what'. I am just wondering which 'how' is an appropriate mathematical model for baseball. I would think that the statistical models for baseball, were they to be as precise and accurate as possible, would eventually become so convoluted as to make Joe Morgans out of all of us.

I think you may have been right when you posited that I would become a baseball fan out of spite. And due to the fact that a computer cannot teach me anything about baseball, I'll rely on you, Steve Phillips, and John Kruk.

Also, just to be a dick:

Doesn't all of this talk about equivalent runs and statistical exponents 'calculated in the run environment' kind of end the Runs vs. Outs debate? I haven't seen (because I haven't looked) any sort of predicative model based on outs, so there.

Scottish Bastard,

Obviously, the answer to the first is that we're walking in less than halfway through the trial, so it's nearly impossible to judge the adequacy of the model based on the data available (and the deltas of teams like the Cubs, Yankees and Diamondbacks). I'm still trying to find ASs from previous seasons, which would be a better measure of the system's efficacy. I remember being very impressed when I first saw some year-end results, and that's the reason I'm so enamored with the measures now.

As for linear analysis vs. game theory applications, I think a proper predictive metric requires both. Baseball is a stunningly simply game at its core, particularly when assessing outcomes. The reason the Pythagorean Model has held up is because the correlation between run differential and success is extremely predictive. Yes, there are outliers like the 2006 Cleveland Indians, who played under their Pythag by close to 10 wins, which is absurd. It's worth mentioning that there are very few extreme examples to the converse; while many teams with good run differentials can lose more than expected, few teams with negative run differentials can sustain inflated winning percentages.

The Monte Carlo approach is useful when attempting to extrapolate the rest of the season, but it needs to be based on valid information. I don't know if there's a better way to mine that data than by using concrete measures like actual W-L record to date and peripheral measures like EqR.

But I understand what you're saying. I suppose that, outside of being able to use past seasons as tests of the model, that it's the best that's out there right now. I would not be surprised in the least if a better or more refined one popped up sometime in the near future.

I don't quite understand the Joe Morgan comment, but that's probably because my field of vision turns scarlet every time I see his name.

Runs vs. Outs is a chicken-egg argument. Most stat heads go for outs because it's the currency, but I'm not sure one's more valid than the other. Runs can't happen without outs, but they don't count outs at the end of the game. But it tends to be a fruitless argument, I've found, because I don't really think runs people are "wrong." They just approach the same question from a different angle.

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