From Guillen to Jones

December 14, 2007

All current indications seem to point to the Mariner lineup staying nearly static from the past year with a lone exception. This is going to be a rudimentary, quick peek into what we might expect from that one change.

In 2007, Jose Guillen batted .290/.353/.460. He was pretty lucky to have done so, with a higher than expected BABIP, but that’s tangential to our intended discussion here since Jose Guillen’s 2008 performance is not what we are concerned with. According to The Hardball Time, Guillen played 1273 innings and snagged 234 of 273 balls in zone and 34 out of zone. Taking the league rates for rightfielders, the average rightfielder would have gotten to 237.5 balls in zone and 47.5 out of zone. Adding these up and you get that Guillen made 17 fewer plays than our expected average defender over the course of 1273 innings.

With the performance in 2007 established, we move on to the more difficult part; projecting our 2008 performance. This is going to come primarily from Adam Jones. Jones is the subject of a few favorable projections already, notably ZiPS which pegs him as a .276/.335/.477 hitter next year. While I am sure that seems tad optimistic, let us not dismiss it outright, but instead delve a little deeper and see where we feel afterwards. Jones is not the easiest projection since he has such a limited big league sample to draw from. Luckily, I prefaced this entire investigation by saying it would be rudimentary so any statistical qualms I have are easily ignored. Are you not glad that I have such flexible morals?

Here is what we do know about Jones 147 big league plate appearances, spread almost equally between 2006 and 2007. Jones posted a 26.9% and 27.3% line drive rate each year. That is a very very good number, almost certainly too good to sustain itself. If they were done in seasons long enough to qualify, those numbers would rank 7th and 3rd highest respectively among single season line drive percentages over the past four seasons. In other words, unless you think Adam Jones is going to be the best line drive hitter in Major League Baseball next year, that number is going to come down.

How far down? For that, we turn to Jones’ Tacoma numbers where we get the benefit of an additional 886 plate appearances over the same time span. Those figures were lower in Tacoma, hovering a few ticks above 20%. That is still quite good if he can maintain that level. I am unsure if anyone has looked at how line drive rates move between AAA and MLB so for now, let’s just leave it as is and project a 22% LD% in 2008. Applying a (little less than standard) +11% to go from LD% to BABIP (not that robust, but again, good enough for this), we arrive at around a .330 BABIP.

We’re missing homeruns and strikeouts in order to figure out an estimate for batting average. Strikeouts are fairly straight forward; Jones Ks in about 29% of PAs over the course of his career. That’s going to improve with time, but in 2008 I would not count on much, let’s call it 28%. Jones hits groundballs at about a 40% clip, leaving us with 38% flyballs. Of those 38%. Jones smacked about one out of every five flybals over the fence in Tacoma, significantly less in Seattle. For 2008, I expect something in the middle and call it 13.5%. So in a 100 at bat sample, we expect something like 28 strikeouts, a little over five home runs and 67 balls in play yielding a little over 22 hits. Add it all up and you have a projected .272 average. It is worth reiterating that .272 accounts for a regression in line drive rate, virtually no progress in reducing strikeouts and just an average home run per flyball rate. The latter two points, middle especially, Jones could easily surpass.

For walk rate, I am just going to assume he holds at his 2007 level of 5.6% and that he both gets drilled and lays a sac down once every 100 PAs. That means 6.6 free passes per 100 PAs and 92.4 atbats giving us an on-base percentage of .318. For slugging, we’ve already anticipated homeruns, and using an average of 2006 and 2007 at both Tacoma and Seattle yields expected rates of 4.2 doubles and 0.9 triples per 100 at bats next season. Subtracting 5.1 from the 22.1 non-HR hits gives us 17 singles and a grand total of 48.63 bases in 100 at bats. Putting it completely together we have a .272/.318/.486 line for 2008. That is pretty close to ZiPS. The power output seems high to me, but again, you expect high power from somebody striking out nearly 30% of the time so if you think Jones is going to struggle hitting for power in 2008, you have to acknowledge that he might adjust and start going more for contact thereby reducing his strikeout rate and upping his batting average and OBP.

Turning to defense, Jones in 2007 played 176 innings and snagged 31 of 34 balls in zone and 8 out of zone. Taking the league rates for rightfielders (I understand Jones did not play exclusively in RF), the average fielder would have gotten to 29.5 balls in zone and 6 out of zone giving Jones 3.5 plays above average per 176 innings. Prorating that up to 1273 innings leaves us with 25 plays above average. That’s a 42 play improvement over 2007 Jose Guillen. Is that reasonable? Jones is a centerfielder playing rightfield, so we definitely expect him to be above average, but 25 plays? Half of that seems much more likely. That would roughly paint Jones as a league average centerfielder in terms of defense which seems about right for now.

One more time, there are huge sample size issues at stake here. Nonetheless I am just searching for a broad picture of what we might be looking at. Given the assumptions stated above the Mariners will move from a .290/.353/.460 hitter to a .272/.318/.486 hitter. Assuming 600 at bats (reasonable barring injury for a full time player) and using a simplified formula, we arrive at 92.7 runs created with Jones’ bat compared to Guillen’s 96.3 in 2007. So we lose 3.6 runs of offense. On defense however, we gained 29.5 plays, which works out to at least 23.6 runs using Tango’s established 0.8 runs = 1 play conversion. Funny how in the end we end up with nice round number, but there it is. -3.6 + 23.6 = 20 run improvement.



December 4, 2007

I’ve been asked to give an explanation of PrOPS. Since it is a stat that I expect will be used frequently, at least by me, at this site, I’ll oblige with a little crash course in PrOPS. PrOPS is available at the stats section of The Hardball Times.

First, lets think way back to a time when we thought ERA was the best measure of a pitcher’s talent, ouch! Finally, as I assume most people know, Voros McCracken came up with DIPS, defensive independent pitching. His most basic conclusion is that you can better predict ERA by taking away hits then including them. As time progressed it was David Gassko who finally gathered coefficients for all the batted ball types and came up with a new dips formula that relied on the type of batted balls. The difference between DIPS 3.0 and what McCracken came up with was the same as the difference between McCracken’s formula and just using ERA. Basically, the improvement was huge. This is one of the most important concepts in the evolution of Sabermetrics, the luck of the single. By establishing that pitchers did not have control of balls in play, things changed. Could this work for hitters. Enter PrOPS.

First, let me post this table once more, from and Dave Studeman.
FB .265 .720 .978
GB .236 .259 .495
LD .719 .948 1.667
This is what PrOPS is based on. There is clearly a relationship between the type and outcome.
PrOPS was invented by JC Bradbury, using batted ball data from BIS. He developed a formula that includes the following information: LD rate, GB: FB ratio, walk rate, HBP rate, K Rate, HR Rate, and home ball park. It was discovered that PrOPS was a very good indicator of what a players OPS would be minus luck. Most importantly, PrOPS explained OPS the next year better than actual OPS did. The basic result is that players who got abnormally lucky on batted balls got their numbers normalized. If you hit more line drives than another player, you should do better. Since most of the value of a flyball is dependent on homeruns, player’s averages on those should differ more than any of the others. Clearly Sexson is going to have more productivity from his flyballs than J-Lo, and PrOPS factors that in.

One of the reasons I love this stat is that, obviously, it works. If there were 1million game seasons, PrOPS would be unnecessary, but for stats like BABIP to stabilize, they need much more than the 600 pa’s in a season. If you asked me to predict Jose Guillen’s stats for next year, I could better do it with his HR rate, LD rate, etc than I could by actually looking at his OPS. That’s pretty important. Almost all players that severely over/underperform their PrOPS will return towards the total by PrOPS. BABIP (a factor in OPS) is a horrible stat to predict future performance, and this does better. There is a huge relationship between over/underperformance and rise/decline in the following year. JC hints that the formula is something close to [PrOPS-OPS)*.80]+OPS. Basically take 80% of the difference between PrOPS and OPS and add it to OPS. I believe this only works after a season, not during.

There are criticisms. Shouldn’t Ichiro! have a higher BA on GBs than Jose Vidro (there is no adjustment for speed). JC insists that there is no long-term correlation between speed and over/under performance. I would speculate that players that are faster tend to be weaker, and perhaps have lower averages on their FB’s and LD’s and it might tend to even out. Another criticism is that players do in fact have some control over their batting averages on batted ball types. This control is small, however, and except in a few severe cases (Ichiro! perhaps) I wouldn’t guess it would be a huge deal. It could also be a subject of improvement in the future.

PrOPS is one of the best, if not the best at spotting luck in a player. Most good sabermetricians are not going to be happy simply saying that Richie Sexson got unlucky, they want a number. I assume most people can look at a site like fangraphs and decipher that if Yu-Bet is hitting .254 on BIP, he was getting unlucky, but how unlucky, what should his BABIP be, given how he has hit the ball? That is where you use PrOPS. It is not good, however, for what has already happened. If you are trying to evaluate the past, things like linear weights and base runs are what you should use in those cases. What should have happened is irrelevant after it does happen, and PrOPS tells you what should have happened. So naturally it would be a good projection tool, right? Well, it kind of was. Tom Tango ran regressions with it and found it scored up with the PECOTAs and ZIPs of the world, but JC was not very compliant with using it that way. A real system might be slightly limited by a lack of batted ball knowledge. PECOTA is using 100 years of data, PrOPS at the most would use like 8. Also as far as I know it never included injury or age adjustments, which would be important. That it still scored as high as other projections with these limitations tells me something good was going on there. I believe there will be a stat that comes out sometime soon that uses batted ball data even better than PrOPS, and hopefully whomever does this will make a projection system out of this. For now PrOPS is what it is though. It is a great way to both identify and quantify luck, so we can say that Richie Sexson was one of the unluckiest guy in baseball last year, and he was this unlucky. I am very sure I will be using it a lot at the beginning of the year when Beltre is hitting .150 or William F. Bloomquist is up around .450. After this year I’ve already used it to say Sexson is better than Vidro, regardless of last year. PrOPS is a limited stat, but certainly a good one to add to your repertoire, when used correctly it can give good information as to what is likely to go on in the future.

The Value of Defense

November 18, 2007

Defensive Sabermetrics
As Sabermetrics progress, stats become more accurate and cover more ground. Recently some of the best out there have been turning their attention to defense.

Usually when people talk about defense, they like to phrase it in the following format:
Player X is (an all-star, above average, an asset, terrible) because his defense is worth (exactly the amount of runs it would take to prove the point in question), didn’t you see (one random play in a sample of hundreds that is indisputable evidence of player x’s greatness/deficiency). It’s an exercise in selective memory and egregious misuse of numbers

Recently, a few people have begun to think that defense is the next OBP. As it becomes more and more quantifiable people say that it is the most undervalued stat around. Defense is a skill that contributes to a team’s success. Not quantifying it into an evaluation of a player is foolish if there is a way to quantify it. Luckily, there is.

But how much is defense worth????
As the Mariners found out, on a team basis this is very valuable, on an individual basis, it is still worth a good amount. The Bill James Fielding Bible lists all players on a plus/minus scale. The info is compiled by Baseball Info Solutions. They describe the methodology on the site, but it appears that each play is painstakingly reviewed, and all plays a player makes that at least 1 player missed is worth +1, all plays a player misses that at least one player made is worth -1. While objective, this has been hailed as the best system ever, as a masterpiece, I’d say it really adresses the problem with things like zone rating and would say this is one of the best systems available now. The +/- system does what many people would say is ideal the way to evaluate defense, but wouldn’t even dream of investing the time to actually compile. Overall, a play is valued as slightly less than half of a run (no explicit formula stated). So what does it say???

At every position there are a few guys worth at least a win over the average defender. Albert Pujols (+37 plays) is worth about 17 runs, or 1.7 wins just with is glove. Derek Jeter (-34) is at -15 runs. (I use +/-*.45 and round). For a majority of players the results are pretty small.

Mariners players in the top 10 or bottom 5 at their positions
Player +/- approx. runs
Richie Sexson -15 -7
Adrian Beltre +7 +3
Raul Ibanez -23 -10
Ichiro! +4 2

All players are not listed (only the top 10 and bottom 5), but it is pretty safe to assume that all other players are worth between -2 and +2 runs, and at that level I wouldn’t feel confident saying a player was below or above average. Next time you compare Ibanez to the average player, subtract 10 runs, his defense cost the team a win. His Base Runs Above Average rated him at 32 runs; you can factor his defense down to 22 runs above average. Still a good player, but that difference is quite a few OPS points.

Can it be used?
Defense matters. There is likely to be improvements as with all stats, but the numbers at the fielding bible site are pretty good numbers to apply to players, and I would have no problem using them. It should be noted that the baseline is a .500 defender, while replacement level is I believe in the .350 range, so combination with VORP is not applicable, only metrics against the average player. I think defense can be used as an advantage in roster construction, like OBP was. OBP wasn’t used to figure out that Albert Pujols was a good player; it was used to discover Scott Hattebergs. It is possible that some team could garner an advantage this way. Suppose you have two guys, one is +10 runs with his bat and average with his glove, the other is average with his bat and +10 with his glove. Both players would rate as equal in your system, but the first player is going to be more expensive, and even if he was rated slightly higher, the salary difference would likely make the second player a much more money-efficient choice. As defensive metrics improve and more and more teams jump on the bandwagon, it is likely that teams will in fact add accurate defensive numbers like these to their ratings. As with OBP, the first teams to do so will a) run the risk of this whole thing being bologna and blowing up in their face and b) run the risk that they will have more accurate rating systems and will find many players at salaries that are much lower than their values and reap the advantages while other teams catch up.

1. I am willing to say that BIS’ ultra-thorough method of looking at every single play is good enough for me to consider this a good start, and I am willing to say you can put a run value to defense and that this is a pretty close approximation.
2. As with all statistics, more data is good, using 3-year aggregate data is going to be a better way to evaluate a defender, unless you have reason to believe (injury, age decline) that he is not the same defender.
3. If defense is quantifiable, and I believe it is, than teams that incorporate defense into their player evaluation methods, whether on data from BIS or their own, stand to take a competitive advantage over the teams that do not.

New Study on Pythagorean Baseball

October 22, 2007

Bill James released a study on the Pythagorean theorem of baseball, looking specifically at teams that over perform their record. His paper on the study can be found in the comments section.

The Mariners this season had a ridiculously high difference between their actual wins and their Pythagorean wins. Even higher was the Arizona Diamondbacks (9th highest overperformance in baseball history). Fans are fond of saying that the local 9 will continue to outperform their pythag for whatever reasons (reliever, clutch hitting, William F. Bloomquist), and everybody is sure they will, but will they?

I’ll make it quick, the answer… kind of. James looked at the top 100 over and underperforming teams in history. He compared their over/underperformance of year 1 with the next year. The results: Teams that were in the top 100 next year DID over perform their Pythagorean record(the Mariners’ over performance is #28 in baseball history), although by only 1/2 a win. These are the teams that outperformed by the most and they only outperform by ½ win. Whatever magic they had didn’t seem to carry over. Teams that underperformed would do so again, but by an even smaller margin. For all teams in baseball history the correlation coefficient between year 1 and year 2 was .04. Negative 1 would represent a perfectly negative relationship (as one went higher, the other went lower), 1 would represent a perfectly positive relationship (as one went higher, the other went higher). .04 essentiallly means it is pretty random and over/underperforming one year had almost no relationship with over/underperformance last year. Teams just do not possess that skill.

On an interesting note, when comparing a team that overachieved with a team that didn’t overachieve, but had a similar RS/RA ratio, the team that overachieved performed better than the other by about 3.5 games.

Conclusion: It could go either way. The Mariners are far from a lock to beat their pythag again. There is about a 50% chance they will do better than expected next year, but there is a 50% chance they won’t. Teams have not shown the ability to consistently outperform their runs ratio. Going forward, we will need to look at the Mariners as what they are. They are a 79 win club that needs to add at least 10 wins to consider themselves playoff contenders.