Tuesday, January 30, 2007

As you know, the Angels under Mike Scioscia have become known for playing a brand of "small ball"; often low on sluggers, the club has had to maximize the output of its baserunners in order to score runs and win games -- or, at least, that's how the theory goes.

One aspect of this is a willingness to employ the sacrifice bunt. Since Scioscia took over the club in 2000, the team has ranked (progressively) sixth, fourth, first, fourth, second, fourth, and eighth in the American League in successful sacrifice hits.

I thought I'd take a look at our bunts from last season, to see if they helped or harmed the team's offense. Though it seems odd to look at the year in which the Angels bunted the least frequently under Scioscia, it is the most recent season, which, to me, anyway, is of the most interest.

You can find links to boxscores and play-by-play for every game that contained an Angel sacrifice hit here, thanks to the wondrous and magnificent Baseball-Reference Play Index. The Angels sacrificed successfully in 26 games, and ended up going 20-6 in those games.

Let's take a closer look. But before we do, let me clarify: the data I am examining will not allow us to determine whether or not we were hurt by all bunts called, we're just looking to see if the bunts executed correctly ended up backfiring on the offense.

What's the background here?
After years of support from everyone in baseball, in the late 1970s and early 1980s the sacrifice bunt came under assault from some within baseball (most notably Earl Weaver) and sabermetric authors such as Bill James and Pete Palmer.

Anti-bunt theory holds that your twenty-seven outs are sacred, and should only be given away in extreme circumstances. Further, giving away outs was considered likely to decrease the chances of a team scoring in that inning. Empirical studies bore this out; in The Hidden Game of Baseball, Palmer and John Thorn printed a run expectancy matrix (an updated one can be found here, with some from the past here) that showed that teams bunting a runner from first to second were giving up runs; in the case of the updated matrix, with a runner on first and no outs an average team would score .953 runs (i.e., a team in this situation 1,000 times would score 953 runs), but only score .725 with a runner on second with one out. Just about the only time permissible to bunt, according to such theories, would be in late innings of close games where one run is of paramount importance. The notion that a successful sacrifice bunt actually harmed the bunting team became a key belief of sabermetric dogma.

In an essay called "Rolling in the Grass" in his indispensable (and underrated) Guide to Managers, Bill James questions many of these assumptions (assumptions he had once trumpeted). For one, the run expectancy matrix was based on average hitters against average pitchers; for another, other things (errors, beating out hits) can happen when you bunt which are advantageous to the batting team, and the possibility of these must also be accounted for.

In The Book, Mitchel Lichtman -- at great length (the chapter runs 51 pages, and is the longest in the book) -- further explored the question of when bunting should and should not happen, exploring factors from the positioning of the defense to the groundball propensity of the batter. Lichtman's work really re-opens the question of how the bunt works; the former sabermetric knee-jerk against it seems, to me, at least, overly simplistic.

Given all these factors, how can we determine if any specific bunt is a good play or not?
Well, it's hard. And probably impossible. But we can make a best guess.

The Book employs another toy, a Win Expectancy chart, this a baby of the Tango Tiger. It basically takes a situation -- say, the home team is up in the bottom of the fifth, down by two runs with a guy on first and one out -- and tells you the chances of that team winning -- in this case, a winning percentage of .304. Hitting a home run raises it to .570. (You can, courtesy of Studes, download a spreadsheet to calculate this kinda stuff here.)

Of course, the Win Expectancy chart is also based on average hitters being up all the time, which isn't always the case.

But there are ways to deal with that, too.

Is this about to get technical?
Yeah, a bit. But I'll put a big ***** where the technical stuff ends in case you want to skip that and get to the good stuff.

I am a nerd, and cannot wait to read this part. Please do not disappoint me.

It probably helps for you to download that spreadsheet to play along.

First of all, you'll see that it wants you to enter a run-scoring environment. What I did for this was take the park-adjusted league-average ERA for each park from BB-Ref (it was 4.38 for the Big A last year) and add .50 for unearned runs.

This doesn't really make a huge difference; in a 4.5 environment, bunting a guy from first to second in a 3-3 game in the bottom of the ninth "loses" you .009 wins; make that a 4.75 environment, and it's .010. 5.25? .013.

So even if I got an environment wrong, it's going to be within a few thousandths of where it should be, which I can personally live with.

The rest of the spreadsheet is pretty self-explanatory; I just plugged in each situation and recorded the change in WinEx.

The next step was to adjust for the quality of the batter. I posed the question of how to do this to Tango on his blog and got a spectacular response, which you can read there.

Basically, I figured out how many runs per plate appearance (using a basic linear weights, park-adjusted) each of our bunting batters was in 2006 compared to the league average. Divide that by 10 to get an estimate of wins above average, then multiply that by the Leverage Index for the situation ... say you have a batter up in that 4.5 environment situation, the 3-3 score, blah blah blah. The WinEx going in is .711. The batter is bad, -.005 runs per plate appearance. The LI is 3.1, so he decreased that by .016, so the WinEx is now .695. A successful sacrifice will raise it to .702, so, if he can bunt, well, that successful sacrifice helps the team.

After doing that, it became obvious to me that I should have accounted for how specific batters do against righty and lefty pitchers, as well as look at more than one season (where available) for each batter in order to best gauge his true talent level.

So I took the last four seasons (or, up to, for players who haven't been in the majors that long) of each of the bunting batters and broke them down into vs. RHP and vs. LHP, essentially creating profiles for two batters where there had been only one. From that point on, everything was the same as described above. (Honestly, I probably should have tried to regress some of that stuff, too, but we're dealing with such fractions that I don't know if anything would have turned out very differently.)

Really, you could keep going, accounting for the quality of pitcher, the opposing defense, groundball tendencies of batter and pitcher, etc. But at a certain point you're creating work and not really making huge strides in being right. I think the level of adjustment I've put in should be enough to give us a general view of the situation.


How many times did the Angels sacrifice in 2006?
31, though two of those came from starting pitchers in interleague play. Though under normal circumstances deciding whether or not your pitcher should bunt is a strategic consideration, in the case of interleague play, I think it's just a manager protecting his pitcher. "Go out, bunt, come home safely." So I don't count those two in any of the analysis I'm doing.

What kind of situations did we bunt in?
Broken down:

  • Man on first, no one out: 14 times
  • Men on first and second, no one out: 6 times
  • Man on second, no out: 7 times
  • Men on first and third, one out: 1 time
  • Man on third, one out: 1 time

    All told, for the 29 bunts, there were 36 men on base, and 22 eventually scored.

    Is that good?
    Well, I don't know.

    You know the Run Expectancy Matrix I linked above? That can be further broken down. This chart tells us that, from 1999 through 2002, if a team had a guy on first base with no one out, that team would score one run .176 of the time. That doesn't necessarily mean that it's the guy currently on first who scores that run (if that guy gets thrown out stealing, then the next guy hits a home run, that's still a run for the purposes of the chart), but I think that should be close enough for us to make some guesses; if anything, that will mean our estimate of how many runs should have scored may be a bit high.

    We had that situation and sacrificed 14 times last season; 11 of those times, the guy sacrificed to second scored. From 1999 through 2002, we would expect one run (or more) to score .437 of the time (if two runs score, that first run has to score first). In 14 situations, that would be 6 runs, so we're five runs ahead.

    Going through each situation:

  • Man on first, no one out: 14 times x .437 = 6.118 runs
  • Men on first and second, no one out: 6 times x .641 = 3.846 runs
  • Man on second, no out: 7 times x .632 = 4.424 runs
  • Men on first and third, one out: 1 time x .655 = .655 runs
  • Man on third, one out: 1 time x .661 = .661 runs

    That's a total of 15.704 runs we would have been expected to score with average hitters up in these situations; as we (as we'll soon see) generally bunted with below-average hitters, we would expect to score less.

    In fact, we scored more often, getting 22 runs home. This indicates to me that Mike Scioscia was choosing his spots well, and probably got some luck on his side.

    However, there was a lot of guesstimation on this, so don't take that as the God's Truth. It's a scarcely-educated guess, nothing more.

    We can also look at the total number of runs expected to score each inning vs. how many we scored in innings with a sacrifice bunt. Here are the relevant situations from The Book:
    1--, 0: .950
    12-, 0: 1.585
    -2-, 0: 1.192
    1-3, 1: 1.249
    --3, 1: .999
    Going through math above, we find that the Angels, in innings where they sacrificed, "would" have scored 33.402 runs (again, this is with average hitters against average pitchers). As it turned out, the Halos scored 40 runs in such innings, hinting once again that Scioscia called bunts (1) wisely and/or (2) and benefited from luck.

    Who was asked to bunt, and against whom?
  • Orlando Cabrera: 3 (1 against RHP, 2 against LHP)
  • Darin Erstad: 1 (against RHP)
  • Legs Figgins: 5 (3 against RHP, 2 against LHP)
  • Maicer Izturis: 5 (2 against RHP, 3 against LHP)
  • Adam Kennedy: 3 (1 against RHP, 2 against LHP)
  • Casey Kotchman: 2 (1 against RHP, 1 against LHP)
  • Jose Molina: 7 (5 against RHP, 2 against LHP)
  • Tommy Murphy: 1 (against RHP)
  • Reggie Willits: 2 (against RHP)

    What about all that win expectancy stuff you made me read/scroll past?
    Without adjusting for the quality of the batter, the successful sacrifices by the Angels cost the team a whopping .224 wins.

    That's nothing; that's two runs a season. If I adjust for the quality of the batter, that goes up from -.224 to -.094. Once I account for the handedness of the pitcher, which is as far as I went, that went up to -.080.

    This is, of course, pretty negligible, and given the levels of estimation required at every step here, is tantamount to saying "These sacrifices did not cost the Angels at all," in my opinion.

    In fact, it appears that Mike Scioscia had a pretty good grasp over who should bunt, and when.

    Or, at least, I think so. I haven't looked at other managers; maybe they all come out better under such analysis. It's certainly possible that every team is close to zero in this regard, and given the low number of sacrifice hits in the modern game, that would be my default assumption.

    Here is each batter listed by how many wins his bunts gained/lost for the team:

  • Orlando Cabrera: -.005 (+.005 vs. RHP, -.010 vs. LHP)
  • Darin Erstad: -.021 (vs. RHP)
  • Legs Figgins: -.077 (-.045 vs. RHP, -.032 vs. LHP)
  • Maicer Izturis: +.007 (-.028 vs. RHP, +.035 vs. LHP)
  • Adam Kennedy: -.017 (-.014 vs. RHP, -.003 vs. LHP)
  • Casey Kotchman: +.009 (.000 vs. RHP, +.009 vs. LHP)
  • Jose Molina: +.018 (.049 vs. RHP, -.031 vs. LHP)
  • Tommy Murphy: +.027 (vs. RHP)
  • Reggie Willits: -.021 (vs. RHP)

    What does the win expectancy chart say were the wisest bunts executed?
  • Jose Molina vs. Chris Ray, man on 2nd, no outs, and a 2-2 score in the bottom of the ninth: under normal circumstances, the WinEx going into this situation would be .817, with a .835 with the guy on third and one out. Molina is not a good batter against RHP, however, lowering the going-in WinEx to .798. The Fast Molina's successful bunt raised the win expectancy .037; the Orioles proceeded to walk the bases loaded, and Orlando Cabrera popped out and Vlad grounded out to end the inning.

    The Angels won in the bottom of the tenth when Adam Kennedy, with runners on first and second, hit a three-run home run (more on this later).

  • Tommy Murphy vs. Miguel Batista, Tim Salmon on 3rd, one out, we lead 1-0 in the top of the second: a squeeze bunt was a great call here, as Murphy proved to struggle against RHP all year.

  • Maicer Izturis vs. Tim Byrdak, 1st-and-3rd, one out, we're up 5-2 in the top of the eighth: not only a squeeze, but Maicer ended up reaching on a fielder's choice, raising the WinEx from .947 to .973.

  • Jose Molina vs. Huston Street, man on 1st, no outs, we're up 4-2 in the top of the ninth: Jose got his man over; the insurance run didn't score, but with Jose vs. a top RHP, it was a good move, increasing our chances from .910 to .928 (the starting point would have been .932 with an average batter at the plate).

  • Jose Molina vs. J.J. Putz, man on 1st, no outs, tied 2-2 in the bottom of the ninth: sensing a theme here? Jose got his man (Reggie Willits) over to second, and Legs Figgins promptly knocked him in to win the game.

    Of the 29 bunts, 12 had results that were neutral or better, and another 6 were within .010 of neutral, which for me would still sit in the "too close to call" camp.

    What were the worst bunts?
    I'm not going to go through them individually, but each of the worst five:

  • came with a man on first with no out;
  • and with a tie score.

    Four of the five came in the ninth inning or later, and the one that didn't came in the seventh.

    Also, four of the five instances led to the runner scoring, and the Angels taking the lead.

    I'm actually not convinced that the WinEx models get extra innings right (or perhaps I was mistaken to use the ninth-inning values for extra innings); it is also possible that teams are wrong to play for one run as often as they do in such situations.

    You're only talking about successful bunts here. What about unsuccessful ones, or ones that turn into hits?
    A good question; unfortunately, the data is such that there is no easy way to ferret out such circumstances.

    And, to clarify: yes, I just praised a question that I wrote to myself.

    Remember that Adam Kennedy home run I said I'd come back to? Here is that game. Check out the bottom of the tenth:
    Bottom of the 10th, Angels Batting, Tied 2-2, Julio Manon facing 5-6-7
    Sit Pit Batter Result
    --- 4 G Anderson Single to CF
    1-- 2 R Willits Single to 1B/Bunt; Anderson to 2B
    12- 2 A Kennedy Home Run (RF); Anderson Scores; Willits Scores
    Two things pop out here; one, Willits had a bunt single. This was certainly a case where, had Willits been thrown out, he would have been credited with a sacrifice. Instead, he beat it out for a hit. Mike Scioscia, in calling for this bunt, obviously knew Willits, a speedy runner, had a chance to beat it out (or reach via an error), so if you wanted to go through and assign Scioscia some kind of score for the bunts he called, this would be a credit. The result of the play added .104 in win expectancy (which in itself is greater than the -.080 brought to us by our sacrifices); had it been a sacrifice, it actually would have been a slight loss (-.011, before adjustments).

    That's the first thing; the second thing is ... look at Adam Kennedy: his plate appearance took two pitches. This is what they were:
    1. Foul Bunt
    2. Ball in Play
    So here's a situation where Scioscia called for the bunt, Adam didn't get it down, and he took off the bunt. Adam went deep. How would we credit that? I don't know.

    Also, I don't know how many situations happened such as in this game:
    Bottom of the 7th, Angels Batting, Behind 3-4, Roy Halladay facing 7-8-9
    Sit Pit Batter Result
    --- 2 M Napoli Home Run (CF)
    --- 1 R Quinlan Single to RF
    Chone Figgins pinch runs for Robb Quinlan batting 8th
    1-- 1 T Murphy Single to SS/Bunt; Figgins to 2B
    12- 1 A Kennedy Groundout: P-3B/Forceout at 3B; Murphy to 2B
    Remember that groundout by Adam? It was a bunt, and Adam took exception to what he was thought was a poor jump by Chone Figgins from second, and all hell broke loose in the locker room after the game. I remember that because I remember things like this, but I don't remember every instance, and the gamelog doesn't even record the fact that it was a bunt.

    What's more, look at Tommy Murphy, right before Adam comes up: guy on first, no outs, lays down a bunt late in a tie game ... and gets a hit! A situation just like the one we just finished looking at with Reggie Willits.

    The fact is, you can't really evaluate whether a bunt was a good or bad call without examining every possible outcome, or at least reasonably possible outcome.

    What I wanted to look at here was a narrow question: did the sacrifice bunts we got down hurt us? The probabilities say: "If so, it was ever so slightly." The results say: "The Angels actually seemed to do better in innings in which they successfully sacrificed than they would have otherwise."

    What have we learned from this?
    I have learned that, with the right combination of batter, pitcher, and situation, a sacrifice bunt can be a valuable weapon. If you have a hitter like Jose Molina, who is not fast, a double play threat, a poor hitter against right-handers, but is a more than competent bunter, a sacrifice will often be a good call in certain situations. If you have an overmatched left-handed hitter, like Adam Kennedy vs. a top southpaw, a sacrifice will often be a good call.

    Mike Scioscia may get a bit cute with such calls from time to time (he asked Mike Napoli to squeeze last year, for God's sake), but he appears to have a pretty good grasp of when a bunt does and does not help the team. Hopefully this will continue, as our offense looks as punchless as ever, and we'll need as much help as we can to score runs and compete in a tough division.

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  • Comments:
    Fantastic, Blackhawk. Glad to see my spreadsheet being put to great use.

    Here's a question, though. The WE of a situation is dependent on not only a specific batter, but the talent of all the following batters (and opposing pitchers). So if you change the run environment for a specific at bat, you're essentially changing the skill level of that batter and every other batter following. In other words, not just that batter. Of course, you're doing that for both teams, so I'm not sure how it really shakes out.

    One of the things I've meant to do is someday figure out how to make the spreadsheet work for a specific batter or pitcher, keeping every other spot in the batting order at an average level. Very tricky to do.

    Anyway, did you account for that at all?
    Thanks, Studes.

    No, I didn't get into the effect of antecedent batters on the WE (or what changing the WE for one batter does to those that bat behind him). I'm not sure how you would do that, actually, short of using some kind of Markov chain (or something similar beyond my capabilities).

    Thankfully, outside of Vlad the Angel lineup is pretty mediocre, so I'm not sure there would be a large effect.
    Excellent article. Very well thought out. I think it is clear that all bunts are not created equal just like all batters are not. It is highly dependent on all of the factors in any situation.

    Something that I think is important and probably impossible to calculate is the psychology of baseball. It is a long season of game situations played by human beings. How much does confidence play into a teams success and how much impact does a manager have on that?
    Awesome article. Two comments

    1) If you were able to toss in unsuccessful bunt attempts isn't it likely that bunting, on the whole, has a negative outcome on the win expectancy giving that successful bunts hover around the break even point? Also, can you work backwards then to calculate a break even success rate? Finally, can you use the framework of your study to find out when Barry Bonds should bunt? Sort of like when Tango looked at when to walk Barry Bonds.

    2) Pitch-by-pitch Win Expectancy. Has no one created this yet? :) In your example where Adam Kennedy hits the HR after the failed bunt attempt, the foul bunt actually lowers the win expectancy because hitters succeed less often in an 0-1 count than an 0-0 or 1-0. Now, if it is more likely that the first pitch ends up a strike in a bunt attempt than a normal AB that's a knock against bunting.
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    A greater likelihood of bunting also forces the defenders and even the pitchers to adjust their strategies, which is hard to quantify, but definitely exists. A third or first baseman playing in reduces his fielding range on a liner and If you're hitting and the pitcher is thinking you're likely to bunt, on average, you're going to see more high strikes.
    1) If you were able to toss in unsuccessful bunt attempts isn't it likely that bunting, on the whole, has a negative outcome on the win expectancy giving that successful bunts hover around the break even point?

    I guess that's possible, but remember that I'm also not including bunts that turn into hits. So it may wash out. There are also game theory issues to consider, esp. in regard to the positioning of the defense.

    2) Pitch-by-pitch Win Expectancy. Has no one created this yet? :)

    I'll wait for Tango to take car eof that ...
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