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Friday, June 08, 2007

Should you walk the bases loaded in a tie game in the ninth inning?

By Tangotiger, 11:36 AM

Craig Burley at Batter’s Box was asking about intentionally walking the bases loaded in the 9th inning of a tie game.

Here’s the situation:

It’s the bottom of the 9th in Toronto, tie game, one out, Matt Stairs is on 2nd base.  Based on the charts I provided Fangraphs, the win probability is .706.  Based on one of my old charts, it’s .703.  (All numbers presume average hitters coming up.)


Frank Thomas was IBB, so now we have runners on 1B and 2B.  The only runner we care about is the guy on 2B, since if he scores, the game is over.  Putting Thomas on 1B means you can now get a DP.  The win probability however has now increased to .716 or .711, depending on the chart you select.  So, it seems that the extra hope for the DP is balanced against the other things that can happen when you have guys on 1B and 2B.

However, let me interject something.  When I create those charts, I presume everything is average, including an average game state.  On average, you need to hold the runner on 1B, and leaving the hole open.  But in this case, we don’t care about the runner on 1B, unless we really need to keep him close for the DP.  But this is Frank Thomas.  I don’t know how the Rays fielders were playing.  When I apply the event-frequency and state-to-state transitions, I don’t have a separate one for 9th inning, tie game (though I definitely should).  So, these numbers are rough approximations, which makes presumptions that may not apply here.

As well, if Thomas is a better hitter than the next guy, it would make this play more acceptable.  The next hitter however was Troy Glaus.  He’s at least as good, and likely better.  So, that doesn’t really help.

Now the fun part.  You have a passed ball, putting runners on 2B and 3B.  The data I gave Fangraphs now says .850, while the other chart says .839.  What happens if you load the bases?  Incredibly, the win probability DROPPED to either .838 or .835.  What happens here is that you’ve now got a force set up at every base.

Again, remember my interjection.  The events and their frequency for bases loaded, based on my charts, does not take into account the inning/score.  This means that how the Rays (or any teams) defenses this situation (bases loaded, tie game, bottom of the 9th) will be different than in other situations (say loaded, down by 4, top of the 3rd), and therefore, the frequency of possible events, and their subsequent state-to-state transitions, will also be different.

The subsequent batter (Aaron Hill) is likely a worse hitter than Glaus, which makes the IBB a bit more appealing.  Of course, you’d want to also use the knowledge of whether a batter is a GB or FB hitter.

When I get home, I’ll check what Andy’s IBB chart says in The Book for these two situations.

While I normally caution against using sample data (you need one MILLION plays to get it reliable to the third decimal place), in this case, because of my stated presumptions, it might give us a bit of insight.  We can use this win probability finder, to see what has happened historically:
Runner on 2B: .704 wins (on 1241 situations)
Runner on 1B/2B: .747 wins (on 1092 situations)

Those numbers are 3 SD apart, so it seems that the second situation is a better situation for the batting team.

Runners on 2B/3B: .796 wins (on only 225 games)
Bases Loaded: .834 wins (on 610 games)

Note:
1B and 3B is .838 (on 419 games)
3B only is .831 (266 games)

So, it seems that whether you use my win probabilty numbers, or whether you use actual data, if you have a runner on 3B (in the bottom of the 9th and 1 out), it doesn’t matter if you have other runners on base.  The win probability will be roughly the same (.83 or so).  That loading the bases to get the force at any base is one of a series of parameters to consider, including the identities and abilities of the fielders themselves, and how the pitcher responds to such a situation.

All-in-all, it seems that the decision to walk or not walk was justifiable in either case.

#1    Mike Green      (see all posts) 2007/06/08 (Fri) @ 11:58

There were a couple of unusual circumstances.  Normally teams in this situation have their closer or set-up man pitching. In this case, the Rays had Tim Corcoran, who is far from either and who has had control issues.

Also, describing Thomas and Glaus as better hitters than Hill might be right in the general sense, and certainly over their careers, but in the particular context, it’s probably wrong.  Both Thomas and Glaus have a superior ability to hit the long ball, which is of decidedly less value in this context than usual.


#2    Guy      (see all posts) 2007/06/08 (Fri) @ 12:20

"historically:
Runner on 2B: .704 wins (on 1241 situations)
Runner on 1B/2B: .747 wins (on 1092 situations)”

Tango, I would think this is somewhat contaminated by different roads to these states.  In the historical data, some of the 1B/2B states reflect a pitcher giving up 2 hits or a hit and a non-intentional BB, and so could be telling us the pitcher is ineffective (compared to pitcher who gives up a 2B then elects to walk next hitter).

I agree that real world data is useful in these unusual situations, where defensive alignments and both teams’ strategies may be atypical, but you may need to control for quality of pitcher and hitter to know what it’s telling you.


#3    Tangotiger      (see all posts) 2007/06/08 (Fri) @ 13:01

Guy, I agree.

I should also point out that the significance test only shows that the 1B/2B situation leads to more wins, but it does NOT show how much more. It is certainly not a .033 win difference as the sample is showing.

I agree with Mike that you need to consider the total profile of the hitter, similar to when I looked at Bonds/Mayne, in that infamous game.  You need to construct the game-state-specific wOBA or LWTS, for the batter, pitcher, and fielders.


#4    Matt Finkelstein      (see all posts) 2007/06/08 (Fri) @ 15:43

I just wrote a post on The Fantasy Baseball Generals blog about a similar scenario.  If you have any thoughts I would love to hear them:

Last night’s Mets-Phils game was extremely painful to watch, and even more painful for Endy Chavez. For those of you who don’t know, the Mets squandered 6 innings of shutout ball when Heilman gave up a 3 run job on a 1-2 count in the top of the 7th. The Mets rallied in the next inning, getting runners on second and third, with none out, down by one.

From 30 years of data, compiled and presented by wallkoffbalk:
home teams have won at a 71.1% rate (59/83) when faced with that situation. The Mets pinch hit Julio Franco in the pitcher’s slot. The Marlins did not play the infield in, even at the corners.

Allowing the run to score while getting the out at first is a fairly win neutral play, with home teams winning at a 69% rate (306/442) with a runner at third, one out, in a tie game.

If the runner at third is does not attempt to score, and the batter is out at first base, then with runners on second and third, one out, the win expectancy drops to 56.3%(165/293).

If the runner on third, moving on contact, is thrown out at home on a hard hit ball to the infield, then with runners on first and second, one out, the home team’s win expectancy is 47.7%(358/751).

If the runner on third, moving on contact, is safe at the plate, then with runners on first and second, none out, tie game, the home team’s win expectancy rate is 74.4%(285/383).

So what does this all mean?

With the runner at third running on contact, the win expectancy ranges are 74.4% (safe on play at play to plate), 69% (scoring uncontested, with batter out at first), and 47.7% (out at the plate).

With the runner running “tentatively"or “conservatively” in failing to try to score, the win expectancy is 56.3%.

The numbers clearly call for aggressive running in close situations. The reward of scoring a run (69-74% chance to win) is far better than the consequence of making an out at home. Failing to attempt to score results in only a less than 10% gain in win expectancy over the unsuccessful attempt to score, while a successful attempt to score results in a 13 to 18% gain in win expectancy. This means that staying put at third is the best play only if there is a very good chance that the runner would be out at home. Of course, running on contact with the infield back will also result in an uncontested tying run a certain percentage of the time, which is another reason for the runner to be aggressive at third.

What about playing the “infield in”? The consequence of this strategy is that more balls leave the infield, and the runner on second will likely score the go ahead run. If that happens, with a runner on first, none out, and two runs in (one run lead), the home team’s win expectancy jumps to 85.5% (1,591/1,860).

So what happened to the Mets? Julio Franco hit a hard grounder up the first base line, and Ryan Howard makes a diving stop from his fairly deep position behind first base. Howard calmly walks to the first base bag for the force; it did not even seem like he cared about Ruben Gotay, who remained at third base.

I’m sorry, but not only is aggressive running the right play on most batted balls, when Howard hits the dirt to make the play, Gotay’s gotta dig it for home.

Actions have consequences: Reyes was walked to load the bases, and on a 3-2 count, after fouling off ball four, Endy Chavez strains his hammy while trying to beat the throw at first, which was an inning ending double play. The Mets have their first three game losing streak of the season, and Endy will be out a month.

I don’t know what Howard Johnson’s advice was to Gotay before the pitch to Julio Franco, but if he told Gotay not to score unless he was pretty sure he’d be safe, the numbers indicate that Gotay should be going on contact, and stopping only if he was pretty sure that he’d be out at the plate.


#5    Tangotiger      (see all posts) 2007/06/08 (Fri) @ 16:06

Can you restate your numbers using this data:
http://www.tangotiger.net/welist.html

As well, I’d caution using words like “only”.  The difference between a great pitcher and an average one is .020 wins in an inning (.680 minus .500 divided by 9).  And getting a walk is worth .030 wins for a plate appearance.

So the difference between 71% and a 69% win probability is in effect fairly significant.


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