For any interested readers, Matt and I re-wrote Matt’s post on the Mets-Marlins game, and did some further analysis, for submission to the next SABR Baseball Research Journal. I am posting the text of our article for anyone’s comment, all of which will be helpful. Thanks in advance to anyone who comments:

AN ANALYSIS OF PLAYING THE INFIELD IN
By Matt Finkelstein and Patrick DiCaprio

On May 26, 2007, in a game between the Mets and Marlins, an intriguing situation arose that led to this article. Here is what happened:In the top of the 9th inning, the Mets had runners on first (Paul LoDuca) and third (speedy rookie Carlos Gomez), with none out. The score was tied 1-1, with Reynel Pinto pitching to Shawn Green. The Mets announcers lambasted Marlins Manager Fredi Gonzalez for having SS Hanley Ramirez and 2B Dan Uggla playing at double play depth. We were struck at the obloquy evident from the rant of the announcers (an ex-ballplayer was the most vociferous). It was our opinion that Gonzalez made the right decision, or at least a justifiable one, and our analysis follows.

Green hit a routine double play ball; a one hopper to Ramirez, who threw home in time to get Gomez, however, catcher Miguel Olivo muffed the throw. All of the runners were safe, one run was in and the Mets now led 2-1. The Mets tacked on 4 more runs and won 6-2. Green’s grounder to Ramirez appeared to be a routine double play ball, it was hit two steps to Ramirez’ left and he had an unobstructed throw to first. Showing his catcher’s fleetness of foot, LoDuca was not even 1/2 way to second when Hanley reached second base.Gonzalez bucked the conventional wisdom by giving his players the apparent “choice” to opt for the conventional double play in that situation. That Ramirez chose to throw home is irrelevant. For Gonzalez’ decision to be correct we pose the following question: does holding the damage to one run (by conceding that run) give the Marlins the best chance to win?

For purposes of simplicity, we start our analysis with the assumption that the chance of executing the double play or getting the out with the infield in play is the same. (In reality, playing the SS and 2B at double play depth will result in more outs, if not double plays, because less balls will get through the infield). In effect, assuming the SS has a “choice” of taking the double play or getting an out while preventing a run to score, what’s the best play? Let’s look at the numbers. David Nichols published an Expected Runs table, which uses 10 years of actual MLB data to give you the expected runs that any given situation will generate in the long run, and provides the probability that the situation will result in at least 1 run. The table can be found at:http://www.nssl.noaa.gov/users/brooks/public_html/feda/datasets/expectedruns.html

With a runner on first and third and 0 outs, the run value to the Mets is 1.75 expected runs (“ER”), and they will score at least one run a whopping 87% of the time.If the Marlins concede the run, but successfully turn the double play, they will have allowed the run, but eliminated all baserunners and obtained two outs, giving themselves an excellent chance of avoiding further damage. In fact, according to the Nichols’ table, after the double play, the expected runs drops from 1.75 to 1.1 (one run is in, and with none on and 2 out, the expected runs is 0.1). According to the table, the chance that the Mets score one or more additional runs after a double play is only 6.7%. This means that by turning the double play in this situation, the Marlins have a 93.3% chance of getting to the dugout down only one run. What are the odds of scoring one run in the 9th? According to Nichols, the Marlins will score at least one run 27.5% of the time. This implies that the Marlins will score in the ninth inning at least 25.6% of the time (.275 x .933), or just over one quarter of the time.

The “infield in” situation is more complex:Assuming that whatever course of action the fielder chooses will be successful, and with the infield in when a ground ball is fielded by the shortstop or second baseman, there are two likely outcomes:

1) The runner on third tries to score and is out at home:
Expected Runs drops to 0.92 ER, with a 42.5% chance of scoring at least one run: (R: 1-2 /1 out = 0.92 ER/.42 >0).

2) The runner “stays put” or gets “looked back” by the defense, which takes “safe” out at 1st base: (R 2-3/1 out = 1.4 ER /0.67 >0).
(Another likely possibility: the runner on third tries to score and is safe at the plate: R 1-2/0 out, one run in = 2.5 ER/0.64>1, is outside the assumption that the play chosen is successfully executed).

Note that the 1.4 ER scored with runners on second and third and 1 out (the situation where Ramirez “looks back” the runner on third) is 0.3 ER greater than the 1.1 ER by getting the double play. This is likely due to the presence of two runners in scoring position with less than two out, and why going for the double play early in games is an easy decision in most circumstances. Throwing out the aggressive runner at the plate generates a residual ER of 0.9, not much less than the 1.1 ER of the double play. This is a key point; the preferred “conventional wisdom” play touted by the announcers is only 0.2 runs better than going for the double play. However, the downside is significantly worse, as will be shown below.

Additionally, with none out, it seems more likely that the runner at third will be a bit more conservative with a drawn in infield, as there are still many ways to score with one out. A successful “infield in” play at the plate reduces the Mets’ odds of scoring 1 run from 87% to 42%. However, a “successful “look the runner back” infield in play only reduces the odds of scoring at least one run to 67%, and still results in more expected runs than the double play (1.1 vs. 1.4 – see above), which means a better chance of scoring multiple runs in the inning. At least in terms of ER Gonzalez’ made the right decision. For this reason we think Gonzalez’ decision is plainly justifiable.

We must address the downside of course. The downside of playing the infield in is that more balls will get through the infield, and if so, the home team is now down a run, with either first and third and no outs (which results in 2.75 ER and at least an 87% chance of scoring at least one additional run), or first and second and no outs (2.5 ER and a 64%>1 run deficit). If this happens, it’s disastrous to the home team’s chances of winning, as shown below.

Of course, we can also look directly at historical data on a team’s chance of winning in various scenarios. In this regard, a fascinating toy and potential managerial tool is located at:http://walkoffbalk.com/This site uses up to 30 years of historical data to demonstrate a team’s chances of winning in any situation, any inning, of a ballgame. In order to obtain the largest sample size, we will use the data for all 30 years.

With runners on first and third and none out, this tool demonstrates that teams have won 20.8% (27 wins out of 130) games (using data from 1977-2006). Using the same data, choosing the double play (down one run, bases empty, two outs) resulted in a home team win rate of 15.2% (968/6373)
With a Successful “infield in” play we have two probable outcomes:

Runners on Second and Third, one out: home team’s win rate 31.8% (77/242)

Runners on First and Second, one out: home team’s win rate 41.2% (328/797)

Assuming both are approximately equally likely to occur, we will take the average and say that the home team will win 36.5% of the time ((31.8 +41.2)/2)

Let’s look at what happens to the win rate with an unsuccessful “infield in”. The unsuccessful “infield in” play will
have the following probable outcomes:Runners on First and Second, 0 out, 1 run in: home team’s win rate: 10.3% (27/261)

Runners on First and Third 0 out, 1 run in: home team’s win rate: 6.2% (9/144)
Again, assuming that both outcomes are approximately equally likely, the home team will win just 8.25% of the time.

Choosing the double play increases the chances of winning over and above the unsuccessful infield in play by a significant margin. But what about as compared to the successful “infield in” play? The successful “infield in” play results in a 36.5% chance of winning versus a 15.2% chance if the double play is successful. So at first glance the Marlins would have to get 2.4 times as many double plays as successful infield in plays to break even. On the other hand as compared to the failure of the “infield in” play the double play depth play doubles the Marlins chances of winning, from 8.25% of the time to 15.2% of the time.

However, this ignores other favorable outcomes. Another benefit of playing the middle infielders at double play depth is that less balls will make it through the infield, and even if they cannot turn the double play, they may be able to get the force at second or an out at first, with the runner advancing to second:

Runner on first, 1 out, 1 run in: home teams win rate 14.8% (253/1707);

Runner on second, 1 out, 1 run in: home team’s win rate 16.2% (178/1099)

An equal weighting here results in a 15.5% chance of winning. So here is a summary of the results:

Double play: 15.2% chance of winning
Getting one out: 15.5% chance of winning
Successful “infield in” play 36.5% chance of winning.
Failed infield in play: 8.25% chance of winning

Adding both positive outcomes from the double play depth decision now reveals that the double play depth decision will result in a Marlins win 30.7% of the time, as compared to the successful infield in play win rate of 36.5%, for a 6% edge to the infield in play. But the downside is that if it fails you will win only 8.25% of the time. So given these facts it appears that the double play depth decision is at least arguably correct as you trade a small decrease for a large one if it fails.

We also note for completeness that the home team has no control over whether the runner on third will be going on contact with the infield in, and the numbers demonstrate that being aggressive in that situation is generally not advisable.

Whether Fredi Gonzalez’s decision in this case was actually “correct” in terms of expected runs depends upon several factors, including:
The speed of the runner on third;
The speed of the runner on first;
Speed of the batter;
Proficiency of the double play combo;
Defensive ability of the catcher;
The batters “on deck”;
The batters due up next inning;
The visiting team’s closers relative ability to pitch a scoreless inning.

Based upon the gross numbers alone, it seems to us that taking the double play in this situation is probably correct. At a minimum it limits the downside of disastrous outcomes where you win less than 10% of the time.

A thinking manager should not and will not dismiss any strategy out of hand; we believe that Fredi Gonzalez displayed courage (a characteristic too often lacking among baseball managers) and independent thought that likely was the best for his team in that situation, despite the conventional wisdom to the contrary. Perhaps the fact that Gonzalez is a rookie manager made him open to giving his players the opportunity to making an unconventional play to give his team the best chance of winning the game.