## The power to influence results

Ever since Jim wrote a great article on why you do not want your best reliever to be your closer (could not find the link!), I am intrigued by "high leverage index" and the way we use our relievers. What is "high leverage index"? According to the definition of MLB: Leverage Index measures the importance of a particular event by quantifying the extent to which win probability could change on said event, with 1.0 representing a neutral situation. To me personally that does not say much, and I prefer a definition of leverage I encountered at Cambridge Dictionary: The power to influence results.

The definition stated by MLB uses an example to clarify Leverage Index (LI): For instance, if a team trailing by three runs had the bases loaded with two outs in the eighth inning, the ensuing plate appearance would register an LI above 1.0. This is because the outcome of the game could dramatically change on that one plate appearance. Conversely, if a team trailing by four runs has a man on first with one out in the top of the ninth inning, the ensuing plate appearance would register an LI below 1.0.

That example clarifies well the headaches that the LI causes me: If Archie Bradley pitches to a batter with the bases loaded and a with a 3 run lead and two outs, the corresponding LI would be above 1.0. But if Archie Bradley threw his first pitch with 2 outs and no man on base, than he has created that high leverage situation pretty much himself by screwing up all of his at bats. There are ways to counter this situation, for example by taking into account the Leverage Index when the starter entered the game and when he left the game (read a short introduction to it on fangraphs, by courtesy of Jack Sommers - thanks for the link you provided in a comment to me).

So, without digging into sabermetrics, and just like I did in a previous article, I am just going to have a look at some data I gathered and will be gathering the rest of the season. If you have any specific questions or requests, please, feel free to comment and I will try to get or provide some additional information in a follow-up article.

Data gathered: all MLB games played by the D-backs until May 31st including the final game of the Rockies' sweep at Coors Field. 57 games, providing us 902 at bats from our relievers. How do you get those data: writing down stats from each at bat: Reliever name, Game #, the opponent, Home/Away game, Inning, Batter name, Order in batting lineup, Result of the at bat, Balls-Strikes counts, Outs when the at bat took place, Run differential at that moment, runners on 1B, 2B and 3B and conclude if there was a Runner in scoring position, if there was Mound visit during the at bat (just curious if it is of any influence), if the batter was a Pinch hitter, if it was a Pitcher, if it was the First batter the pitcher faced, how many at bats did the pitcher have in the inning and if the result lead to an RBI.

Some general information: of these 902 at bats, almost 50% is a match-up with either Andriese, Koch, Hirano or Bradley. Talking about a possible overusage of your favourite relievers. Matt Koch was DFA'd almost 4 weeks ago, so it is pretty clear where his value was, despite the pretty lousy overall performance. In total, we have used 15 relievers so far this season, including our two positional players JRM and Joseph. Lopez used to be the guy for the 6th, but nowadays this land is McFarland's. Hirano in the 7th, Bradley in the 8th and Holland in the 9th. All others can be seen in any inning, especially Andriese who also pitches in the extra innings.

But, my intention is to have a look at the high leverage situations. All the at bats I have gathered are mapped to the High Leverage table so each At Bat has a leverage value. The mapping was a bit of a mind twister, because the table always uses the home team perspective. I had to rethink several times if I was applying the right values for our pitchers. In case you want a short summary of the high leverage table: if you hit the link the first table that appears as "Top of inning one" can be read as Greinke opening the game at Chase Field. The last table "Bottom of inning nine" would be Holland closing out a game in an away game with a 4, 3, 2 or 1 run lead.

There are some data I do not quite understand, like that an at bat with a runner in scoring position with no outs in the top of the first inning has a lower high leverage index than a runner on first with no outs. We can also see easily what the highest of all high leverage situations is: home team down by 1 run, bases loaded and 2 outs. Translating this for the Dbacks pitchers: that would be pitching in an away game, protecting a 1 run lead, bases loaded and 2 outs. Good for a high leverage index of 10.9. So, this is where the drum starts (you will have to imagine it), the curtains open and you see ... nothing. D-backs pitchers have not been (yet) in this situation so far.

The most stressing moment we have experienced so far was in game #32, a 10-9 win at Coors Field on May 3rd, when the Diamondbacks pitchers started the bottom 9th inning protecting a 4 run lead and eventually ended the inning with runners on 2nd and 3rd and a 1 run lead. Holland provided the final strikeout with an at bat that was good for a value of 8.4 on the leverage index. If we take a look at the detail of the game we can see that, although Chafin started the trouble, Holland entered the game with a 2 run lead and the bases empty. So, the high leverage situation was created by Holland himself as well, something we would not like to see.

To find out how reliable our relievers are in leverage situations I calculated the "Expected Leverage Index" or the "Desired Leverage Index" for the At bat. The "Expected LI" assumes that for the first batter the pitcher faces, the "Individual LI" or the "Real LI" is the same as the "Expected LI". The "Expected LI" for the next at bat would be the same situation as the previous at bat, but with an extra out.

Let me clarify this with an example: if a pitcher starts the inning with the bases empty, the "Expected LI" would be the same as the "Individual LI": 0 outs and no one on base. The "Expected LI" for the second at bat would be the value that corresponds to 1 out and the bases empty (the result of the previous at bat), but if the hitter in the first at bat reached first base the "Individual LI" for this second at bat will be higher than the "Expected LI". For the third at bat, we would calculate the "Expected LI" again with the situation for the second at bat, a runner on first base, but with an extra out.

These values can be mapped to a graph and the more often we see the "Individual LI" above the "Expected LI", the more volatile the pitcher is in important situations. What is important in the graph is to observe the deviation between the blue and orange lines, because although the lines are continuous the pitching is not continuous. Both lines always converge several times in the continuum, because for a pitcher's first at bat his Real LI is the same as the expected one.

Let's take a look at the graph of Greg Holland who is probably our most respected pitcher thus far:

What do we see here? On the horizontal axis progress in time, expressed by a number that combines game number, inning and batter position faced. On the vertical axis the high leverage index is given. You can see the wild deviation in game #32 where the "Individual LI" deviates from the "Expected LI", but in general it looks like a process under control. It would be interesting to see how the Josh Hader lines would look like, I guess they would show very little deviation, but in general Holland seems to do fine but can be shaky at moments.

Of course we are going to take a look now at the same graph for our favourite pitcher here, Archie Bradley:

This process is much more out of control. A lot of blue peaks reflect that Archie pitched himself into many high leverage situations, most notably games #2, #4, #34, #37. On the right hand side you can see the "Individual LI" dropping far below the "Expected LI" which in this case was the single he gave up to Arenado in game #54 and cost the Dbacks the 2 run lead. In a follow-up article I will incorporate the information on RBIs in the situation or not.

The following one is Andrew Chafin's and could be a true reflection of a not so reliable LOOGY: In general quite consistent, the blue lines follow the orange one most of the time, but with some heavy disturbances.

It would be nice to have a chart of another reliable reliever and Yoan Lopez comes close:

Lopez has not seen many high leverage thus far except for the ones he pitched himself into, most noticeable game #57 with the Rockies where we were all longing so much for an arm that would hold a lead. Other than that, his current performances are quite hopeful.

Because the high leverage values are highly related to the inning and the pitchers have pretty much a fixed order, it is quite hard to find out who will thrive best in what high leverage situations. Besides many of our pitchers look like a toss up at the moment. But here are a few take aways:

Runner in scoring position and two outs: Andriese takes him out 80% of the time.

Manny Machado coming up: Lopez takes out the 3rd and 4th batter 70% of the time. Sherfy is an ace when facing the top order as well, but with a smaller sample size than Lopez.

Straighten me out and I get the job done: after each of the 4 mound visits he received, Lopez got an out.

Can you imagine Sherfy and Lopez dealing with the top order in the 8th and 9th inning and Torey taking out Holland to let Andriese get that final out? That would be something revolutionary! My guess is he will let Bradley keep on grinding though.

To finish the article for today, these are the current standings in the schmuck categories:

Do not let me pitch with a runner in scoring position: 1. Bradley (29% of the runners score), 2. Hirano (27%). 3. Holland (25%). I took into account games with a 2 run differential.

No need for a mound visit: 1. Andriese (55% of the times a runner reaches base after the mound visit). 2. Duplantier (49%) 3. Bradley (40%).

Walk this way: 1. Bradley (17% of the batters walk) 2. Andriese (15%). 3. Chafin/Holland (12%). Chafin walks 10% of the first batters he faces, but Hirano even more (12%). Leader is Sherfy, but very small simple size (1 in 5).

The pinch hitter will eat me: 1. Andriese (46% of pinch hitters reach base). 2. Hirano (44%). 3. Holland/Chafin (40%) A pinch hitter is in this case a guy that only had one at bat and did not stay in the game.

I'd rather have the next batter: 1. McFarland (37% of the first batters he faces when entering the game get on base). 2. Hirano/Chafin (36%). 3. Bradley (33%)

Avoid the top order: 1. Chafin (47% of the batters of the top order, the first four batters in the lineup, reach base) 2. Andriese/Holland (41%) 3. Hirano (38%)

I will keep on refining the data and in an other article I will take a more in depth look at situational hitting, because I think the situational aspect makes a big difference:

- Pitching to Kyle Hendricks with the bases loaded and two outs is not the same as pitching to Anthony Rizzo (or Zack Greinke) in that same situation.

- Pitching against the top order with a runner in scoring position in the 8th at a tie is perhaps of more importance than pitching against the bottom order in the 9th when protecting a lead.

Leverage Index does take this situational hitting somehow into account. You can read it over here, but I want to see myself what is behind.