Alex Reyes and Accepting High-Leverage Walks

On July 20, the Cardinals dropped a game to the Cubs despite going into the ninth inning with a 6–1 lead. Based on Greg Stoll’s win expectancy calculator, when the home team is winning by five runs in the top of the ninth, that’s a victory 99.7% of the time. The Cardinals acted accordingly, bringing in veteran journeyman Luis Garcia for his 2021 debut. This was mop-up duty … until it was not.

Garcia struck out Patrick Wisdom to start the inning, but he was able to reach first base on a dropped third strike. Nico Hoerner followed Wisdom with a single, and Jake Marisnick walked. The odds were still in the Cardinals’ favor; the win expectancy calculator gives the home team in this spot (up five, no outs and the bases loaded) a 97.2% chance of pulling it out. Nevertheless, manager Mike Shildt felt the heat enough to bring in his closer, Alex Reyes. But things did not go as planned. Reyes went walk, strikeout, walk, single, double; a 6–1 lead had turned into a 7–6 deficit in the blink of an eye.

The double did the most damage, but the walks are a theme with Reyes. The surface-level numbers are fantastic; dig one step deeper, and things look a little concerning. On the season, he has posted a 29.3% strikeout rate but also a 19.2% walk rate, leading to a 1.38 WHIP (league average is 1.29) and a 1.53 K/BB ratio that’s about 41% worse than the average pitcher. Reyes’ FIP is 3.68 despite the issues with walks, a testament to his strikeout prowess (led by a slider, curveball, and changeup that generate whiff rates of 46.4%, 57.9%, and 40.0%, respectively, per Baseball Savant) and his ability to induce groundballs with his bowling-ball sinker.

Still though, that walk rate is an issue, but what I want to do here is assuage some of the concerns and help reinforce a point made by Baseball Prospectus’ Jonathan Judge on Twitter just last week: that often a walk or hit-by-pitch is the next best outcome after a strikeout (compared to a ball in play). He noted that while Reyes is toeing the proverbial walk rate line, he has the tools to make that extreme profile work, especially with his ability to generate groundballs with his sinker.

The amount of vitriol derived from walks and high walk rates is a product of how we interpret those events. We traditionally consider the value (or lack thereof) of an event in terms of its run value. From 2019 through ’21, the value of all walks and hit by pitches has been 8,558 runs over 34,379 plate appearances. That comes out to about a quarter of a run (0.2489 to be exact) per event, or about 25 runs per 100 events. On the other hand, in that same timeframe, balls in play yielded 14,547.7 runs over 241,749 batted ball events — 0.0602 runs per event, or about six runs per 100 batted balls. The preference from the pitching team’s perspective is clear: batted balls are a much more desirable outcome than walks/hit-by-pitches.

So pitchers who walk a ton of hitters in favor of allowing the defense to make plays (for a given strikeout rate) are costing their team runs, correct? This, however, is a product of the decoupling of run expectancy and win expectancy as the game progresses. Based on 2020 data, in the first three innings of a game, the relationship between change in run and win expectancy on a play is strong, with a coefficient of determination of 0.85 (85% of the variation in win expectancy added can be explained by variation in change in run expectancy). In the middle six innings, that drops to 0.65; by the time we get to the final three innings of the game (excluding extras), it’s 0.39. This phenomenon is the result of a combination of single runs having an outsized effect on win expectancy in close games but generally less impact in the latter portions of the contest because there is very little baseball left to be played.

When evaluating the efficacy of a high-leverage reliever, therefore, we should be looking more at win expectancy than run expectancy. For starting pitchers and hitters, run values do the trick because much of their performance occurs at points of the game where changes in run and win expectancy scale well. High-leverage relievers, though, generally throw at points in the game where the two quantities diverge.

Let’s get back to walks (which from here on out include HBPs) versus balls in play. In games within two runs in the seventh, eighth, or ninth innings (i.e., high leverage spots), a walk, on average, costs the pitching team about 4.5 points of win probability versus 0.8 points for a ball in play. Some of you may be saying ‘I told you so,’ but this is just the average and lacks any context. Here are the distributions for changes in win expectancy for walks and balls in play in my definition of high-leverage situations (which I admit is an arbitrary cut-off but simplifies the analysis):

Often, a batted ball is the better outcome for the pitching team, but there are situations where a walk is preferred, which you can see on the left side of both distributions. Batted balls have more variability than a walk; they can result in a fly out, groundout, single, double, home run, etc. Take that variability one step further: a fly out with two outs and no one on is very different than a fly out with a runner on third and no outs. Walks, meanwhile, are simply walks; the only time they result in a run being scored is if the bases are loaded. Sure, they increase the hitting team’s run expectancy, but in close games where you want to maximize win probability, you do not care about minimizing that as much as preventing a single runner from scoring. As you can see in the table below, there are certain situations where the pitcher would prefer walking the batter to allowing a ball in play, or it’s close enough that walking a batter would avert risk:

WPA for Walk Vs. BBE
Base-Out State Walk BBE Diff
0 outs _ _ _ -5.9 -0.4 -5.5
0 outs _ _ 3b -2.4 -2.7 0.3
0 outs _ 2b _ -1.6 -0.9 -0.7
0 outs _ 2b 3b -1.8 -0.9 -0.9
0 outs 1b _ _ -8.4 -0.8 -7.6
0 outs 1b _ 3b -1.1 1.3 -2.4
0 outs 1b 2b _ -11.3 -2.1 -9.2
0 outs 1b 2b 3b -7.6 -2.6 -5.0
1 outs _ _ _ -4.0 -0.6 -3.4.0
1 outs _ _ 3b -1.4 -2.2 0.8
1 outs _ 2b _ -2.0 -1.5 -0.5
1 outs _ 2b 3b -1.0 -5.3 4.3
1 outs 1b _ _ -5.8 -0.4 -5.4
1 outs 1b _ 3b -5.2 -2.9 -2.3
1 outs 1b 2b _ -10.8 -3.4 -7.4
1 outs 1b 2b 3b -11.6 -0.7 -10.9
2 outs _ _ _ -2.3 -0.3 -2.0
2 outs _ _ 3b -2.1 0.1 -2.2
2 outs _ 2b _ -1.2 -2.7 1.5
2 outs _ 2b 3b -1.6 -4.2 2.6
2 outs 1b _ _ -2.5 0.2 -2.7
2 outs 1b _ 3b -3.3 -4.4 1.1
2 outs 1b 2b _ -4.9 -3.3 -1.6
2 outs 1b 2b 3b -15.0 -0.9 -14.1
SOURCE: Baseball Savant
WPA in % and from perspective of pitching team

You can see the situations where it is more advantageous to walk a hitter then allow a ball in play (on average), and these make sense; a walk prevents a run from scoring, but a ball in play can lead to a run whether it is fielded for an out or not. There are situations, too, where the difference in expected win probability swing is less than a single percentage point. For example, take one out and a runner on second. The chart would indicate that allowing a ball in play is a better outcome than a walk, but if the ball in play is a fly ball — the batted ball type with the lowest BABIP — then we would expect that to be caught, and probably in a spot where the runner cannot advance to third. A soft line drive into the outfield, on the other hand, would most often send the runner home. There is more nuance to be applied to these calculations to bear this out, but considering batted balls overall gets you close enough and helps define where these edge cases exist.

What does this mean for Reyes? Despite sabermetric orthodoxy, there are situations where having a pitcher with his shape of production is better than one who substantially paces him in our favorite pitching stats, like K-BB% or FIP. I tested this by taking the strikeout, walk, and batted-ball rates against for four different pitcher archetypes: the average rates across the majors for pitchers who throw in my definition of high-leverage situations, the rates for Reyes, the rates of Richard Rodriguez (who has a middling strikeout rate but excellent walk rate and has posted much better underlying results than Reyes), and the rates of Craig Kimbrel.

Player Archetype Rates
Archetype K% BB% BBE%
Average High Leverage 26.5 11.2 62.3
Alex Reyes 29.5 18.9 51.6
Richard Rodriguez 22.1 3.6 74.3
Craig Kimbrel 46.6 9.2 44.3
SOURCE: Baseball Savant

I multiplied these percentages by the changes in win expectancy for each event type in each base out state. This weighted average represented the theoretical expected win probability change in each state if each pitcher was on the mound. I then compared these expected changes across the four sets of percentages I defined above (note that win expectancy changes are defined from the perspective of the pitching team, so positive is good and negative is bad).

WPA Rates for Each Pitcher Archetype
Base-Out State Avg High-Leverage Reyes Rodriguez Kimbrel
0 outs _ _ _ 0.1 -0.2 0.3 1.1
0 outs _ _ 3b -0.2 0.1 -0.6 1.7
0 outs _ 2b _ 1.0 1.2 0.8 2.6
0 outs _ 2b 3b 1.9 2.2 1.5 4.1
0 outs 1b _ _ 0.0 -0.4 0.3 1.3
0 outs 1b _ 3b 2.9 2.9 2.7 4.3
0 outs 1b 2b _ -0.2 -0.6 0.0 2.2
0 outs 1b 2b 3b -0.8 -1.0 -0.9 1.0
1 outs _ _ _ -0.1 -0.2 0.0 0.7
1 outs _ _ 3b 1.4 1.9 0.8 4.1
1 outs _ 2b _ 0.4 0.6 0.2 1.9
1 outs _ 2b 3b -0.6 0.2 -1.6 2.5
1 outs 1b _ _ 0.4 0.1 0.6 1.5
1 outs 1b _ 3b 1.0 1.3 0.5 4.2
1 outs 1b 2b _ -1.6 -1.9 -1.5 0.5
1 outs 1b 2b 3b 1.3 0.8 1.6 4.0
2 outs _ _ _ 0.0 0.0 0.1 0.5
2 outs _ _ 3b 1.8 1.8 1.6 3.3
2 outs _ 2b _ -0.3 0.1 -0.8 1.3
2 outs _ 2b 3b -0.6 -0.1 -1.4 1.8
2 outs 1b _ _ 0.8 0.7 0.9 1.6
2 outs 1b _ 3b -0.9 -0.4 -1.5 1.7
2 outs 1b 2b _ -0.8 -0.6 -1.1 1.3
2 outs 1b 2b 3b 0.9 0.2 1.4 3.7
SOURCE: Baseball Savant

I highlighted the situations where you would prefer a pitcher like Reyes to a pitcher like Rodriguez. Someone with the latter’s skills should be the more desired pitcher in the plurality of situations, but there are some jams where the manager should prefer using a Reyes type.

One quibble with Reyes’ approach is that he walks a fine line. Walks are not necessarily the end of the world for a relief pitcher, but there is a tipping point where he becomes unusable. The following is a similar table where I took Reyes’ nominal rates, held the strikeout rate constant, and added or subtracted three and six percentage points to his walk rate and batted ball against rate, with the “best version of Reyes” in each base out state highlighted.

Reyes with Constant K% and Differing BB%
Base-Out State Reyes Reyes +3 Reyes +6 Reyes -3 Reyes -6
0 outs _ _ _ -0.2 -0.4 -0.5 0.0 0.1
0 outs _ _ 3b 0.1 0.1 0.2 0.1 0.1
0 outs _ 2b _ 1.2 1.2 1.2 1.2 1.3
0 outs _ 2b 3b 2.2 2.1 2.1 2.2 2.2
0 outs 1b _ _ -0.4 -0.7 -0.9 -0.2 0.0
0 outs 1b _ 3b 2.9 2.8 2.7 3.0 3.0
0 outs 1b 2b _ -0.6 -0.9 -1.1 -0.3 0.0
0 outs 1b 2b 3b -1.0 -1.1 -1.3 -0.8 -0.7
1 outs _ _ _ -0.2 -0.3 -0.5 -0.1 0.0
1 outs _ _ 3b 1.9 1.9 1.9 1.8 1.8
1 outs _ 2b _ 0.6 0.6 0.6 0.6 0.6
1 outs _ 2b 3b 0.2 0.3 0.5 0.1 0.0
1 outs 1b _ _ 0.1 -0.1 -0.2 0.3 0.4
1 outs 1b _ 3b 1.3 1.2 1.2 1.4 1.4
1 outs 1b 2b _ -1.9 -2.1 -2.3 -1.7 -1.4
1 outs 1b 2b 3b 0.8 0.5 0.2 1.2 1.5
2 outs _ _ _ 0.0 -0.1 -0.2 0 0.1
2 outs _ _ 3b 1.8 1.8 1.7 1.9 2.0
2 outs _ 2b _ 0.1 0.1 0.2 0 0.0
2 outs _ 2b 3b -0.1 0.0 0.1 -0.1 -0.2
2 outs 1b _ _ 0.7 0.7 0.6 0.8 0.9
2 outs 1b _ 3b -0.4 -0.4 -0.3 -0.4 -0.5
2 outs 1b 2b _ -0.6 -0.7 -0.7 -0.6 -0.5
2 outs 1b 2b 3b 0.2 -0.2 -0.6 0.6 1.1
SOURCE: Baseball Savant

After reading close to 2,000 words on walk rates and win probability, these results hopefully make sense. There are situations late in close games where a walk is not that damaging, so the cost of a few extra ticks added to Reyes’ walk rate are either marginal or nonexistent. The situations where a ball in play is clearly a better outcome than a walk obviously degrade upon an increase in walk rate.

Reyes’ performance this year is tricky to evaluate. The massive chasm between his ERA and FIP would indicate that his results are outstripping his actual performance, but his FIP is still a solid figure for a high-leverage reliever. That also goes to show that walk rate is not the best tool in evaluating relief pitchers, and that there are situations where a team should prefer a pitcher with high walk and strikeout totals to one with elite control but less strikeout prowess. That is not to say I would prefer Reyes to Rodriguez; the distribution of base-out stats is not uniform, and Rodriguez has the edge in those which occur most often.

I will be the first to say that my analysis lacks some nuance. My filtering of high-leverage plate appearances was arbitrary, and considering the top of the seventh the same as the bottom of the ninth misses meaningful context. I also grouped all batted balls together; fly balls and groundballs can have vastly different effects on the outcome of a plate appearance, and while a ball in play might seem worse than a walk on average, that depends 0n the pitcher on the mound. Finally, I did not consider the frequency with which each base-out state occurs, which would play into which pitcher you might prefer in general versus certain situations.

But with all that said, I do think this analysis is instructive in how we grade relievers. Reyes might have some warts, but they are not as detrimental as they seem at first blush, and that goes for any reliever with a bloated walk rate. The key is finding the correct balance and (pardon the pun) walking that fine line in maintaining effectiveness in the face of handing out free passes.

Carmen is a part-time contributor to FanGraphs. An engineer by education and trade, he spends too much of his free time thinking about baseball.

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Joseph Meyermember
1 year ago

Great piece. I really appreciate the acknowledgement of where this analysis could be refined.