Third base coaches: nerves of steel, and human calculators

­­­On Outside the Hangar recently, I’ve been writing about my experiences as a fan of the Melbourne Aces. They’ve been away on ABL duty in Brisbane this weekend, and to cheer myself up after their 3-1 series loss to the Bandits I’ve decided to write this brief piece about the perfect confluence of three things that spell happier times for me – attending an Aces game, making new friends in the stands, and seeing plenty of action on the basepaths when the ball is in play.

My new acquaintance and I, along with the rest of the fans were out of our wind-chilled seats early in the first inning of the Melbourne Aces game against the Brisbane Bandits last Sunday. With two out and runners at the corners, Dylan Cozens lined a ball to deep right field. Scott Wearne scored easily, while Kellin Deglan came flying around the bases but was held up at third by manager Tommy Thompson, who (not uniquely, at least in minor leagues, a co-Aces fan spectator tells me) pulls double duty as third-base coach:

bball

The decision paid off. The Aces’ next hitter, Josh Davies doubled in Deglan and Cozens for 3-0 lead and a productive first inning.

Was Thompson’s call the right one? The temptation is to judge it retrospectively – the runners did score, so he did the right thing. But the decision not to send the runner in no way guaranteed Davies’ success – it was just one of many possible outcomes, in this instance favouring the Aces, of what was simply a risk management decision.

In the early innings of a baseball game, each manager should (arguably) be trying to make decisions which will maximise their team’s run production; in later innings, the emphasis may be on increasing the probability of scoring a single run, even at the cost of decreased probability of scoring further runs.

A great resource to help with this decision is at Tango Tiger: a very neat set of tables, showing the average runs scored in an inning following each of the eight combinations of baserunners and three possible out totals (8 x 3 = 24 total situations).

tango1

Using the 1993-2010 data, the expected runs to score following Thompson’s hold-up sign, leaving runners at second and third with two outs, is 0.626. If the runner was sent and failed, that’s the third out and obviously a zero-run inning for the Aces. If the runner was sent and scored, leaving (most likely) Cozens at third following a play at the plate with Deglan trying to score, the Aces will immediately score 1 run, and have an average of 0.385 runs more still to come, based on a runner at third with two outs.

At the split second that the third base coach makes the decision to send Deglan, the expected number of runs for the inning depends entirely on the probability that the runner will score. The decision becomes a good one when that probability generates a higher expected number of runs than 0.626. Once the probability of Deglan getting home nudges 45.2%, sending him is a good call:

(In each of these tables, the red fields are directly from Tango Tiger, the green are probabilities inserted to make the two decisions have a balanced outcome, and the orange are the calculations based on the red and green figures.)

chart1

So often, coaches are judged by the outcome of their decisions – your team scores a run and youre a genius; they fail and you’re a goat. But, in a scenario will the assumptions above, the risk management approach which over the long term will deliver the most runs, will also “fail” the majority of the time.

We’ll never know what the probability was of Deglan scoring – being able to estimate it quickly is perhaps the skill of the third base coach. Also feeding into the decision is the understanding that all of the figures are based on average hitters and pitchers, in the true sense of average – calculated from tens of thousands of plate appearances, across the disparity of skills you’d expect to find in the major leagues.

The decision on sending a runner, therefore, can’t be purely the application of a statistical chart, but also an understanding of the relative strength of the hitting and pitching to come. In another scenario, with the bottom of the order about to face a fireballing strike-out specialist, you might think it’s a good idea to send a runner home if they have a much smaller chance of scoring – far better to take on the outfielder’s arm than the pitcher’s.

Returning to the Aces, several hours later: the ninth inning arrived with the Aces trailing 4-3, and struggling to keep the game alive. With one out and Jeremy Young on second, it was a classic coach’s dilemma (in the statistical sense) – maximise the probability of scoring a single run? Or maximise scoring overall, and go for the win? A new set of charts from Tango Tiger, which can be used to derive the probability of scoring > 0 runs in an inning, sets the scene:

tango2

Scott Wearne blooped a ball into left-centre field, Thompson waved Young through and he came storming home safe – but not before the ball pitched just in front of Bandits catcher Maxx Tissenbaum and deflected off his mitt to safety:

ball

If you’re maximising runs, the equation balances at around 63% probability of the runner getting home safe:

chart2

Counter-intuitively, if you’re just playing for a single run, you only need to feel 56% confident that the runner will score (the tradeoff is that in the run-maximising scenario, sending the runner and failing just puts too much of a dent in the chances of a big inning):

 table3

(Writing on Sunday evenings is fine, but I should complete the maths in advance! … the simpler way of doing this is of course to work out the probability of scoring 0, which is [prob (thrown out at the plate) x prob (no further runs in the inning)] = 44.4% x 77.7% ~ 34.5%, which is the complementary chunk of the 65.5% probability of a run scoring.)

This, of course, comes with all the same caveats – the main one being whose pitching and hitting is better, relative to the league’s prevailing averages. That’s where are great manager and / or a great third base coach can really bring something to the team – making sound decisions based on what they know about the abilities or their team and their opponents. That must be doubly hard in the ABL – at least there is an ocean of data to support your decisions in the MLB, whereas in the ABL, as in every minor league, the numbers are no doubt subtly (or not so subtly) skewed, if indeed they’re available and reliable.

Ultimately, the Aces lost this game in the eleventh inning, one of an incredible six straight one-run games with the Bandits, bracketed by two rather unpleasant blowouts. My new friend and I (now sitting in the sun after moving from the freezing upper deck under the commentary booth) shook hands and headed for the car park. (Further note: with the Sunday chill-fest fresh in my mind, I sat in the sun for part of the similarly cold Monday early-start game, and got sunburnt. Yay Melbourne weather.)

As I look ahead to Thursday night, and the arrival of – thank the Ceiling Cat – someone other than the Bandits at Melbourne Ballpark, I commend these calculations to Tommy Thompson and his staff (who am I kidding – I bet they’d memorised it all before pre-season even started) and hope that for fans, they’ve provided some solace (or maybe just confusion) to take our minds off the win-loss columns for one evening and get ourselves ready for the boisterous support which (science proves) our boys will need this weekend.

h/t: @FiveThirtyEight’s Nate Silver, whose work inspired this piece.

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