Firebase TypeError: ref.transaction is not a function

I have an issue with firebase database functions. The documentation contains the following minimal example to work with transactional data:

var upvotesRef = db.ref("server/saving-data/fireblog/posts/-JRHTHaIs-jNPLXOQivY/upvotes");
upvotesRef.transaction(function (current_value) {
  return (current_value || 0) + 1;
});

Now, my firebase database structure looks like the following

/game-results
    /RaUALJvTZVea5y6h1lzqGJPMpuI3
        /distance
        /score
        /timestamp
    /3ItAqKHL0XRUOum2Ajdz9hHQxMs1
        /distance
        /score
        /timestamp
/statistics
    /total-distance
    /total-score

And I would like to sum up the scores and distances to a total. I'm using the following function, here for total-distance:

const functions = require('firebase-functions');

exports.updateTotalDistance = functions.database.ref('/game-results/{userId}/distance')
    .onWrite(event => {
        const newDistance = event.data.val();
        const distanceRef = functions.database.ref('/statistics/total-distance')
        return distanceRef.transaction(function(currentDistance) {
        console.log('currentDistance', currentDistance);
            return (currentDistance || 0) + newDistance;
        });
    });

However, I can not wrap my head around why I get the following error in the firebase function logs:

TypeError: distanceRef.transaction is not a function
    at exports.updateTotalDistance.functions.database.ref.onWrite.event (/user_code/index.js:19:22)
    at /user_code/node_modules/firebase-functions/lib/cloud-functions.js:35:20
    at process._tickDomainCallback (internal/process/next_tick.js:129:7)

Why is the Database reference not allowing me to write transactional data? All I want to do is to sum up all scores and distances.

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